Strategic Forecasting of Monthly Patent Application Filings: Analyzing Seasonality for Sustainable R&D Governance

Abstract

Intellectual property (IP) is a cornerstone of sustainable industrial growth, yet unpredictable fluctuations in patent application filings pose a challenge to the administrative efficiency and sustainable governance of patent offices. This study aims to enhance strategic R&D governance by analyzing the seasonality of patent application filings using monthly data from the Republic of Korea (January 2001 to July 2024) and proposing a time series forecasting model that reflects this seasonality. To verify seasonal patterns, visual analyses (graphs, time series decomposition, and autocorrelation function plots) and the Kruskal–Wallis test were conducted. The results confirmed a clear 12-month seasonal pattern, characterized by a distinct “December Rush” at the end of each year. Based on these findings, we compared the autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models, demonstrating that the SARIMA model offers superior predictive performance by effectively capturing these cyclical fluctuations. Furthermore, by segmenting data into private and public R&D sectors, we observed that private R&D exhibits more pronounced seasonal volatility, necessitating differentiated management strategies. This study highlights the critical role of seasonality in forecasting patent volumes and provides a data-driven framework for sustainable governance, offering actionable insights for optimizing resource allocation and policy support in the innovation ecosystem.

1. Introduction

With the advent of the Fourth Industrial Revolution and the era of the digital economy, Intellectual Property (IP) has evolved beyond a mere legal right to become a cornerstone for achieving Sustainable Development Goals (SDGs), particularly in fostering innovation and resilient infrastructure [1]. As highlighted in recent studies, patent data serves as a reliable proxy for measuring innovation and tracking progress toward sustainable development targets [2,3]. As efforts to gain a competitive edge in the technology market through technological innovation and research and development (R&D) continue, intellectual property has become a key indicator for evaluating national competitiveness [4,5,6]. Among these, patents are a representative output of innovation based on new ideas and technological creation and are recognized as an important indicator for quantitatively measuring technological innovation activities and productivity by country as well as evaluating the possibility of conversion into actual economic value [7]. Since patents can only be registered after they have been recognized for their originality and progressiveness through an examination process following the application, they play a very important role in evaluating the technological competitiveness and innovation capacity of countries and companies [8,9], and numbers of studies support this by showing that the more patents a company has, the greater its innovation capacity [10].

From a sustainability-oriented innovation perspective, Science, Technology, and Innovation (STI) is widely recognized as central to progress toward the Sustainable Development Goals (SDGs), and patent data is often used to trace technological development on a scale. Recent empirical work reinforces this connection; for instance, Hajikhani and Suominen [11] utilized machine learning to map patent data to specific SDGs, demonstrating that patents serve as a critical proxy for quantifying the contribution of technological innovation to sustainable development goals. This perspective is further supported by Omri [12], who empirically demonstrated that in high-income economies, technological innovation serves as a catalyst for simultaneously advancing economic growth, environmental quality, and social progress. Thus, optimizing patent administration is essential for leveraging these innovations to achieve the multidimensional targets of the SDGs.

Accordingly, patent offices of governments and industries around the world are strengthening their efforts to closely analyze patent application trends and establish various policies to expand the creation and utilization of sustainable intellectual property by forecasting technological development trends and economic growth [13,14]. This aligns with the United Nations Sustainable Development Goal 9 (Industry, Innovation, and Infrastructure), which emphasizes the promotion of inclusive and sustainable industrialization and fostering innovation [15]. In a situation where the number of patent application filings is increasing every year, analyzing the changes in the number of patent applications is an important basis for evaluating the performance of existing policies and predicting the size of future intellectual property, and this provides essential information for establishing new technology commercialization policies, intellectual property policies, and patent office policies for continuous innovation.

In the Republic of Korea, the number of patent application filings has increased much faster than the number of examiners in the past 10 years, leading to a rapid increase in the number of patent applications, while the number of patent registrations has shown a relatively slow increase [16]. According to data from 2021, the number of patent examiners in Korea is approximately 1000, which is over 13 times fewer than that of China, where 13,704 examiners are employed. Consequently, each Korean examiner must process an annual average of 197 cases, indicating a substantial workload burden. This imbalance delays the patent examination period and creates a bottleneck phenomenon due to processing delays [17]. This is not a problem limited to the Korean Intellectual Property Office (KIPO) but has been raised as a similar problem in the European Patent Office (EPO) [18]. Such administrative inefficiencies are not merely operational issues but represent a failure in sustainable governance, potentially stifling the lifecycle of technological innovation. To secure the sustainability of the national innovation ecosystem, it is imperative to move from reactive administration to proactive, data-driven strategy planning.

To address these systemic bottlenecks, this study draws on the concept of anticipatory governance, which emphasizes the capacity of public institutions to anticipate recurrent demand and maintain reliable service performance under uncertainty. In this view, forecasting is not merely a technical exercise but a governance capability that supports resilient and accountable institutional operation through proactive capacity planning. From this standpoint, persistent delays represent a failure in sustainable governance, potentially stifling the lifecycle of technological innovation. Therefore, securing the efficiency and transparency of patent administration through accurate forecasting is not only an administrative necessity but also a strategic bridge between SDG 16 (Effective, Accountable Institutions) and SDG 9 (Resilient Innovation Infrastructure), ensuring that the institutional capacity can sustainably support the lifecycle of technological innovation [19,20].

In today’s rapidly shortening technology life cycle, if the patent examination period is prolonged, the market may decline before the inventor secures the patent. In addition, the validity period (duration) of the patent right that occurs after the patent registration is 20 years from the date of application, and the longer the examination period, the more disadvantageous it is for the applicant, as the validity period is shortened. This problem has a negative impact on the rights acquisition of companies that continuously seek to lead innovation, and there is a risk that the quality of examination will deteriorate as the examination environment deteriorates, ultimately lowering the credibility of the patent office.

Prior studies suggest that patent filings may be associated with a range of external factors (e.g., macroeconomic conditions, industrial structure, and policy environments in the short run, and R&D investment and innovation infrastructure in the long run) [21]. However, rather than modeling these determinants, this study focuses on univariate forecasting using historical monthly filings to identify intrinsic temporal patterns (especially annual seasonality) and to improve prediction accuracy for operational planning.

The predicted number of patent applications provides a basis for understanding future technology development trends in advance and thus for the patent office and related ministries to efficiently manage human resources [22]. Continuous changes in policy strategies through future forecasting will directly affect the organization, personnel, and budget management based on application, examination, and registration fees of the patent office, which is the main ministry related to patent rights [23,24]. This makes it possible to establish policy strategies that can adapt to the rapidly changing innovation cycle.

In order to forecast the fluctuations in patent applications, recent studies have utilized machine learning and deep learning techniques. However, most existing studies have focused on annual statistics or industry groups, and there is a relative lack of research analyzing the seasonality of monthly patent applications. This is largely because high volatility and data limitations make modeling difficult. Consequently, the field of seasonal analysis in patent data remains under-researched. If it is confirmed that patent applications have seasonality, a forecasting model that reflects this can make more accurate predictions, enabling the establishment of innovative patent policies that account for seasonal trends.

This study was conducted based on monthly patent application data provided by the Korea Intellectual Property Office (KIPO). According to World Intellectual Property Statistics by the World Intellectual Property Organization (WIPO), the Republic of Korea ranked 5th in the number of international patent applications through the Patent Cooperation Treaty (PCT) from 2010 to 2019 but rose to 4th place in 2020 and has maintained that ranking to date. In this respect, the KIPO is one of the top five patent offices in the world, along with the United States Patent and Trademark Office (USPTO), the Japan Patent Office (JPO), and the European Patent Office (EPO), and is evaluated as an organization that can represent global patent application trends [25].

The main goal of this study is to examine whether monthly patent application filings in Korea exhibit a statistically significant annual seasonal pattern and to evaluate whether incorporating seasonality improves forecasting accuracy. The study proceeds in two parts. First, we identify seasonality in the monthly patent application filing fluctuations and verify it statistically using the Kruskal–Wallis test. Second, we compare the forecasting performance of a seasonality-aware SARIMA model against a non-seasonal ARIMA model. By doing so, this study aims to support the transition toward “sustainable governance” by providing accurate forecasting data essential for optimizing resource allocation. It is important to clarify that our design is predictive rather than causal; thus, we focus on intrinsic temporal patterns rather than estimating the causal effects of external economic variables.

The results of this study will provide important implications for understanding the monthly variability of patent application filings and preparing policy responses through predictions. It is expected that understanding the seasonal characteristics of patent application filings and utilizing a prediction model that reflects this will make a substantial contribution to patent administration and, through this, to the establishment of national technological innovation policies and strategic decisions in the industry [26].

The structure of this paper is organized as follows: Section 2 reviews the literature on patent forecasting models and formulates the research hypotheses. Section 3 describes the dataset and the statistical methodologies employed, specifically the Kruskal–Wallis test and the ARIMA/SARIMA modeling frameworks. Section 4 presents empirical results, which include the verification of seasonality, a performance comparison between the forecasting models, and a sectoral analysis distinguishing between private and public R&D patterns. Section 5 provides a comprehensive discussion on the robustness of these seasonality against macroeconomic shocks, interprets the sectoral disparities, and suggests policy implications for sustainable governance. Finally, Section 6 summarizes the conclusions, significance, limitations, and directions for future research.

2. Literature Review

2.1. Overview of Patent Application Forecasting Models

With the rapid increase in patent application filings, various efforts are continuously being made worldwide to maximize the performance of intellectual property rights. The reason why patents are receiving so much attention is that patents are essentially related to innovation processes and scientific and technological changes that are essential to the economic development of a country [27]. Accordingly, there has been a demand for an accurate and efficient forecasting system not only for individual countries but also for supranational intellectual property organizations such as WIPO and EPO to encourage patent applications and develop the patent system.

The introduction of a patent application filing forecasting model can contribute to streamlining the operational structure of patent offices and improving the quality of services provided to patent application clients. This process of optimization is valuable in that it can reduce costs and prevent potential bottlenecks that may occur during the application and registration process. Patent-related organizations in each country have been continuously developing models to predict patent application filings, and representative organizations include the European Patent Office (EPO), the World Intellectual Property Office (WIPO), the United States Patent and Trademark Office (USPTO), the Japan Patent Office (JPO), the Korea Intellectual Property Office (KIPO), and the Swiss Federal Office for Intellectual Property (SFIIP). Most organizations utilize traditional statistical-based methodologies to predict patent application filings. These methodologies include trend extrapolation based on recent average growth rates, detection of decaying trends using Holt-Winters exponential smoothing, and econometric techniques such as AR, ARMA, and ARIMA. Some patent offices are further improving the accuracy of predictions through surveys of IP experts or users. Qualitative analysis methods include surveys that investigate applicants’ intentions to apply for new patents and trademarks and have the advantage of being able to very accurately predict changes in future application demand [28]. These qualitative methods are often used in conjunction with statistical methods.

Previous studies on precise patent application filings forecasting have been mainly developed by researchers at major patent offices around the world. Adams et al. [29] proposed three types of models for patent application prediction at the United States Patent and Trademark Office (USPTO). They used the Naive model (Holt exponential smoothing model), ARIMA model, and econometric models to predict annual and quarterly patent applications. Hingley and Nicolas [13] described two specific prediction models being used at the EPO to find models for patent application patterns that can be utilized worldwide. One of these models is a linear model based on time series-based trend analysis, and the other is a transition model based on regression analysis.

Domestic studies have also attempted to forecast patent application filings using various methodologies. Lee et al. [30] analyzed patent applications and fee elasticity using the VAR model, VEC model, and system dynamics technique using long-term time series data from 1981 to 2013. Kang and Lee [31] used univariate and multivariate models such as the AR model, VAR model, and VEC model to predict and analyze future patent applications and fees. In a relatively recent study, Kim [32] used the VAR model to analyze macroeconomic indicators that affect patent application filings fluctuations and evaluated the relative influence of each indicator. In addition, Lim et al. [17] predicted the number of patent applications using the ARIMA model based on annual industrial property right application data.

Recently, research on forecasting the number of patent application filings using machine learning and artificial intelligence (AI) techniques has been actively conducted. Although these techniques may be difficult to interpret, they provide higher prediction accuracy than existing statistical models. Xu et al. [33] predicted the number of patent applications in China using Gray SVM (Support Vector Machine), one of the machine learning techniques. Havermans et al. [23] extracted exogenous variables effective for forecasting through cross-correlation analysis and performed automated prediction using SVM, artificial neural networks (ANN), and linear regression models based on these variables and compared the performance of each methodology. Tsai [34] forecasted the number of patent applications using Random Forest (RF), Extra Tree (ET), Gaussian Process Regression (GPR), Radial Basis Function Network (RBFN), Convolution Neural Network (CNN), and Long Short-Term Memory (LSTM), which is strong in time series forecasting. These studies suggest the applicability of various statistical and machine learning techniques in patent application filings forecasting and provide important basic data for improving forecasting accuracy through additional research on the forecasting performance and limitations of each methodology.

As confirmed in previous studies, despite the recent advancement of time series forecasting models and the introduction of machine learning and deep learning techniques, there are still limitations in explaining the essential parts of economic phenomena. As a result, economic analysis and future outlook research using simpler time series models are continuously being conducted [17]. In particular, since the 2008 global financial crisis, complex and advanced macroeconomic and financial time series models have been questioned in terms of predictive power and explanatory power, and the need for prediction research using simple time series models has been highlighted again.

Representative time series models used to forecast patent application filings include the ARIMA model, the VAR (vector auto-regressive) model, the VEC (vector error correction) model, and the macroeconomic model. These models can be divided into multivariate and univariate time series models. In the case of multivariate time series models (VAR, VEC), the interpretation of the analysis results becomes more complicated as more variables are considered, and there is a possibility that the predictive power of the model may decrease in the process of considering the correlation between variables. This is because multivariate models have difficulty explaining overfitting problems or interactions between variables as the number of variables increases. On the other hand, the ARIMA series models, which are univariate time series models, have the advantage of being able to predict with only a single time series data, although they cannot specifically explain the relationship with the main variables. In addition, the ARIMA model can be applied to non-stationary time series data, so it is useful in various forecasting situations.

In this study, among univariate time series models, the ARIMA model and the SARIMA model are employed to predict monthly patent application filings. While the ARIMA model is robust for general trends, it has limitations in predicting data with strong periodic patterns because it does not strictly account for seasonality. In contrast, the SARIMA model is designed to capture these seasonal repetitions, making it theoretically more suitable for data influenced by recurring administrative cycles.

2.2. Research Hypotheses

In the context of the Republic of Korea, patent filing activities are not randomly distributed but are likely influenced by institutional factors such as the fiscal year-end budget execution and annual performance evaluations of R&D organizations [35,36,37]. These factors are expected to create a recurring “December Rush,” a structural seasonality that standard models might miss. If such distinct seasonality exists, a model that explicitly integrates seasonal parameters should outperform traditional non-seasonal models. Based on this theoretical and contextual reasoning, the following hypotheses are proposed:

Hypothesis 1 (H1).

Monthly patent application filings in Republic of Korea exhibit significant seasonality, specifically characterized by a concentration of filings in December.

Hypothesis 2 (H2).

A forecasting model that explicitly incorporates seasonality (SARIMA) will demonstrate superior predictive accuracy compared to a non-seasonal model (ARIMA).

Furthermore, the impact of these institutional factors is not uniform across all R&D entities. Previous literature suggests that private companies are highly sensitive to financial incentives, such as tax deductions for job creation and R&D expenditures, which are often claimed at the end of the fiscal year [36]. Conversely, public research institutes and universities are primarily driven by fixed government evaluation cycles and budget expiration dates [37]. Due to the flexibility of private budget management and the direct financial benefits of tax incentives, the private sector is expected to show more erratic and intense seasonal spikes compared to the public sector. Considering these structural differences, we propose the third hypothesis:

Hypothesis 3 (H3).

The private R&D sector will exhibit greater seasonal volatility than the public R&D sector, driven by corporate strategies related to tax incentives and year-end budget execution.

3. Data & Methodology

The research procedure of this study largely consists of four stages: data collection, visual and statistical analysis to identify seasonality, time series model development and evaluation, result interpretation, and policy implications. This research procedure is summarized in Figure 1 below, and each stage systematically explains the process of analyzing and predicting the seasonality of patent applications in accordance with the purpose of the study. In the first stage of this study, monthly patent application filings data from January 2001 to July 2024 were collected through the Monthly Intellectual Property Statistics Report [38] provided by the Korea Intellectual Property Office (KIPO). After data collection, the seasonal pattern of patent application filings data was identified through visual analysis and statistical verification methodology. Through this, the volatility of monthly patent applications was confirmed, and the presence of seasonality was explored. In the next stage, a time series forecasting model for monthly patent applications was developed and its performance was evaluated, and the ARIMA and SARIMA models were applied for this purpose. Afterwards, additional experiments were conducted to divide monthly patent applications into private R&D and public R&D and to confirm the seasonality in each case using the same method.

3.1. Data

The time series data used in this study are based on monthly patent application filings data collected from the “Monthly Intellectual Property Statistics” published by KIPO [38]. KIPO regularly publishes various statistical publications, and among them, the Monthly Intellectual Property Statistics is an important source of monthly industrial property statistics, which is announced on the 20th of each month. This data includes data from January 2001 to July 2024, and the sample period used in the analysis was set from January 2001 to July 2024. A total of 283 monthly samples were used in the analysis, which reflects all available data from the extraction time. The basic statistics for the data used in this study can be found in

Table 1. Descriptive statistics of patent applications (Jan 2001–Jul 2024).

Month	Count	Mean	Std. D.	Min	Max
January	24	13,126.54	3526.40	6008	19,257
February	24	13,026.25	3202.90	6740	18,239
March	24	14,526.25	3314.16	7867	19,703
April	24	14,268.08	3347.16	7570	18,201
May	24	14,061.21	3012.45	8303	17,620
June	24	15,550.50	2837.44	8455	19,584
July	24	15,477.71	3488.37	8379	20,546
August	23	14,577.74	3359.48	8443	19,317
September	23	15,081.83	3559.31	8804	20,459
October	23	15,857.78	4131.88	7869	21,780
November	23	18,334.48	5228.11	9059	27,041
December	23	23,259.04	4195.71	14,471	30,393
Total	283	15,563.34	4449.52	6008	30,393

.

3.2. Methodology

3.2.1. Kruskal–Wallis Test

The Kruskal–Wallis test is a nonparametric statistical method used to determine whether there is a statistically significant difference in the medians between three or more independent groups [39]. This is useful when one-way analysis of variance (ANOVA) assumptions, such as normality and homogeneity of variance, are not met. The Kruskal-Wallis test uses the rank of data instead of the mean to evaluate whether the rank distribution between groups is different; therefore, it can be reliably used even with ordinal data or data for which it is difficult to assume a normal distribution [40]. The Kruskal–Wallis test statistic was calculated using Equation (1):

$$H={\displaystyle \frac{12}{N\left(N+1\right)}}\sum _{i=1}^g{\displaystyle \frac{R_i^2}{n_i}}-3\left(N+1\right)$$

(1)

where g represents the number of groups (12 months in this study), N is the total number of observations, $n_i$ is the number of observations in the ith group, and $R_i$ is the sum of ranks for the ith group. The test statistic H follows a chi-square distribution with g-1degrees of freedom, and statistical significance is determined when the p-value is less than 0.05.

To verify seasonality in patent applications, we analyzed monthly data from 2001 to 2024 using Python’s scipy.stats.kruskal function. The data was grouped by month, creating 12 distinct groups (e.g., the January group containing data from January 2001 through January 2024). This approach allows us to test whether the monthly patent application distributions are significantly different, thereby indicating seasonal patterns [41,42]. The presence of seasonality is confirmed when the test rejects the null hypothesis of equal monthly distributions, suggesting systematic variations in patent filing activities across months.

3.2.2. ARIMA and SARIMA Model

ARIMA and SARIMA are widely used statistical methodologies for modeling and forecasting time series data. These two models focus on identifying patterns in time series data to predict future values, and each has strengths in removing non-stationarity and reflecting seasonality [43]. It is important to emphasize that these methodologies are univariate time series models. Unlike multivariate approaches that analyze the impact of external variables (e.g., GDP, R&D budget), this study utilizes ARIMA and SARIMA to forecast future volumes solely based on the intrinsic stochastic properties and historical patterns of the patent filing data itself. Therefore, this research focuses on accurate forecasting and seasonality detection, rather than attempting to statistically verify causal relationships with exogenous economic factors.

The ARIMA model is a representative statistical method for forecasting time series data developed by Box and Jenkins in the early 1970s [44]. This model explains current time series values using past observations, errors, and differencing procedures and includes both autoregressive (AR) and moving average (MA) elements. To apply the ARIMA model, the time series data must first satisfy stationarity; if non-stationarity is present, it is transformed into a stable time series through the difference (or integration) process, and then modeled using AR and MA components.

The basic form of the ARIMA model is ARIMA (p,d,q), where p represents the order of the AR term, d represents the order of the difference, and q represents the order of the MA term. This model explains the current value by utilizing autoregression and forecasting errors in time series data, and the ARIMA model is expressed by the following Equation (2):

$${\varphi }_p\left(L\right){\left(1-L\right)}^d{Z}_t=\mathsf{\delta }+{\theta }_q\left(L\right){ϵ}_t$$

(2)

Here, $Z_t$ is the raw series data, t is time, ${ϵ}_t$ is white noise with mean 0 and variance ${\sigma }^2$, and L is the backshift operator. The AR component ${\varphi }_{p}L$ represents the influence of previous time points of the time series on the current value, and the MA component ${\theta }_q\left(L\right)$ represents the influence of the past forecast errors on the current value. The MA element (q) represents the MA of the forecast error, which indicates how past forecast errors affect the current time point. The differencing term ${\left(1-L\right)}^d$ transforms non-stationary data into stationary form.

While ARIMA shows strong prediction performance for non-seasonal time series, but has limitations in time series with periodic characteristics, including seasonality. In these cases, the SARIMA model is applied. The SARIMA model is an extends capabilities by incorporating seasonal components, The SARIMA $(\mathrm{p},\mathrm{d},\mathrm{q})\times {\left(\mathrm{P},\mathrm{D},\mathrm{Q}\right)}_{\mathrm{s}}$ model is given by Equation (3):

$${\varphi }_p\left(L\right){{\Phi }_P\left(L^s\right)\left(1-L\right)}^d{\left(1-L^s\right)}^D{Z}_t=\mathsf{\delta }+{\theta }_q\left(L\right){{\Theta }_Q\left(L^s\right)ϵ}_t$$

(3)

where P, D, and Q represent the orders of seasonal autoregression (SAR), seasonal differencing, and seasonal moving average (SMA), respectively, and s denotes the seasonal period. The seasonal components ${\Phi }_P\left(L^s\right)$ and ${\Theta }_Q\left(L^s\right)$ capture periodic patterns in the data.

In this study, we employed Python’s pmdarima library [45] to automatically identify optimal model parameters based on AIC and BIC criteria [46]. The selection between ARIMA and SARIMA was determined through time series decomposition and ACF analyses, with SARIMA being chosen when significant seasonality was detected. The model-building process included stationarity testing, parameter optimization, and residual analysis to ensure model adequacy.

4. Experimental Results

4.1. Identifying Seasonality

Time series data are generally assumed to consist of trending, cyclical, seasonal, and irregular fluctuations. Seasonal fluctuations refer to seasonal changes that repeat in a one-year cycle and are caused by various customs. The most basic method for identifying the seasonality of time series data is visual confirmation through graphs. In this study, time series data were analyzed visually as the first step in analyzing the seasonal patterns of monthly patent applications. Visual analysis of patent applications over time. Figure 2 reveals clear cyclical patterns repeated annually. The data shows consistent fluctuations, with applications typically decreasing at year-beginning and increasing at year-end.

Next, to analyze these patterns more rigorously, we applied the seasonal decomposition of time series (STL) technique [47] (Figure 3). This decomposition method separates time series data into trend, seasonal, and residual components [48]. The trend component confirms steady long-term growth in patent applications, with particularly rapid increase during 2014–2015, followed by continued upward movement. The seasonal component exhibits consistent annual patterns, notably characterized by year-end increases in application activity. This pattern suggests systematic timing in patent filing behavior, potentially influenced by institutional and economic factors. The residual component shows minimal volatility except for the period after 2022, indicating effective capture of the main patterns in our decomposition.

To verify the seasonal structure of patent applications, we analyzed the autocorrelation function (ACF). The ACF graph (Figure 4) reveals significant autocorrelation at various lags, with particularly distinct peaks occurring at 12-month intervals. This pattern provides strong evidence of annual seasonality in patent filing behavior. The strong correlation at 12-month intervals is consistent with the previous time series graph and decomposition analysis results, further verifying the existence of seasonality.

Finally, to statistically validate these observed seasonal patterns, we first determined the appropriate testing method based on the data distribution. We conducted the Shapiro–Wilk test to assess the normality of both the entire dataset and individual monthly groups [49].

As shown in

Table 2. Results of Shapiro–Wilk Normality Test (Overall and Monthly).

Month	Statistic (W)	p-Value	Normality
Overall	0.977	<0.001 ***	No
January	0.967	0.595	Yes
February	0.961	0.454	Yes
March	0.942	0.182	Yes
April	0.912	0.038 *	No
May	0.898	0.020 *	No
June	0.918	0.054	Yes
July	0.948	0.246	Yes
August	0.934	0.135	Yes
September	0.943	0.213	Yes
October	0.952	0.325	Yes
November	0.964	0.558	Yes
December	0.945	0.229	Yes

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

, the results indicated that the overall patent application data did not follow a normal distribution (W = 0.977, p < 0.001). Furthermore, the monthly breakdown revealed that specific months, such as April (p = 0.038) and May (p = 0.020), significantly deviated from normality.

Since the assumption of normality required for parametric tests like One-Way ANOVA was violated in both the overall dataset and specific monthly groups, we employed the Kruskal–Wallis H test, a non-parametric alternative, to rigorously evaluate the statistical significance of monthly differences. The test yielded a statistic of 70.45 with a p-value of < 0.001 (

Table 3. Kruskal–Wallis test result (monthly patent applications).

Data	Kruskal–Wallis Test Stat	p-Value
Monthly Patent Application filings	70.447	p < 0.001 ***

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

), strongly indicating that the differences in monthly patent applications are statistically significant. In other words, the results strongly support the hypothesis that there is seasonal variation in monthly application filings. The results of the Kruskal–Wallis test statistically confirmed the seasonality identified in the visual review and time series decomposition. This extremely low p-value confirms that the observed monthly variations are not random but reflect systematic seasonal patterns.

In conclusion, the seasonal variation in patent applications was statistically significant through visual analysis, STL, ACF analysis, and the Kruskal–Wallis test. The significant result of the Kruskal–Wallis test supports the visual confirmation of seasonality and time series decomposition results presented above and is also consistent with the annual periodicity revealed through ACF analysis. These consistent results explain the seasonal characteristics of patent applications more clearly and emphasize the need to consider seasonality in application prediction models.

4.2. SARIMA Modeling of Monthly Patent Application Filings Time Series

4.2.1. Differencing Time Series and Augmented Dickey–Fuller (ADF) Test

In time series modeling, if the data to be analyzed are unstable, the reliability of the prediction is low. Therefore, a stability test should be performed before applying the Box-Jenkins methodology. As confirmed in Figure 1 and the seasonality analysis, patent applications showed a gradually increasing monthly trend over the entire period, with a repeating pattern observed every 12 months. Therefore, to apply the model, differencing is essential to stabilize the time series, and the data must be stationary.

The ndiffs function in the Pmdarima library determined the optimal differential order as the first difference. The differenced time series graph is shown in Figure 5. The stationarity of the differenced time series was confirmed using the augmented Dickey–Fuller (ADF) test and correlogram analysis. In the ADF test, if the test statistic is less than the critical value, the null hypothesis is rejected [50]. The ADF test results (

Table 4. ADF test result of the transformed patent applications time series.

Objects	ADF Statistics	p-Value	Critical Value (5%)	Result
Patent Applications (Differenced)	−3.562	0.006 **	−2.872	Stationary

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

) showed a p-value less than 0.05, indicating that the data were stationary.

In addition, the stationarity was further confirmed through ACF (autocorrelation function) and PACF (partial autocorrelation function) analysis of the time series to which the first difference was applied. As shown in Figure 6 and Figure 7, the analysis results showed that only some peaks were outside the confidence interval, indicating that the differenced time series data met the stationarity. ACF and PACF analyses showed that autocorrelation almost disappeared in the differenced time series, which supports that it is a normalized time series [51].

As a result, the time series data secured stationarity through the first difference, making it ready for ARIMA and SARIMA model application. The data sufficiently secured non-seasonal stationarity with only the first difference, confirmed by the ADF test results. This suggests that the 12-month seasonal pattern can be modeled with only the first difference, without seasonal differencing. The seasonal term of the SARIMA model was utilized to reflect seasonality, constructing a model that can adequately explain the data pattern without additional seasonal differencing.

4.2.2. Comparison of SARIMA and ARIMA

After identifying the optimal differencing order (d = 1) through the stationarity tests described above, we determined the optimal hyperparameters $(\mathrm{p},\mathrm{d},\mathrm{q})$ and ${\left(\mathrm{P},\mathrm{D},\mathrm{Q}\right)}_{\mathrm{s}}$ for the ARIMA and SARIMA models based on the Akaike Information Criterion (AIC) [52]. Model optimization was performed using the auto_arima function from the pmdarima library in Python [45], which implements the Hyndman-Khandakar stepwise algorithm. This algorithm is preferred over a brute-force grid search due to its computational efficiency in identifying the global minimum AIC.

To ensure a robust search within the hyperparameter space, we explicitly configured the search constraints based on the code implementation. First, the differencing order was fixed at $\mathrm{d}=1$ for both models to maintain stationarity. Second, to cover high-order autoregressive and moving average processes, we set the search range for $\mathrm{p}$ and $\mathrm{q}$ to start from 0 with a maximum limit of 10. Third, the stepwise selection was enabled to iteratively prune the search space.

For the SARIMA model, the seasonality parameter was activated with a period of 12 to capture annual cycles. Conversely, for the non-seasonal ARIMA model, the seasonal parameter was deactivated to serve as a baseline for comparison. Through this rigorous iterative process, the models minimizing the AIC were identified as $\mathrm{A}\mathrm{R}\mathrm{I}\mathrm{M}\mathrm{A} (\mathrm{2,1},1)$ and $\mathrm{S}\mathrm{A}\mathrm{R}\mathrm{I}\mathrm{M}\mathrm{A} (\mathrm{2,1},0)\times {\left(\mathrm{1,0},1\right)}_{12}$, respectively. These optimal models were then evaluated using indices such as log-likelihood, AIC, BIC, and Hannan-Quinn information criterion (HQIC), as shown in

Table 5. Model estimation of the SARIMA model.

Parameter	Coef	Std Err	z	p > |z|	[0.025]	[0.975]
$\mathbf{A}\mathbf{R}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$	−0.726	0.034	−21.163	<0.001 ***	−0.794	−0.659
$\mathbf{A}\mathbf{R}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$	−0.425	0.036	−11.810	<0.001 ***	−0.497	−0.355
$\mathbf{S}\mathbf{A}\mathbf{R}\mathbf{\left(}\mathbf{12}\mathbf{\right)}$	0.974	0.010	102.152	<0.001 ***	0.956	0.993
$\mathbf{S}\mathbf{M}\mathbf{A}\mathbf{\left(}\mathbf{12}\mathbf{\right)}$	−0.537	0.059	−9.068	<0.001 ***	−0.654	−0.422
${\mathsf{\sigma }}^2$	$1.722\times {10}^6$	$8.65\times {10}^{-9}$	1.99 × 1014	<0.001 ***	$1.72\times {10}^6$	$1.72{\times 10}^6$
AIC	3927.842		Log Likelihood	−1958.921
BIC	3944.922		Ljung–Box Prob (Q)	0.67
HQIC	3934.736		Heteroskedasticity (H)	0.70

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

and

Table 6. Model estimation of the ARIMA model.

Parameter	Coef	Std Err	z	p > |z|	[0.025]	[0.975]
intercept	48.645	29.638	1.641	0.101	−9.445	106.736
$\mathbf{A}\mathbf{R}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$	0.152	0.072	2.126	0.033 *	0.012	0.293
$\mathbf{A}\mathbf{R}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$	−0.170	0.100	−1.711	0.087	−0.366	0.025
$\mathbf{M}\mathbf{A}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$	−0.908	0.033	−27.527	<0.001 ***	−0.973	−0.844
${\mathsf{\sigma }}^2$	$7.229\times {10}^6$	$6.38\times {10}^5$	11.334	<0.001 ***	$5.98\times {10}^6$	$8.48\times {10}^6$
AIC	4204.104		Log Likelihood	−2097.052
BIC	4221.185		Ljung–Box Prob (Q)	0.92
HQIC	4210.998		Heteroskedasticity (H)	0.48

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

.

The fit evaluation of the ARIMA (2,1,1) yielded a log likelihood of −2097.052, AIC of 4204.104, BIC of 4221.185, and HQIC of 4210.998. By contrast, in the case of the SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$, showed improved metrics with a log likelihood of −1958.921, AIC of 3927.842, BIC of 3944.922, and HQIC of 3934.736. This indicates that the SARIMA model demonstrated a better fit than the ARIMA model.

The Ljung–Box Q test was used to verify the fit of both models. The null hypothesis of the Ljung–Box Q test is the hypothesis that “residuals follow white noise,” and the prob(Q) value was 0.92 for the ARIMA and 0.67 for the SARIMA [51]. This means that the null hypothesis is not rejected at a significance level of 0.05, and both models conclude that the residuals do not show autocorrelation and follow a white noise time series. These results suggest that the models were appropriately fitted.

Both models satisfied diagnostic tests with the Ljung–Box Q test, and the prob(Q) value was 0.92 for the ARIMA and 0.67 for the SARIMA, confirming residuals follow white noise at the 0.05 significance level [52]. Additionally, heteroscedasticity testing showed prob(H) values of 0.70 for SARIMA and 0.48 for ARIMA, indicating no heteroscedasticity in either model’s residuals [53]. However, when considering all evaluation criteria together, the SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$ model emerges as more appropriate for predicting monthly patent application filings, particularly due to its ability to incorporate seasonal patterns.

According to the diagnostic results of the SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$ shown in Figure 8, standardized residuals fluctuating around zero without specific patterns, indicating an appropriate model fit, though with some sharp increases suggesting potential outliers. The residual distribution approximates normality, with well-aligned KDE and normal distribution curves, showing only slight asymmetry and kurtosis [54]. The normal Q-Q plot demonstrates strong linear alignment [55], while the ACF graph shows residuals within confidence intervals near zero, confirming the absence of significant autocorrelation. These diagnostics support the SARIMA model’s appropriateness for capturing temporal structure.

However, when analyzing the diagnostic results of the ARIMA (2,1,1) model in Figure 9, some periodicity appeared in the standardized residuals, suggesting that the model may not have properly explained some of the temporal structure of the data. While its histogram roughly follows a normal distribution, it shows greater distortion than the SARIMA model, with the Q-Q plot revealing significant tail deviations and the ACF showing substantial autocorrelation at early lags.

Comprehensive analysis through information criteria (log likelihood, AIC, BIC, HQIC) confirms the SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$ model’s superior performance in capturing time series patterns, particularly seasonality. While the ARIMA (2,1,1) model shows periodic residuals and persistent autocorrelation due to unaddressed seasonality, the SARIMA model demonstrates stable residuals through effective seasonal factor incorporation.

Subsequently, the prediction performances of the two models were compared using the validation dataset (from November 2019 to July 2024), and the SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$ model showed an overall better performance than the ARIMA (2,1,1) model, as shown in

Table 7. The performance measure values.

Model	MAE	MAPE	RMSE
ARIMA (2,1,1)	2742.268	0.129	3740.830
SARIMA (2,1,0)$\times {\left(\mathrm{1,0},1\right)}_{12}$	1278.207	0.065	1610.092

. For the evaluation, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) indices were used (

Table 8. Formulas for performance metrics (MAE, MAPE, RMSE).

Model	Calculation
MAE	$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}|y_i-\widehat{y_i}|$
MAPE	$MAPE={\displaystyle \frac{100}{n}}{\displaystyle \sum _{i=1}^n}{\displaystyle \frac{(y_i-\widehat{y_i})}{y_i}}$
RMSE	$RMSE=\sqrt{{\displaystyle \sum _{i=1}^n}{\displaystyle \frac{{(y_i-\widehat{y_i})}^2}{n}}}$

). The smaller the MAE, MAPE, and RMSE values, the closer the predicted value was to the actual value [56]. The MAE of the SARIMA model was reduced to approximately half that of the ARIMA model, and the MAPE of the SARIMA model was 6.5%, which was less than half that of the ARIMA model (12.9%). In addition, the RMSE of the SARIMA model is much lower than that of the ARIMA model, indicating that the SARIMA model has a relatively lower error rate and shows more accurate forecasting performance.

The SARIMA model’s enhanced performance when incorporating the seasonal order (12) confirms its ability to capture the annual cyclical patterns previously identified through time series decomposition, ACF analysis, and the Kruskal–Wallis test. While the ARIMA model’s residuals retained seasonal patterns and showed significant autocorrelation at certain lags due to its inability to account for seasonality, the SARIMA model achieved a better fit by effectively capturing these seasonal fluctuations and eliminating residual autocorrelation.

The SARIMA model’s predictive performance for the validation dataset (November 2019 to July 2024), as visualized in Figure 10, demonstrates that seasonality is crucial for long-term forecasting accuracy. The model’s better performance across all metrics (MAE, MAPE, and RMSE) indicates that the annual seasonal cycle is a fundamental characteristic of monthly patent applications that must be considered for accurate predictions.

These findings confirm that while the ARIMA model without seasonal components struggled to explain long-term patterns and volatility, the SARIMA model incorporating 12-month seasonality provided more accurate forecasts by properly accounting for data volatility. This underscores the essential role of seasonality in monthly patent application patterns and the necessity of using seasonally adjusted models for time series forecasting.

4.3. Sector-Specific Seasonality Analysis: Private vs. Public R&D

To investigate the sources of seasonality more deeply, we conducted an additional experiment to analyze whether the seasonality of patent applications differs between private and public R&D. The analysis procedure is shown in Figure 11. The reason for conducting an additional experiment is that private and public R&D have different economic motivations and operating structures, and there is a high possibility that there will be differences in the timing and patterns of patent applications.

In additional experiments, data collected from January 2011 to February 2024 from the Republic of Korea R&D Intellectual Property Information System (RIPIS) (R&D Intellectual Property Information System) [57] were used. The data used here are from the Korean Intellectual Property Office, which includes patents for which government R&D project information is described in patent applications. The monthly patent application statistics are calculated based on the Regulations on Management of National Research and Development Projects of Republic of Korea.

Figure 12 shows the monthly patent applications for private and public R&D visualized over time. Both datasets exhibit repetitive patterns, suggesting the presence of seasonal factors. In addition, by comparing the time series decomposition results for private and public R&D, we can see that both time series contain trends and seasonality. First, private R&D increased sharply between 2012 and 2014, declined, and then showed a gradual upward trend after 2018. However, public R&D trends have maintained a steady upward trend from 2012 to the present, suggesting that continuous investment in public R&D is taking place.

In the case of seasonal components (Figure 13 and Figure 14), both private and public R&D showed distinct seasonality and repeated similar patterns every year. In particular, private R&D shows greater volatility than public R&D, suggesting that R&D activities in the private sector tend to fluctuate more significantly depending on the season. This suggests that R&D activities in the private sector may be more sensitive to economic conditions than those in the public sector, or that research activities may be concentrated during specific periods. The results of the residual analysis showed that the residuals for both private and public R&D were distributed relatively randomly and no distinct patterns or trends emerged.

In addition, the analysis of the ACF for the monthly patent application filings of private and public R&D showed significant seasonal autocorrelation in both datasets. Looking at the ACF graphs of private and public R&D (Figure 15 and Figure 16), the correlation coefficient is again high at lags 12, 24, and 36. This indicates seasonality that repeats every year, suggesting that monthly patent application filings show a similar pattern over a one-year cycle. This result is consistent with the seasonality shown in the time series decomposition results, implying that private R&D activity changes regularly in specific months.

Finally, the Kruskal–Wallis test results (

Table 9. Kruskal–Wallis test result (public R&D and private R&D).

	Kruskal–Wallis Test Stat	p-Value
Public R&D	25.762	0.007 **
Private R&D	92.745	<0.001 ***

Note: *** p < 0.001, ** p < 0.01, * p < 0.05.

) reveal p-values of less than 0.05 for both private and public R&D (Private: <0.00 1***, Public: 0.007 **), confirming a statistically significant difference in monthly patent application distributions. This supports the existence of distinct seasonality, where patent activities are concentrated in specific periods regardless of the sector. From a sustainable governance perspective, this concentration represents a systemic instability that challenges the consistent management of national intellectual property.

5. Discussions

Prior to discussing the implications, we summarize the verification of our research hypotheses. Our empirical analysis strongly supports Hypothesis 1 (H1), confirming the existence of a statistically significant “December Rush” in Republic of Korea’s patent filings through the Kruskal–Wallis test (p < 0.01) and visual decomposition. Furthermore, the forecasting performance comparison validates Hypothesis 2 (H2); the seasonality-aware SARIMA model (MAPE 6.5%) significantly outperformed the non-seasonal ARIMA model. Based on these validated hypotheses, we discuss the robustness and sectoral interpretation of the findings below.

5.1. Robustness of Seasonality Under Macroeconomic Uncertainty

A critical implication of our forecasting results concerns the robustness of the identified seasonality against external shocks. The validation period of this study (2019–2024) includes the global COVID-19 pandemic and periods of significant macroeconomic uncertainty [58,59,60]. This raises the question of whether the pandemic caused structural breaks in established seasonal patterns or whether the validation results are biased by this volatility.

However, our visual analysis of the year-over-year seasonal cycles reveals a compelling finding. As observed in Figure 17, the distinct "December Rush" in total patent application filings persisted with high intensity even during the lockdown periods and economic downturns caused by the pandemic. The trajectories for the pandemic years exhibit a high degree of synchronization with the historical baseline, showing no signs of structural deviation. This persistence suggests that the seasonality of patent application filings in the Republic of Korea is structurally anchored in internal institutional factors—specifically fiscal budget cycles, tax incentives, and year-end performance evaluations—rather than being easily disrupted by external economic trends.

To further verify the source of this stability, we examined the sectoral breakdown as shown in Figure 18 and Figure 19. Figure 18 illustrates the Private R&D sector, which generally exhibits higher monthly volatility. However, even within this sector, the recurring upward trend toward the end of the year was maintained during the pandemic years, showing no significant deviation from the historical seasonal shape. Figure 19 reveals an even more distinct persistence in the Public R&D sector. The filing volume in this sector maintained its characteristic pattern—relatively flat from January to October, followed by a sharp spike in November and December—across all pandemic years. The fact that the pandemic period replicated this specific ‘flat-then-spike’ pattern without temporal deviation confirms that the seasonal signal remained dominant regardless of external health or economic crises.

Consequently, relying on a single training-validation split that includes this volatile period serves as a rigorous “stress test” for the model. The fact that the SARIMA model maintained superior predictive accuracy (MAPE 6.5%) even under these extreme conditions demonstrates its robustness. It confirms that the identified seasonal patterns are not transient anomalies dependent on stable periods but are deeply rooted in the administrative ecosystem. Therefore, the validation results derived from this period provide strong evidence that the model is reliable in both stable and uncertain times.

5.2. Interpretation of Sectoral Seasonality

Following the forecasting analysis, we examined the sectoral breakdown of these seasonal patterns. As presented in Section 4.3, both private and public R&D sectors exhibit distinct seasonality, but the private sector demonstrates significantly higher volatility. This finding supports Hypothesis 3 (H3), suggesting that these distinct patterns likely reflect structural responses to different institutional incentives and economic motivations.

Regarding the Private R&D sector, the high volatility is driven by profit maximization strategies and market demands. As hypothesized in our experimental design, private companies tend to align patent applications with their fiscal year-end to maximize corporate performance metrics. First, Companies align patent applications with year-end budgets, particularly small and medium-sized enterprises (SME) that manage budgets more flexibly and utilize remaining funds at year-end [35]. Second, the Republic of Korea’s tax deduction benefit for job invention compensation influences year-end application timing. With 100% expense deduction and additional tax benefits compared to the standard 30% R&D expense deduction for SMEs, this creates significant tax advantages [36]. Although the impact was somewhat moderated when the tax-free limit for job invention compensation was adjusted in 2017 (taxing amounts exceeding 7 million KRW as earned income), it remains a powerful incentive. Third, in competitive industries, companies strategically file year-end applications to secure innovative advantages. With approximately 240,000 annual patent applications in the Republic of Korea, companies rush to establish priority over potential competitors.

In contrast, the Public R&D sector is structurally locked into the administrative governance cycle rather than market competition. This is because researchers tend to concentrate on their patent applications at the end of the year, aligning with the institutional performance evaluation and the closing of national R&D projects. This interpretation is supported by Liebman and Mahoney [61], who empirically demonstrated that “use-it-or-lose-it” budget expiration rules precipitate a significant surge in year-end activities and a corresponding decline in quality within the public sector. Consequently, the sharp seasonal spike in public patent filings is likely a structural byproduct of similar administrative rigidities, where fiscal deadlines override the natural timing of innovation outcomes. According to a 2007 report of the Korea Intellectual Property Research Institute (KIIP) [37], government-funded research institutes and universities tended to rush to file patent applications before performance evaluation at the end of the year. This implies that the current evaluation-centric governance structure inadvertently promotes unsustainable spikes in administrative demand.

5.3. Policy Implications for Sustainable Governance

The confirmed ‘December Rush’ represents a systemic instability that challenges the consistent management of national intellectual property. From a sustainable governance perspective, this seasonality hinders the resilience of the innovation infrastructure (SDG 9) and undermines the effectiveness of public institutions (SDG 16). Therefore, analyzing patent data enriches strategic policymaking, guiding stakeholders to effectively manage their contributions to the realization of SDGs [11]. To restore institutional resilience, a two-pronged strategy involving both corporate agility and government policy innovation is required.

First, firms may benefit from adopting counter-cyclical IP strategies by shifting filings to off-peak periods (e.g., Q2 or Q3), which could reduce congestion-related delays and contribute to a smoother administrative workload distribution. This is not merely a tactical adjustment but a move toward sustainable R&D management that distributes workload evenly, preventing researcher burnout and ensuring higher-quality IP creation [62]. For instance, an AI company observing Q4 saturation can strategically front-load R&D outcomes to Q2, securing a competitive edge while contributing to ecosystem stability.

Second, a balanced R&D schedule is required throughout the year. By moving away from the existing year-end-centered R&D schedule, dividing the R&D schedule into quarters and setting an interim evaluation point to regularly review the research results, continuous innovation activities can be carried out. This can alleviate the problem of quality deterioration caused by focusing on year-end performance evaluation. In SDG terms, such a balanced R&D schedule contributes to SDG 9 by sustaining continuous innovation processes, rather than compressing inventive activity into a narrow time window.

Furthermore, Governments must transition from rigid administration to data-driven anticipatory governance to resolve bottlenecks and ensure high-quality examinations. The seasonality of applications is a governance challenge that requires structural intervention.

First, flexible human resource governance, such as a part-time patent examiner system, is essential. With the average examination period in Korea extending to 17.6 months [63], rigidity in staffing is a barrier to innovation. Adopting Frakes and Wasserman’s [64] suggestion, a distributed work environment can enhance examination quality. The KIPO’s recent hiring of 60 specialized contract examiners in strategic fields (Bio, AI) [65] is a commendable step toward agile governance, effectively buffering the year-end workload surge.

Second, incentive restructuring is critical to smoothing volatility. The government could implement time-variant incentives, such as offering higher tax deductions or reduced filing fees for applications filed during off-peak months (Q1-Q2). This market-based governance approach would naturally guide companies toward a balanced R&D schedule, alleviating administrative pressure without coercive regulation. Given that the job invention compensation system is one of the most recognized tax support programs among companies, its improvement could serve as an immediate solution to mitigate seasonality [66].

Third, diversifying the recruitment schedule for patent support programs is necessary. Consistent with prior studies demonstrating that government R&D policies have a significant impact on corporate patent application filings [67], the Republic of Korea’s government currently operates 13 patent application support programs as of 2024. However, most programs accessible to SMEs are concentrated on recruitment during early-year periods (January–February) with outcomes finalized by year-end (November–December). This structure inadvertently reinforces year-end-centric R&D schedules among companies aiming to leverage government support. By decoupling patent support programs from the rigid calendar-year cycle, governments can promote a more continuous innovation rhythm, thus reinforcing SDG 9 and enhancing the long-term stability of the innovation ecosystem.

In conclusion, addressing seasonality is not just about administrative efficiency but about establishing sustainable governance for the national innovation ecosystem. By harmonizing corporate IP strategies with adaptive government policies—such as flexible staffing, smart incentives, and diversified program schedules, stakeholders can mitigate systemic bottlenecks and foster a more resilient environment for technological growth.

6. Conclusions

This study analyzes the seasonality of monthly patent application filings and compares the performance of time series forecasting models. The study was conducted based on the number of patent application filings from January 2001 to July 2024 and included an experiment to confirm seasonality by dividing the data into private and public R&D sectors. Consequently, a seasonal pattern was discovered, with patent applications concentrated at the end of the year. Every analysis demonstrated that patent applications had a clear 12-month seasonality, and the same results were obtained when dividing the data into private and public R&D sectors. The results of this study can be summarized as follows.

First, the analysis validated Hypothesis 1 (H1) by confirming that the “December Rush” is not a transient fluctuation but a statistically significant structural phenomenon. Notably, this seasonal concentration persisted even during the COVID-19 pandemic (2020–2022), demonstrating that the seasonality of patent application filings is deeply anchored in institutional factors rather than being swayed by external macroeconomic shocks. This finding provides a compelling rationale for shifting from reactive administration to proactive governance that anticipates these fixed cyclical patterns. This shift is theoretically significant as it moves patent administration from a focus on short-term efficiency to long-term “institutional sustainability,” by providing the empirical evidence required to reinforce the resilience of the innovation infrastructure (SDG 9).

Building on this structural identification, the comparative forecasting analysis validated Hypothesis 2 (H2), demonstrating the superior suitability of the SARIMA model over traditional methods. The SARIMA $(\mathrm{2,1},0)\times {\left(\mathrm{1,0},1\right)}_{12}$ model, which explicitly incorporates seasonal orders, achieved a MAPE of 6.5%, reducing the error rate by approximately half compared to the non-seasonal ARIMA $(\mathrm{2,1},1)$ model. This quantitative result confirms that incorporating seasonality is essential for optimizing resource allocation, thereby serving as a foundation for building effective and accountable public institutions (SDG 16) that utilize administrative resources transparently and efficiently.

Furthermore, the sectoral breakdown confirmed Hypothesis 3 (H3), revealing distinct seasonal behaviors between private and public entities. As hypothesized, the Private R&D sector exhibited greater seasonal volatility, suggesting that it is sensitively driven by flexible factors such as corporate budget cycles, tax benefits, and competitive strategies. In contrast, the Public R&D sector showed a more rigid pattern locked into administrative cycles. This distinction highlights the need for differentiated governance strategies: flexible incentives for the private sector to disperse filings, and structural improvements in performance evaluation systems for the public sector.

The methodological implications of this are noteworthy as they differ from previous studies. First, while previous studies have mainly utilized annual data, this study analyzed monthly patent application filing data to explain the detailed time series variability of patent applications more accurately. Furthermore, by rigorously validating the non-normality of the data (Shapiro–Wilk test) and applying the appropriate non-parametric tests (Kruskal–Wallis test), we established a more robust statistical standard for seasonality analysis. Second, by presenting a time series forecasting model that reflects seasonality, we emphasized the importance of seasonal variation, which had not been addressed in previous time series forecasting studies. Particularly, by comparing the performance of the ARIMA and SARIMA models, we emphasized the need for a forecasting model that includes seasonal factors in patent application forecasting. This study serves as an important reference for the development of a patent application-related forecasting model that considers seasonality to derive more sophisticated results in patent application filing forecasting.

Meanwhile, this study has several limitations. A primary limitation is that this study focuses on univariate time series analysis. While effective for forecasting intrinsic patterns, this approach does not account for the causal impact of external macroeconomic indicators or specific policy changes. Therefore, the causal links suggested in the discussion are interpretative rather than statistically proven by the model. In future studies, it is expected that adding external factors such as economic variables through seasonal multivariate time series analysis will allow researchers to empirically test these causal mechanisms and analyze their impact on the number of patent applications. Alternatively, conducting a hierarchical analysis segmented by industry, company type, and domestic and foreign applicants could help identify more specific R&D activities and patent application trends in greater detail.