Search Results (100)

Selecting an appropriate model for discharge simulation remains a fundamental challenge in modeling. While artificial neural networks (ANNs) have been widely accepted due to detecting streamflow patterns, they require large datasets for efficient training. However, when short-term datasets are available, training ANNs becomes problematic. Autoregressive integrated moving average (ARIMA) models offer a promising alternative; however, severe volatility, nonlinearity, and trends in hydrological time series can still lead to significant errors. To address these challenges, this study introduces a new adaptive hybrid model, ARIMA-iGARCH, designed to account volatility, variance inconsistency, and nonlinear behavior in short-term hydrological datasets. We apply the model to four hourly discharge time series from the Schwarzbach River at the Nauheim gauge in Hesse, Germany, under the assumption of normally distributed residuals. The results demonstrate that the specialized parameter estimation method achieves lower complexity and higher accuracy. For the four events analyzed, R² values reached 0.99, 0.96, 0.99, and 0.98; RMSE values were 0.031, 0.091, 0.023, and 0.052. By delivering accurate short-term discharge predictions, the ARIMA-iGARCH model provides a basis for enhancing water resource planning and flood risk management. Overall, the model significantly improves modeling long memory, nonlinear, nonstationary shifts in short-term hydrological datasets by effectively capturing fluctuations in variance. Full article

This study proposes a hybrid approach to analyze and forecast non-stationary financial time series by combining statistical models with deep neural networks. A model is introduced that integrates three key components: the Generalized Autoregressive Score (GAS) model, which captures volatility dynamics; an attention mechanism (ATT), which identifies the most relevant features within the sequence; and a Long Short-Term Memory (LSTM) neural network, which receives the outputs of the previous modules to generate price forecasts. This architecture is referred to as GAS-ATT-LSTM. Both unidirectional and bidirectional variants were evaluated using real financial data from the Nasdaq Composite Index, Invesco QQQ Trust, ProShares UltraPro QQQ, Bitcoin, and gold and silver futures. The proposed model’s performance was compared against five benchmark architectures: LSTM Bidirectional, GARCH-LSTM Bidirectional, ATT-LSTM, GAS-LSTM, and GAS-LSTM Bidirectional, under sliding windows of 3, 5, and 7 days. The results show that GAS-ATT-LSTM, particularly in its bidirectional form, consistently outperforms the benchmark models across most assets and forecasting horizons. It stands out for its adaptability to varying volatility levels and temporal structures, achieving significant improvements in both accuracy and stability. These findings confirm the effectiveness of the proposed hybrid model as a robust tool for forecasting complex financial time series. Full article

We investigate the affine term structure models (ATSMs) with unspanned stochastic volatility (USV). Our aim is to test their ability to generate accurate cross-sectional behavior and time-series dynamics of bond yields. Comparing the restricted models and those with USV, we test whether they produce both reasonable estimates for the short rate variance and cross-sectional fit. Essentially, a joint approach from both time series and options data for estimating risk-neutral dynamics in ATSMs should be followed. Due to the scarcity of derivative data in emerging markets, we estimate the model using only time-series of bond yields. A Bayesian estimation approach combining Markov Chain Monte Carlo (MCMC) and the Kalman filter is employed to recover the model parameters and filter out latent state variables. We further incorporate macro-economic indicators and GARCH-based volatility as external validation of the filtered latent volatility process. The $A_1\left(4\right)$USV performs better both in and out of sample, even though the issue of a tension between time series and cross-section remains unresolved. Our findings suggest that even without derivative instruments, it is possible to identify and interpret risk-neutral dynamics and volatility risk using observable time-series data. Full article

Bitcoin and other cryptocurrency returns show higher volatility than equity, bond, and other asset classes. Increasingly, researchers rely on machine learning techniques to forecast returns, where different machine learning algorithms reduce the forecasting errors in a high-volatility regime. We show that conventional time series modeling using ARMA and ARMA GARCH run on a rolling basis produces better or comparable forecasting errors than those that machine learning techniques produce. The key to achieving a good forecast is to fit the correct AR and MA orders for each window. When we optimize the correct AR and MA orders for each window using ARMA, we achieve an MAE of 0.024 and an RMSE of 0.037. The RMSE is approximately 11.27% better, and the MAE is 10.7% better compared to those in the literature and is similar to or better than those of the machine learning techniques. The ARMA-GARCH model also has an MAE and an RMSE which are similar to those of ARMA. Full article

Existing stock volatility forecasting models predominantly rely on same-frequency market data while neglecting mixed-frequency integration and face particular challenges in incorporating low-frequency macroeconomic variables that exhibit temporal mismatches with financial market dynamics. To address this limitation, this study develops a novel hybrid approach for stock market volatility forecasting, which synergistically combines a deep learning model (CNN-BiLSTM-Attention) with the GARCH-MIDAS model. The GARCH-MIDAS model can fully exploit mixed-frequency information, including daily returns, monthly macroeconomic variables, and EPU. The deep learning model can effectively capture both spatial and temporal patterns of multivariate time-series data, thus effectively improving prediction accuracy and generalization ability in stock market volatility forecasting. The results indicate that the CNN-BiLSTM-Attention model yields the most accurate forecasts compared to the benchmark models. Furthermore, incorporating additional predictors, such as macroeconomic indicators and the Economic Policy Uncertainty Index, also provides valuable information for stock market volatility prediction, notably enhancing the model’s forecasting effect. Full article

We explore the impact of time series behavior on model errors when working under an elliptically contoured distribution. By adopting a time series approach aligned with the realistic dependence between errors under such distributions, this perspective shifts the focus from increasingly complex and challenging correlation analyses to volatility modeling that utilizes a novel likelihood framework based on dependent probabilistic samples. With the introduction of a modified Bayesian Information Criterion, which incorporates a ranking of degrees of evidence of significant differences between the compared models, the critical issue of model selection is reinforced, clarifying the relationships among the most common information criteria and revealing limited relevance among the models based on independent probabilistic samples, when tested on a well-established database. Our approach challenges the traditional hierarchical models commonly used in time series analysis, which assume independent errors. The application of rigorous differentiation criteria under this novel perspective on likelihood, based on dependent probabilistic samples, provides a new viewpoint on likelihood that arises naturally in the context of finance, adding a novel result. We provide new results for criterion selection, evidence invariance, and transitions between volatility models and heuristic methods to calibrate nested or non-nested models via convergence properties in a distribution. Full article

Volatility forecasting for financial institutions plays a pivotal role across a wide range of domains, such as risk management, option pricing, and market making. For instance, banks can incorporate volatility forecasts into stress testing frameworks to ensure they are holding sufficient capital during extreme market conditions. However, volatility forecasting is challenging because volatility can only be estimated, and different factors influence volatility, ranging from macroeconomic indicators to investor sentiments. While recent works show promising advances in machine learning and artificial intelligence for volatility forecasting, a comprehensive assessment of current statistical and learning-based methods is lacking. Thus, this paper aims to provide a comprehensive survey of the historical evolution of volatility forecasting with a comparative benchmark of key landmark models, such as implied volatility, GARCH, LSTM, and Transformer. We open-source our benchmark code to further research in learning-based methods for volatility forecasting. Full article

This paper introduces a novel numerical approach for solving fractional stochastic differential equations (FSDEs) using bilinear time-series models, driven by the Caputo–Katugampola (C-K) fractional derivative. The C-K operator generalizes classical fractional derivatives by incorporating an additional parameter, enabling the enhanced modeling of memory effects and hereditary properties in stochastic systems. The primary contribution of this work is the development of an efficient numerical framework that combines bilinear time-series discretization with the C-K derivative to approximate solutions for FSDEs, which are otherwise analytically intractable due to their nonlinear and memory-dependent nature. We rigorously analyze the impact of fractional-order dynamics on system behavior. The bilinear time-series framework provides a computationally efficient alternative to traditional methods, leveraging multiplicative interactions between past observations and stochastic innovations to model complex dependencies. A key advantage of our approach is its flexibility in handling both stochasticity and fractional-order effects, making it suitable for applications in a famous nuclear physics model. To validate the method, we conduct a comparative analysis between exact solutions and numerical approximations, evaluating convergence properties under varying fractional orders and discretization steps. Our results demonstrate robust convergence, with simulations highlighting the superior accuracy of the C-K operator over classical fractional derivatives in preserving system dynamics. Additionally, we provide theoretical insights into the stability and error bounds of the discretization scheme. Using the changes in the number of simulations and the operator parameters of Caputo–Katugampola, we can extract some properties of the stochastic fractional differential model, and also note the influence of Brownian motion and its formulation on the model, the main idea posed in our contribution based on constructing the fractional solution of a proposed fractional model using known bilinear time series illustrated by application in nuclear physics models. Full article

This study focuses on the precise forecasting of stock price movement to determine returns, diversify risk, and demystify existing opportunities. It also aims to gauge the difference in terms of the stock volatility of various pharma companies before and during the pandemic era. The prediction of stock market volatility and associated risks is demonstrated by using the GARCH-M model. A sample is collected by clustering daily closing and opening prices from the official websites of the top ten pharmaceutical companies listed on the Bombay Stock Exchange for ten years, from 2012 to 2023. It is evident when using the GARCH-M model, which indicates pharma stock volatility clustering before the COVID-19 pandemic, that a significant relationship is present between risk and return and that these could cause future volatility and significant price movements. Before the COVID-19 pandemic, investors had time to adjust to market conditions, as the volatility was constant but less sensitive to transient shocks. Though it passed faster than ever, the COVID-19 pandemic produced significant market instability. The findings suggest that, especially before the COVID-19 pandemic, the high GARCH(-1) coefficients held Merton’s ICAPM, which maintains that past volatility shapes future returns. This sort of activity is compatible with the way financial markets usually operate. The findings suggest that volatility rose after the COVID-19 pandemic, but this was more because of changes in government policies and vaccines than because of regular market forces. Pricing patterns are dominated by stock interventions, liquidity constraints, and sentiments during a crisis period when volatility becomes irrelevant. Appropriate decision-making by individual investors, portfolio managers, and policymakers regarding the stock market is possible through effective prediction based on time-series analysis. The GARCH-M model is compatible with predicting future stock price changes efficiently. This study uniquely applies the GARCH-M model to the Indian pharmaceutical sector, offering valuable insights into stock volatility and risk–return dynamics, particularly during the COVID-19 pandemic. Full article

The financial markets are highly influential and any change in the economy can be reflected in stock prices and thus have an impact on stock indices. The relationship between stock indices and the way they are affected by extreme phenomena is important for defining diversification strategies and analyzing market maturity. The purpose of this study is to examine the interdependence relationships between the main Euronext stock indices and any changes caused by an extreme event—the COVID-19 pandemic. Copula models are used to estimate the dependence relationships between stock indices pairs after estimating ARMA-GARCH models to remove the autoregressive and conditional heteroskedastic effects from the daily return time series. The financial interdependence structures show a symmetric relationship of influence between the indices, with the exception of the CAC40/ISEQ pair, where there was financial contagion. In the case of the AEX/OBX pair, the dynamics of dependence may have changed significantly in response to the pressure of the pandemic. On the other hand, the dominant influence of the CAC40 before and the AEX after the pandemic confirms that the size and age of these indices give them a benchmark position in the market. Finally, with the exception of the AEX/OBX and CAC40/ISEQ pairs, the interdependencies between the stock indices decreased from the pre- to the post-pandemic sub-period. This result suggests that the COVID-19 pandemic has weakened the correlation between the markets, making them more mature and independent, and less risky for investors. Full article

Machine learning forecasting methods are compared to more traditional parametric statistical models. This comparison is carried out regarding a number of different situations and settings. A survey of the most used parametric models is given. Machine learning methods, such as convolutional networks, TCNs, LSTM, transformers, random forest, and gradient boosting, are briefly presented. The practical performance of the various methods is analyzed by discussing the results of the Makridakis forecasting competitions (M1–M6). I also look at probability forecasting via GARCH-type modeling for integer time series and continuous models. Furthermore, I briefly comment on entropy as a volatility measure. Cointegration and panels are mentioned. The paper ends with a section on weather forecasting and the potential of machine learning methods in such a context, including the very recent GraphCast and GenCast forecasts. Full article

OpenAI’s new flagship model, ChatGPT-4o, released on 13 May 2024, offers enhanced natural language understanding and more coherent responses. This paper investigates ChatGPT-4o’s capabilities in financial data analysis, including zero-shot prompting, time series analysis, risk and return analysis, and ARMA-GARCH estimation. ChatGPT-4o’s performance is generally comparable to traditional statistical software like Stata, though some errors and discrepancies arise due to differences in implementation. Despite these issues, our findings indicate that ChatGPT-4o has significant potential for real-world financial analysis. Integrating ChatGPT-4o into financial research and practice may lead to more efficient data processing, improved analytical capabilities, and better-informed investment decisions. Full article

To address a key issue in functional time series analysis on testing the randomness of an observed series, we propose an IID test for functional time series by generalizing the Brock–Dechert–Scheinkman (BDS) test, which is commonly used for testing nonlinear independence. Similarly to the BDS test, the proposed functional BDS test can be used to evaluate the suitability of prediction models as a model specification test and to detect nonlinear structures as a nonlinearity test. We establish asymptotic results for the test statistic of the proposed test in a generic separate Hilbert space and show that it enjoys the same asymptotic properties as those for the univariate case. To address the practical issue of selecting hyperparameters, we provide the recommended range of the hyperparameters. Using empirical data on the VIX index, empirical studies are conducted that feature the applications of the proposed test to evaluate the adequacy of the fAR$\left(1\right)$ and fGARCH$(1,1)$ models in fitting the daily curves of cumulative intraday returns (CIDR) of the index. The results reveal that the proposed test remedies some shortcomings of the existing independence test. Specifically, the proposed test can detect nonlinear temporal structures, while the existing test can only detect linear structures. Full article

Carbon price forecasting and pricing are critical for stabilizing carbon markets, mitigating investment risks, and fostering economic development. This paper presents an advanced decomposition-integration framework which seamlessly integrates econometric models with machine learning techniques to enhance carbon price forecasting. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is employed to decompose carbon price data into distinct modal components, each defined by specific frequency characteristics. Then, Lempel–Ziv complexity and dispersion entropy algorithms are applied to analyze these components, facilitating the identification of their unique frequency attributes. The framework subsequently employs GARCH models for predicting high-frequency components and a gated recurrent unit (GRU) neural network optimized by the grey wolf algorithm for low-frequency components. Finally, the optimized GRU model is utilized to integrate these predictive outcomes nonlinearly, ensuring a comprehensive and precise forecast. Empirical evidence demonstrates that this framework not only accurately captures the diverse characteristics of different data components but also significantly outperforms traditional benchmark models in predictive accuracy. By optimizing the GRU model with the grey wolf optimizer (GWO) algorithm, the framework enhances both prediction stability and adaptability, while the nonlinear integration approach effectively mitigates error accumulation. This innovative framework offers a scientifically rigorous and efficient tool for carbon price forecasting, providing valuable insights for policymakers and market participants in carbon trading. Full article

This study explores the resilience of the Indian stock market in the face of global shocks in the post-pandemic era, focusing on its volatility dynamics and interconnections with international indices. Through a combination of Vector Autoregression (VAR), DCC-GARCH, and wavelet analysis, we analysed the time-varying relationships between the National Stock Exchange (NSE) of India and major global indices, including those from the U.S., Europe, Asia-Pacific, Hong Kong and Japan. Time series data of the selected indices have been collected for the period 1 January 2021 to 30 September 2024. Results reveal that while the NSE demonstrates resilience through rapid adjustments following shocks, it remains vulnerable to substantial spillover effects from markets such as the S&P 500 and European indices. Wavelet coherence analysis identifies periods of high correlation, particularly during major economic events, indicating that regional and global factors can periodically compromise market stability. Moreover, the DCC-GARCH results show a persistent but fluctuating correlation with specific markets, reflecting a connected and adaptive nature of the Indian market that is influenced by regional dynamics. This study emphasises the importance of strategic risk management. It highlights critical periods and indices that policymakers and investors should monitor closely to understand the economic resilience of the Indian financial market better. Further research could explore sector-specific impacts and the role of macroeconomic factors in shaping market responses. Full article