Montenegrin Stock Exchange Market on a Short-Term Perspective

Abstract

The objective of this study is to analyse the constitution of the emerging Montenegrin stock exchange. Four methodological time-series econometric steps are involved: the augmented Dickey–Fuller (ADF) test, run test, autocorrelation function (ACF) test, and Hurst test. The study utilises a daily data vector from 5 January 2004 to 20 June 2023, with a specific focus on the period encompassing the growth and peak of market stocks in 2007, followed by the significant 2008 financial crisis and subsequent developments thereafter. The analysis culminates on 28 May 2018, which is considered one of the lowest points in the Montenegrin stock exchange market in a comparative time-series assessment. The results of the tests conducted in this study do not provide empirical evidence supporting the random walk theory and its returns on aggregated shocks in the Montenegrin stock exchange market. By reviewing previous empirical studies and presenting new empirical findings, this study confirms the presence of stochastic trends in co-movements in finance, contributing to a deeper understanding of emerging stock exchange markets. Study implications support greater reliance on market efficiency, risk management, and portfolio diversification.

1. Introduction

Investors are increasingly drawn to emerging capital markets, particularly in the aftermath of herding inside crises or shocks (Chen 2022). There is a prevailing notion that some less-developed capital markets are secondarily affected by global market deficiencies, thus making them an ideal option for diversifying investment portfolios (Narcis Firtescu et al. 2020). However, while these emerging markets are gaining popularity among investors, there is a cautious approach towards identifying risk factors. Investors tend to favour transparent emerging capital markets, where all available information is perceived uniformly. As a result, stock exchange prices in such markets exhibit random fluctuations, rendering it difficult to predict their future values.

This study aims to examine whether stock exchange prices in the Montenegrin capital market adhere to the principles of the random walk theory, which is aligned with the efficient market hypothesis (EMH). The random walk theory suggests that stock prices move unpredictably, making it impossible to anticipate or outperform the market. This assignment seeks to determine whether this theory holds for the Montenegrin capital market by analysing the path and behaviour of stock exchange prices.

The random walk path was introduced by Makiel (1973). The idea is that stock exchange prices follow a trajectory composed of a sequence of stochastic steps within a mathematical domain. He stipulated that short-term obstacles in stock exchange prices could not be formed. In the past five decades, financial experts have believed (Fama 1970; Cooper 1982; Keane 1983; Crotty 1990; Bollerslev and Hodrick 1999) that they could define an algorithm for whipping the capital market in the case of specific stock exchanges. The assumption underlying certain investment strategies is that it is possible to generate superior returns by predicting the movements of stock exchange prices, thus outperforming the expected return of the stock exchange (Korley and Giouvris 2021; Kudryavtsev 2021). The random walk theory has been widely applied in the examination of stock exchange markets, including both developed and emerging ones. It is commonly known that less-developed markets are inefficient compared to their developed counterparts, which makes them an attractive prospect for global investors, which is a motivation for this study.

This paper contributes to the study of the researched efficiency of the Montenegrin stock exchange market on omitted methodological purposes since its foundation. More specifically, this paper investigates the Montenegrin stock exchange market. Additionally, it seeks to discover whether it is weak-form efficient. The outcome of this research endeavours to provide a precise and comprehensive depiction of the current state of the Montenegrin capital market. Following the previous empirical literature, time-series data on the Montenegrin stock exchange market are used to apply four methods to provide accurate analysis for investors and policymakers. Therefore, the goal of the research is to present the emerging stock market using comprehensive time-series methods. The specific objective is to analyse several empirical types of research on emerging markets.

The research questions driving this study are as follows: To what extent does the Montenegrin stock exchange market exhibit characteristics of the random walk theory before, during, and after the 2008 financial crisis, and what are the implications of these findings for understanding market dynamics?

The study aims to shed light on the examination of the random walk theory and its impact on the Montenegrin stock exchange market, with a specific focus on the period surrounding the economic–financial crisis in 2008. This research is particularly significant given the limited existing research on the Montenegrin stock exchange market, making it a valuable contribution to the literature in this area. Furthermore, by encompassing the period leading up to 2018, which was noted as one of the worst years for stock exchanges, the analysis provides insights into pre-crisis expansion and subsequent economic developments, further enriching our understanding of the exchange stock market’s behaviour.

Therefore, this study aims to fill the gap in the existing literature by exploring the Montenegrin stock exchange market, which has been relatively under-researched. By examining the random walk theory and its impact on market dynamics, the study contributes to a better understanding of the Montenegrin stock exchange market and its behaviour. The research path of this study involves shedding light on the Montenegrin stock exchange market and providing valuable insights into its characteristics and deviations from the random walk theory.

Furthermore, it is important to note that this study deliberately excludes the exceptional year of 2019, which was characterised as the best year for stock exchanges, and the unprecedented COVID-19 pandemic from its data analysis. These two events represent significant shocks to the stock exchange market that warrant separate investigations as independent research topics. The focus of this study is specifically on the pre-pandemic period and the context of the 2008 financial crisis to gain a comprehensive understanding of the dynamics of the Montenegrin stock exchange market within these specific timeframes. Additional comparative presentations can be found in Appendix A for reference and further analysis.

The paper is structured and organised in the following manner. The subsequent sections undertake a review of prior empirical research, present the empirical data and methodology employed in the study, and finally, the concluding section summarises the findings. The introduction serves to introduce the reader to the paper’s context, offering a brief overview of existing research in the field and outlining the sequential approach adopted throughout the article.

2. Review of the Scientific Literature

This section summarises the main findings and conclusions from previous analyses and studies on the stock exchange market analysis in Southeast Europe (Sinisa et al. 2016; Christopoulos et al. 2014; Saman and Szeles 2020). The overview is helpful to match the research path between this assignment and previous empirical research mostly mentioned in Kubiszewska and Potrykus (2020), specifically for Montenegro (Kaščelan et al. 2014, 2015; Filipovski and Tevdovski 2017; Milošević-Avdalović and Milenković 2017; Stratimirović et al. 2018; Živkov et al. 2019). The random walk theory, as proposed by Fama (1965), is commonly tested in emerging markets to assess their level of efficiency, specifically in terms of weak-form efficiency. Emerging markets exhibit lower levels of efficiency, and empirical evidence tends to support this notion. Numerous studies have consistently identified weak-form inefficiency in less progressive markets, as mentioned in the study by Zhao et al. (2020). Barbu et al. (2019) discuss the impact of financial poverty of the stock exchange market on the capitalisation level of 35.34% to small and medium entrepreneurs (SMEs) regarding inflation, unemployment, gross domestic product (GDP), and other macroeconomic variables.

Configuring the geo-economic location, Montenegro is a developing country with an open economy in Southeast Europe (SEE) (Bacovic 2007; Khodaparasti and Mohammadpour 2016; Simovic 2021). Peša and Festić (2014) analysed stock exchange markets in SEE countries (Bosnia and Herzegovina, Bulgaria, Croatia, Montenegro, Serbia, Slovenia, and Romania). Most of them usually have inexperienced financial institutions, primitive financial instruments, and an inefficient capital market because of no transparent trading with soaring transaction fees (Bernard 1993; Edgar 1996). In mid-1993, the Montenegro Stock Exchange was established. This was under the framework of the Law on Money and Capital Market. However, it is worth noting that despite its establishment in this year (1993), the first transaction involving long-term bond did not occur until the enactment of the Law on Securities by the Parliament in 2002, as referenced in the studies by Karadžić and Vulić (2011) and Kubiszewska and Potrykus (2020).

The Law on Securities plays a crucial role in regulating various aspects of the securities market in Montenegro. It encompasses provisions related to the issuance, public offering, and trading of securities, as well as the rights and obligations of market participants.

The New Montenegrin Stock Exchange (NEX Montenegro) in the capital of Montenegro was established at the beginning of the last third of 2001. It obtained authorisation from the Montenegrin Securities Commission to commence operations in November 2001. For almost a decade, two separate stock exchanges functioned in Montenegro: the Montenegro Stock Exchange and NEX Montenegro. However, at the beginning of 2010, the shareholders of NEX Montenegro voted in favour of merging these two institutions. This union streamlined and consolidated securities transactions in the country, as highlighted in the study by Cerović Smolović et al. (2017). The Montenegrin stock exchange market has experienced notable growth concerning the number of associated companies, market capitalisation, and trade volume within a short period. However, it has also been subject to significant fluctuations, as noted by Stefanova (2015).

In their study, Frimpong and Oteng-Abayie (2007) examined the applicability of the random walk theory within the stock exchange market of Ghana. There is an inefficiency in the weekly existence of trading and prices in the Ghana Stock Exchange if the generalised autoregressive conditional heteroscedasticity (GARCH(1,1)) model and random walk theory are used.

In their study, Mobarek and Keasey (2000) examined weak-form efficiency in Bangladesh’s Dhaka stock exchange market. The objective of their research was to gather evidence that supports the presence of weak-form efficiency in the capital market of the Dhaka stock exchange, spanning from 1988 to 1997. The results obtained from a combination of non-parametric tests, such as the Kolmogorov–Smirnov normality test and the Wald–Wolfowitz run test (run test), as well as parametric tests, including the autocorrelation test, autoregression, and autoregressive integrated moving average (ARIMA) model, collectively support the conclusion that the series of share returns in the examined market are randomly determined in each of the steps. Additionally, the identification of serious autocorrelation coefficients at various lags leads to the rejection of the null hypothesis of weak-form efficiency.

In their study, Awan and Subayyal (2016) examined the hypothesis of weak-form efficiency in six stock exchanges within the Arab states of the Persian Gulf, namely Bahrain, Kuwait, Oman, Saudi Arabia, the United Arab Emirates, and Qatar. The investigation covered the period from 2011 to 2015. The findings suggest that the bond prices in all of the Arab states of the Persian Gulf markets do not adhere to the probability of the same directions of each process and shock. This implies that there is a path of deviation from weak-form efficiency in these markets.

The study conducted by Cajueiro and Tabak (2006) investigated the predictability of stock exchange returns in nine European transition countries. Based on their empirical analysis, the study concluded that stock exchange returns in these countries can be forecasted in the long term. On the other hand, Ukrainian bonds tend to exhibit efficiency.

In the study conducted by Jović (2010), the adaptability of the financial institutions in Republika Srpska was examined. The research focused on testing the hypothesis of weak-form efficiency through the application of various methods. The comparative method was employed, utilising the square-root-of-time rule, along with statistical methods, such as simple linear regression, autocorrelation test, and sign test. Additionally, the study incorporated the use of the technical analysis method. The empirical analysis was based on the progress of stock exchange prices and indices at the Banja Luka Stock Exchange, providing the information foundation for the investigation. His conclusion was not unique, but a weak form of efficiency was present according to the sign and autocorrelation tests.

The research by Ivanov et al. (2012) aimed to assess the market efficiency of septenary less-developed East European stock exchanges by analysing the major stock exchange indices in terms of long-range dependence (LRD), increase, and predicting capabilities. The study focused on utilising historical information to investigate these aspects of the stock exchange indices. The investigation period was from 20 October 2000 to 31 August 2010, and the studied markets manifested inefficiency (Ivanov et al. 2012). Based on the relevant literature, none includes the methodology of several tests; therefore, those are used in this research. Methodology that is scarcely used in the stock exchange market is explained in the next section.

Nevertheless, recent articles and research emphasise the significance of understanding various aspects of the stock market. The study of Montenegro and Molina (2020) proposed a strategy that combines deep learning neural networks with feature selection analysis to support investment decisions in the stock market, showing promising results in improving decision making of investors.

Dospatliev et al. (2022) conducted novel empirical analysis to investigate how the Bulgarian stock market was affected by the COVID-19 pandemic. By employing a fixed-effect panel-data-regression model, the study examined the stock returns of 23 companies listed on the Bulgarian Stock Exchange from 2 January 2020 to 16 November 2021. The results demonstrated that the daily increase in COVID-19 deaths in Bulgaria had a detrimental impact on stock returns, particularly during the fourth wave of the pandemic. Additionally, the study found that various sectors, including healthcare, IT, utilities, and real estate, experienced distinct effects before and during different waves of the pandemic, with both positive and negative influences observed.

The study conducted by Bieszk-Stolorz and Markowicz (2021) explored the impact of various factors, including economic, social, environmental, political, and the COVID-19 pandemic, on energy and fuel companies listed on the Warsaw Stock Exchange in Poland. Using survival analysis methods, such as the Kaplan–Meier estimator, equality of duration curves test, and the Cox non-proportional hazards model, the research examined the probability and intensity of price decline during the first wave of the pandemic in the first quarter of 2020. The findings indicated that initially, the likelihood and severity of price decreased for energy and fuel companies were similar to other industries. However, after 50 days from the peak value, the risk of price declines in energy and fuel companies significantly increased due to a temporary reduction in demand, pandemic restrictions, and investor behaviour in the stock market.

The study by Bieszk-Stolorz and Dmytrów (2021) compared the decline and subsequent increase in stock market indices during the COVID-19 pandemic. Using survival analysis methods, they found that European stock exchanges experienced the highest decline in intensity, followed by American and Asian exchanges. The risk of decline was highest in America, while Africa had the lowest risk. The intensity of increase was highest after the fourth and eleventh week from the minimal value, with American exchanges showing the highest odds of increase. Overall, the increase surpassed the initial decline.

An additional comprehensive literature review is provided in Appendix A. This review presents an extensive analysis of relevant academic research, scholarly articles, and empirical studies that delve into various aspects of the Montenegrin stock exchange market, including its structure, efficiency, and market dynamics. The literature review encompasses a wide range of perspectives, theories, and methodologies employed by previous researchers to explore the emerging financial market in Montenegro. By examining the existing body of literature, this study builds upon previous knowledge and fills gaps in the understanding of the Montenegrin stock exchange market. The insights gained from the literature review inform the research design, methodology, and interpretation of findings, ensuring a robust and well-informed investigation into the emerging stock exchange market in Montenegro.

The most recent article is by Vujanović and Fabris (2021). They highlight the importance of analysing risks to bank and financial system stability in Montenegro. This research emphasises the need to understand the dynamics between competition, bank size, and credit risk to ensure financial stability in Montenegro.

Therefore, the subject of the Montenegrin stock exchange market remains under-researched. Limited attention has been given to exploring the dynamics, efficiency, and behaviour of the Montenegrin stock exchange market during the whole period. This highlights the need for more comprehensive and up-to-date research to bridge the gap in understanding the unique characteristics and challenges faced by the Montenegrin stock exchange market in the post-crisis period.

From Appendix A, which includes a compilation of recent studies, it becomes evident that there is a dearth of research on the Montenegrin stock exchange market. By filling this research gap, the study aims to contribute to a more comprehensive understanding of the Montenegrin stock exchange market and provides insights into its behaviour and potential implications for investors and policymakers.

3. Review of Montenegrin Stock Exchange Market and Hypotheses Development

The Montenegro Stock Exchange, known as Montenegroberza AD, is the sole stock exchange in Montenegro, located in Podgorica. Established in 1993, it holds membership in prestigious organisations, such as the World Federation of Exchanges, the Federation of European Securities Exchanges, and the Federation of Euro-Asian Stock Exchanges. The Montenegro Stock Exchange has encompassed the NEX Stock Exchange since 10 January 2011, consolidating Montenegro’s capital market. Trading activities on the MNSE encompass a wide range of securities, including short and long-term securities, investment funds, government bonds, and shares from government fund portfolios. The primary stock indices on the Montenegro Stock Exchange are MONEX20 and MONEXPIF.

The Montenegro Stock Exchange boasts an extensive selection of financial instruments with a total of 323 tickers listed on its platform (Montenegro Stock Exchange 2023). These tickers represent a diverse range of companies and investment opportunities available to traders and investors. With such a wide array of listed financial instruments, the Montenegro Stock Exchange provides a comprehensive platform for individuals and institutions to engage in trading activities. Whether it be stocks, bonds, or other securities, the abundance of tickers ensures that market participants have ample choices to suit their investment preferences and strategies. This vast selection further solidifies the Montenegro Stock Exchange as a significant player in the financial landscape, catering to the needs of both domestic and international investors seeking exposure to the Montenegrin market.

In May 2007, the Montenegrin stock exchange index (MONEX20) reached its peak value, followed by a significant downturn that dampened investor sentiment in the Montenegrin stock exchange market, as depicted in Figure 1. According to Peša et al. (2017), during the period of economic liberalisation and reduced unemployment rates in Southeast European (SEE) countries, high volatilities were observed in stock exchange markets. Additionally, Vukotić (2003) argued that Montenegro underwent institutional and macroeconomic reforms during this time. However, this study does not focus on the years 2018, 2020, and beyond, which experienced some of the lowest points in the Montenegrin stock exchange market. While these years are not part of the econometric research conducted in this study, the minimum points can be observed in Appendix B.

Furthermore, it is important to note that the exclusion of the years 2018, 2020, and beyond from the econometric research of this study does not diminish their significance. These years witnessed notable events, such as the global COVID-19 pandemic, geopolitical shifts, and economic fluctuations, which undoubtedly impacted the Montenegrin stock exchange market. However, the decision to focus on the pre-pandemic period and the specific context of the 2008 economic–financial crisis allows for a more targeted analysis of the dynamics and patterns within those specific timeframes. By doing so, this study aims to provide valuable insights into the behaviour and efficiency of the Montenegrin stock exchange market during critical economic–financial periods and contribute to the existing literature on emerging stock exchange markets.

Drawing from the existing literature, the formulation of the hypotheses in this study adheres to the prevailing notion that the random walk model, encompassing the null hypothesis H₀, predicts a state of weak-form inefficiency within the stock exchange of an emerging market. Conversely, the alternative hypothesis H₁ posits that the efficiency of the stock exchange in developing countries does not exhibit a significant disparity when compared to that of developed nations.

4. Research Methodology

The processing test of the weak form of market efficiency involves examining historical data to identify any discernible patterns in short-term stock exchange market returns. If no consistent pattern can be identified and the returns appear to follow a random walk process, then it suggests the existence of weak-form efficiency in the bonds.

Several techniques are available to determine criteria in time series. This paper employs three widely recognised inspections of trade ability to assess the performance of the examined markets: augmented Dickey–Fuller (ADF) test, run test, and autocorrelation Function (ACF) test (Granger and Newbold 1977; Green 2000; Gujarati 2003; Hamilton 1970; Hung et al. 2021; Kendal 1953).

The ADF test is indeed one of the most commonly used stationarity tests in empirical finance. It is widely utilised to demonstrate whether a time series is stable or exhibits a unit root, which implies non-stationarity (Kwiatkowski et al. 1992), with two equations:

$$Y_t=\rho ·Y_{t-1}+u_t.$$

(1)

In addition, Equation (1) might be reduced by $Y_{t-1}$ from both sides of the mathematical statement, and the successive form is as follows:

$$Y_t-Y_{t-1}=\rho ·Y_{t-1}-Y_{t-1}+u_t\to ∆Y_t=\left(\rho -1\right)·Y_{t-1}+u_t\to ∆Y_t=\delta ·Y_{t-1}+u_t,$$

(2)

where $Y_t$ is a time-series variable; $Y_{t-1}$ are past observations; $\rho ,\delta$ represent lag correlation in time series, and $u_t$ represents unknown parameters, whereas the null hypothesis can be promoted as $H_0$: $\delta =0$ or $H_0$: $=1$. When the null hypothesis of the ADF test cannot be rejected, it implies that the time series is integrated in some order. In other words, the time series is non-stationary and therefore pursues a random walk process. This means that the series exhibits behaviour where the changes or differences between consecutive observations are unpredictable and unrelated to previous values.

The run test is a non-parametric statistical test used to determine whether a specific time series adheres to the random walk hypothesis. It evaluates whether a distribution of observations can be considered a random order. The sequence can be positive or negative if the test is used on the time series representing stock exchange returns. If the forthcoming changes in stock exchange prices are truly odd, then the null hypothesis of a series of random changes cannot be rejected. In other words, if there is no evidence of a discernible pattern or predictability in future price changes, it supports the notion that the stock exchange prices follow a random process. In the case of a large sample, the normal distribution can be assumed, and the run test is represented as follows:

$$Z=R-E\left(R\right)/{\sigma }_R,$$

(3)

where $R$ is the amount of randomness in the series, and $E\left(R\right)$ and ${\sigma }_R$ are its normal value and standard deviation, respectively.

As per the initial proposition, the Hurst exponent (H) ranges from 0 to 1. If the Hurst exponent has a value of 0.5, it indicates that the time series follows a process by which randomly moving points step away from where they started. On the other hand, if the exponent is less than 0.5, it signifies that the series exhibits anti-persistence. It implies that if the rate of the series was immense in the previous period, it is likely to step down towards the mean value in the forthcoming period (Czech and Pietrych 2021).

To detect non-randomness in data, the autocorrelation function (ACF) and the partial autocorrelation function (PACF) are commonly used. Two significant tests that utilise the ACF are the standard error test and the Box–Pierce Q test. The standard error test examines the autocorrelation function at each lag in the case and endorses which lags exhibit statistically significant autocorrelation. By comparing the calculated autocorrelation values with their corresponding standard errors, the test determines the significance of the autocorrelation. On the contrary, the Box–Pierce Q test adjusts the autocorrelation function for entire rates in the series until a specified lag is reached, denoted as $k$.

The Box–Ljung (BL) test is a diagnostic test employed to assess the adequacy of a time-series model. It is specifically conducted on the residuals obtained from fitting an autoregressive moving average (ARMA(p, q)) model to the data. The test evaluates the autocorrelations of the residuals at $m$ different lags. When the autocorrelation is minimal, we can infer that the model does not display a substantial lack of fit. In general, the Box–Ljung test is defined by a null hypothesis as the model does not exhibit a lack of fit. The test statistic is defined based on a given time series, denoted as $Y_t$ with a length of $n$:

$$Q=n(n+2){\sum }_{k=1}^m\frac{{\widehat{r}}_k^2}{n-k},$$

(4)

where ${\widehat{r}}_k^2$ at lag $k$ provides possible autocorrelation, with $m$ tested lags. The significance level is $\alpha$. If the model does not fit the BL requirements, the null hypothesis is rejected, if $Q>{\chi }_{1-\alpha ,h}^2$, where ${\chi }_{1-\alpha ,h}^2$ is the ${\chi }^2$ distribution table value with degrees of freedom $h$ and level of significance $\alpha$. To ensure that the test accounts for the estimated model parameters, the degrees of freedom should be adjusted accordingly when applying the test to residuals. Specifically, the degrees of freedom ($h$) are calculated as the difference between the number of residuals ($m$) and the total number of parameters ($p+q$):

$$h=m-p-q,$$

(5)

in the ARMA(p, q) model that fits the data.

5. Results

Empirical analysis utilises the return data of the stock exchange market index MONEX20, which is derived from the Montenegro Stock Exchange. The MONEX20 time series captures the price fluctuations of the most significant shares traded on the market segments of the working day exchange, considering a five-day week. The sample period spans from 5 January 2004 to 28 May 2018, encompassing a total of 3762 observations on the actual daily prices. It should be noted that the MONEX index has not reached the same high values observed in 2008, even up until the present day. As of 20 June 2023, the daily price stands at 14,979.78 points, which is significantly lower than the levels observed in 2007, when it reached almost 50,000 points (https://tradingeconomics.com/montenegro/stock-market, accessed on 22 June 2023). This disparity in performance underscores the need to consider the specific context and dynamics of the Montenegrin stock exchange market during different periods, such as the impact of the 2008 economic–financial crisis and subsequent market developments.

Therefore, it is important to clarify that this study does not incorporate the subsequent shocks and events that have occurred in the Montenegrin stock exchange market since 2018. This includes the stock exchange market rise in 2019, the impact of the COVID-19 pandemic, geopolitical conflicts, political and economic changes in Europe and worldwide, as well as any inflationary developments. While these are significant factors that have influenced the stock exchange markets, the focus of this study is specifically on the pre-pandemic period and the context of the 2008 economic–financial crisis, aiming to provide a comprehensive understanding of the stock exchange market dynamics within those specific timeframes.

The volatilities of movement of return on the stock exchange market index MONEX20 are tested with the ADF test. According to the results of the unit root test in

Table 1. ADF unit root test for series RTMONEX20.

ADF	$\mathit{t}$-Statistic −49.66226	Prob. 0.0001
Marginal values	at 1%	−2.565578
	at 5%	−1.940908
	at 10%	−1.616643

Note: ADF—augmented Dickey–Fuller test, t—Student t statistics, RT—a movement of return. Source: (Rupande et al. 2019); Author’s analysis.

where $H_0$ shows that RTMONEX20 has a unit root that shows that the time series RMONEX is stable. $H_0$ posits that the examined time series possesses a unit root, which can be rejected at a significance level of 0.01%. The historical prices of shares on the Montenegrin stock exchange exhibit predictability, suggesting that future prices can be anticipated based on past prices. To verify this conclusion, various methods such as the run test, Hurst exponent, and autocorrelation function were applied. The outcomes of these three methods are presented below. $H_0$, as defined by the run test, aims for the time series under analysis to follow the principles of the random walk theory.

The run test conducted in

Table 2. The run test of MONEX20.

${\mathit{n}}_1$	${\mathit{n}}_2$	$\mathit{N}$	$\mathit{R}$	$\mathit{E}\left(\mathit{R}\right)$	St.dev.	$\mathit{Z}$	$\mathit{Z}\left(0.05\right)$	$\mathit{Z}\left(0.01\right)$
1981	1778	3759	1665	1875.02	30.56185	−6.87	±1.96	±2.58

Note: $R$—observed number of runs; $N$—number of elements (time series); $E\left(R\right)$—the mean and the variance of the observed number of runs; $n_1$ and $n_2$—the number of positive and negative values in the series, respectively; and $Z$—one-sample location test. Source: (NIST/SEMATECH 2012); Author’s analysis.

revealed deviations from the patterns expected in the progress of the return on the MONEX20 stock exchange market index, contradicting the 4andom walk theory. These findings lead to the outcome that the capital market of Montenegro did not demonstrate weak-form efficiency during the period under analysis. To calculate the Hurst coefficient, subsamples of the stock exchange market index return (RTMONEX20) were used. The time series RTMONEX20 was divided into six subsamples of varying lengths. They are 3762, 1880, 752, 376, 80, and 40.

The value of the Hurst coefficient can be interpreted as the slope in regression analysis where $log\left(E\right[R/\sigma \left]\right)$ performs the conditional variable, and $log\left(N\right)$ is the independent one.

Table 3. The Hurst exponent.

$\mathit{N}$	$\mathit{E}[\mathit{R}/\mathit{\sigma }]$	$\mathit{l}\mathit{o}\mathit{g}\left(\mathit{N}\right)$	$\mathit{l}\mathit{o}\mathit{g}\left(\mathit{E}\right[\mathit{R}/\mathit{\sigma }\left]\right)$
40	7.43	1.60	0.87
80	28.99	1.90	1.46
376	33.20	2.58	1.52
752	30.33	2.88	1.48
1880	105.05	3.27	2.02
3762	221.85	3.58	2.35
		$\mathrm{H}$	0.61

Note: $\mathrm{H}$—generalised Hurst exponent; $\sigma$—standard deviation. Source: (Cannon et al. 1997); Author’s processing.

shows the Hurst coefficient, which is 0.61. These findings suggest that the return on the stock exchange MONEX20 can not conform to a random walk pattern, indicating persistence in the capital market of Montenegro.

The criterion defined the number of lags in which $\mathrm{t}$ is identical to $\sqrt{\mathrm{T}}$. One can say that $\mathrm{T}$ is the final count of observations in the time series RTMONEX20. According to $H_0$, an analysed time series is not stationary, characterising the autocorrelation function (AC(F)) and partial autocorrelation function (PAC(F)) values as equal to zero. To determine whether the autocorrelation coefficient is different from zero, the value of the autocorrelation coefficient for all lags is measured with a record at a 95% confidence interval: $\pm 1.96·1/\sqrt{\mathrm{T}}$. If the autocorrelation coefficient at specific lag deviates from the confidence interval, it is considered statistically significant, leading to the rejection of $H_0$, which states that the coefficient is zero. The total count of observations is $3762$, which is used to determine the lowest and highest restriction of the confidence interval: $\pm 1.96$·$\frac{1}{\sqrt{3762}}=\pm 0.032$.

A bit less than half of the ACF and PACF coefficients from

Table 4. Autocorrelations of MONEX20.

$\mathit{t}$	$\mathbf{A}\mathbf{C}\mathbf{F}$	$\mathbf{P}\mathbf{A}\mathbf{C}\mathbf{F}$	$\mathit{t}$	$\mathbf{A}\mathbf{C}\mathbf{F}$	$\mathbf{P}\mathbf{A}\mathbf{C}\mathbf{F}$
1	0.206	0.206	32	0.017	0.004
2	0.031	−0.012	33	0.037	0.030
3	0.030	0.028	34	0.033	0.015
4	0.069	0.061	35	0.017	−0.002
5	0.082	0.058	36	0.018	0.007
6	0.037	0.008	37	0.012	−0.002
7	0.034	0.023	38	0.029	0.018
8	0.048	0.033	39	0.072	0.053
9	0.053	0.030	40	0.034	0.002
10	0.047	0.024	41	0.015	0.005
11	0.029	0.010	42	0.000	−0.015
12	0.024	0.008	43	−0.014	−0.029
13	0.016	−0.001	44	0.020	0.014
14	0.058	0.046	45	0.048	0.036
15	0.083	0.057	46	−0.010	−0.032
16	0.061	0.028	47	−0.010	−0.014
17	0.011	−0.015	48	0.004	−0.006
18	−0.016	−0.028	49	0.004	−0.008
19	0.023	0.015	50	−0.014	−0.023
20	0.058	0.036	51	−0.003	0.006
21	0.006	−0.024	52	−0.043	−0.049
22	0.023	0.022	53	−0.018	−0.012
23	0.038	0.021	54	0.004	0.001
24	0.039	0.013	55	0.016	0.010
25	0.041	0.021	56	0.025	0.023
26	−0.002	−0.021	57	−0.011	−0.009
27	0.014	0.010	58	−0.008	−0.002
28	0.037	0.023	59	0.010	0.004
29	0.007	−0.020	60	0.031	0.026
30	0.006	−0.006	61	0.024	0.010
31	0.018	0.009

Note: PACF—partial autocorrelation function; ACF—autocorrelation function; and $t$—$i$ step of $h$ movements at lag $\rho$. Source: (Popović et al. 2012); Author’s processing.

are not statistically significant. The subsequent step in testing the joint hypothesis that all autocorrelation coefficients are equal to zero involves the Ljung–Box Q-statistics, of which the value is calculated as follows:

$$\widehat{\mathrm{Q}}=\mathrm{T}·{\sum }_{\mathrm{k}=1}^{61}{\mathsf{\rho }}_{\mathrm{k}}^2=3762·0.111874==420.87,$$

(6)

and the critical value of ${\chi }^2$ statistics with a 1% significance level is ${\chi }_{61;0.01}=89.591$. The Ljung–Box Q statistics provide evidence of dependence for the entire sample series, and the first 61 lags rejected $H_0$ at a 1% significance level.

In conclusion, the strong evidence of serial correlation observed in the ACF is further supported by the statistical findings of the Ljung–Box Q test. Its robustness lies in its ability to capture various forms of serial correlation, making it well suited for analysing the dynamic behaviour of stock exchange market returns. By incorporating the Ljung–Box Q test on the Montenegrin stock exchange market, a comprehensive understanding of its underlying dynamics and potential sources of serial correlation is obtained, leading to accurate modelling and proven investment strategies. Consequently, the null hypothesis of no serial correlation for the returns on the stock exchange market index MONEX20 is rejected. This ending is similar to some previous research on different stock exchange markets, which analyses the shocks on the market (Banz 1981; Gultekin and Gultekin 1983; Akerlof and Yellen 1985; Butler and Malaikah 1992; La Porta et al. 1997; Prorok and Radović 2014).

6. Discussion

This paper investigates the applicability of the random walk theory on the capital market in Montenegro with the obtained parametric and non-parametric tests. Characteristics of randomness do not exhibit in the studied country’s stock market. The used tests are the randomness test, stability test, persistence measure, and serial correlation test.

Based on the results of all the conducted tests, it can be concluded that the return time series in the capital market of Montenegro is abnormal. This implies that market participants have the potential to outperform the market and achieve increased profits.

The findings from neighbouring countries’ (Okičić 2015; Trivedi et al. 2021) analyses exhibit similar characteristics in their capital markets, suggesting that factors such as country size, economic development level, institutional quality, and the ongoing transition process play a crucial role. These findings highlight the importance of implementing institutional changes to enhance the functioning of capital and financial markets to foster a more efficient and effective investment environment. These findings were already studied in Japan by Takaishi (2022). Policymakers and relevant institutions are advised to focus on increasing transaction volume in the capital market, ensuring rigorous enforcement of laws and bylaws, and enhancing institutional quality. These measures will help reduce transaction costs. Some similar findings were found by Papavassiliou (2014) for Montenegro. The study highlights the existence of a long-term equilibrium between Montenegro and developed countries in Western Europe and the USA. The research reveals that Montenegro’s stock market operates autonomously, primarily influenced by domestic factors. This pioneering study sheds light on the neglected Montenegrin stock market and its potential integration with the EU. The findings hold significance for regulators and policymakers and offer broader insights applicable to other contexts.

The paper examines the Montenegrin stock market as an institution in the state of the financial market. Four methodological steps were applied to test the established null hypothesis that the random walk model weakly predicts the inefficiency of the emerging stock market. The data vector refers to the period from 5 January 2004 to 28 May 2018, which consists of 3762 observations. The time series of the Montenegrin Stock Exchange Index database for the Montenegrin stock market show price movements daily. The results of the tests show that there is no significance to support the random walk theory and its return to aggregate shocks on the Montenegrin stock market. The paper examines the empirical research that confirms the ideology of stochastic trends in co-movements in finance. Empirical settings on data and methodology are presented, and the last section provides the conclusions. The introduction introduces the reader to the context of the paper. This is the first study of the Montenegrin stock market based on daily returns, and its results are essential for a better understanding of less-developed stock markets.

The results are similar to the previous ones with different methods. The first article by Cerović Smolović et al. (2017) examines the use of GARCH models in measuring risk in the Montenegrin emerging market. The study finds that none of the eight models tested passed the Kupiec test with 95% confidence, except for one model at a 99% confidence level. Three models passed the Christoffersen test at a 95% confidence level, indicating their suitability for capturing volatility clustering. However, none of the analysed models passed Pearson’s Q test at various confidence levels. The second article by Sensoy (2013) examines the time-varying efficiency of nineteen members of the Federation of Euro-Asian Stock Exchanges (FEAS) using generalised Hurst exponent analysis. The study covers the period from January 2007 to December 2012. Results show varying degrees of long-range dependence among FEAS members. The study also highlights a strong positive relationship between efficiency and market liquidity, suggesting alternatives to enhance market efficiency.

From Appendix A, which includes a compilation of recent studies, it becomes evident that there is a dearth of research on the Montenegrin stock exchange market. This lack of attention to more recent developments in the stock exchange market underscores the importance and timeliness of this study in shedding light on the dynamics and efficiency of the Montenegrin stock exchange market. By filling this research gap, the study contributes to a more comprehensive understanding of the Montenegrin stock exchange market and provides insights into its behaviour with potential implications for investors and policymakers. According to Choijil et al. (2022), bibliometric studies have helped explore research trends in specific fields. Their study focused on herd behaviour in financial markets over 30 years using the Web of Science database. The results showed a significant increase in research on this topic, particularly after the subprime crisis. However, there is no consensus on the causes of herd behaviour, but new perspectives have emerged for further research. In another study by Economou et al. (2015), they examined fund managers in frontier markets, such as Bulgaria and Montenegro, to determine if they exhibit herding behaviour intentionally. Their findings revealed that herding is stronger during positive market performance and high volume, and in Montenegro, it is also significant during periods of low volatility. Bulgarian and Montenegrin fund managers clustered significantly before and after the 2008 global financial crisis. Additionally, Dalgıç et al. (2021) found that different types of investors tend to cluster in bear markets at a daily frequency, but herding behaviour disappears or even reverses at intraday frequency.

7. Conclusions

Based on the findings of this study, a direct investment idea could be to develop trading strategies that capitalise on the observed patterns and serial correlation in the Montenegrin stock exchange market. Since the stock exchange market exhibits deviations from the random walk theory and lacks weak-form efficiency, investors may have opportunities to generate abnormal profits by exploiting these predictable patterns.

In conclusion, the research findings indicate that the Montenegrin stock exchange market does not follow the random walk hypothesis, suggesting that it is not weak-form efficient. This implies that market participants may have the potential to outperform the market and achieve abnormal profits. Policymakers and relevant institutions are recommended to focus on increasing transaction volume, enforcing strict implementation of laws and regulations, and improving institutional quality to reduce transaction costs and enhance market efficiency.

7.1. Investment Strategies

One potential investment strategy could involve implementing a trend-following approach. By analysing the persistence and long-term trends identified through the Hurst coefficient, investors can identify stocks or assets that exhibit strong directional movements and align their trades accordingly. This strategy involves buying assets that show upward trends and selling those with downward trends, aiming to capture profits from continued price movements.

Another investment idea could be to utilise autocorrelation information to construct trading signals. By considering the significant autocorrelation coefficients identified in the study, investors can develop systematic trading rules that generate buy or sell signals based on the historical relationship between past and future prices. This approach leverages the predictability of market movements and can be implemented using technical analysis tools or quantitative models.

It is important to note that these investment strategies should be further evaluated and tailored to individual risk preferences, investment goals, and the specific characteristics of the Montenegrin stock exchange market. Additionally, investors should conduct thorough research, monitor market conditions, and apply risk-management strategies to mitigate potential risks associated with investing in any financial market. However, it is important to note that these findings are specific to the period analysed and may not necessarily extend to more recent events, such as the stock exchange market rise in 2019, the COVID-19 pandemic, and other economic and political changes. Therefore, additional research and analysis are needed to fully understand the implications of these recent shocks on the Montenegrin stock exchange market and their potential impact on investment strategies.

Overall, it would be beneficial to conduct comparative analysis across different periods to observe potential variations in the market efficiency of the studied stock exchanges. This could involve dividing the data into sub-periods based on significant events or changes in market conditions. By examining the efficiency of stock exchange markets before and after these events, we can gain further insights into the impact of external factors on market dynamics. Furthermore, conducting cross-country analysis by including additional emerging stock exchanges in the region would provide a broader perspective on the efficiency of emerging stock exchange markets in general. This comparative approach would contribute to a more comprehensive understanding of stock exchange market efficiency and its determinants in the studied regions.

7.2. Limitations and Delimitations of the Research

The limitation of this research is that it focuses specifically on the Montenegrin capital market, which may restrict the generalisability of the findings to other markets or regions. Additionally, the study’s timeframe and data sample size may limit the comprehensiveness of the analysis.

The delimitation of the research is that it primarily examines the weak form of efficiency and the random walk hypothesis in the Montenegrin capital market. Other forms of market efficiency, such as semi-strong and strong forms, are not explored in this study. Furthermore, the research does not consider external factors or macroeconomic variables that may influence stock market movements, which could be considered a delimitation.

7.3. Further Research Proposals and Implications of the Study

An alternative approach for further investigation would involve employing the vector autoregressive model to examine the relationship between the correlation matrix and data vector concerning other time-series variables explored in the literature review. This expanded analysis could encompass a comprehensive set of macroeconomic variables, such as interest rate spreads, inflation rate, GDP per capita, unemployment rate, cost/revenues ratio, and the availability of financing options for SMEs in terms of number and quantity.

For further research, it is proposed to employ the wild bootstrap automatic-variance-ratio test (WBAVR) as an additional methodological tool for analysing the Montenegrin stock exchange market. The WBAVR test is particularly useful in assessing the efficiency and randomness of stock exchange market returns, allowing for robust inference and accurate estimation of the variance ratio. By utilising the wild bootstrap technique, which addresses potential dependencies and heteroscedasticity in the data, the WBAVR test can provide more reliable and accurate results. Incorporating the WBAVR test in future research on the Montenegrin stock exchange market would enhance the analytical toolkit and contribute to a more comprehensive understanding of its dynamics, efficiency, and potential investment opportunities.

The policy implications of this study on the Montenegrin stock exchange may include strengthening market efficiency, enhancing institutional quality, promoting market development, strengthening investor protection, and collaborating with regional exchanges.

7.4. Conclusions in Brief

To sum up, the findings suggest that the Montenegrin stock exchange did not exhibit weak-form efficiency during the analysed period. Policymakers may consider implementing measures to enhance market efficiency. To decrease transaction costs and improve market functioning, policymakers should focus on improving institutional quality. Policymakers can encourage companies to list on the exchange by providing incentives, fostering entrepreneurship, and supporting initiatives that promote access to capital for businesses. Policymakers should focus on implementing and enforcing regulations that safeguard the rights of investors, ensuring proper disclosure practices, and establishing mechanisms for dispute resolution. Policymakers should explore opportunities for cross-border cooperation, information sharing, and harmonisation of regulatory frameworks. These policy implications aim to improve the functioning, efficiency, and attractiveness of the Montenegrin stock exchange, fostering sustainable economic-led tourism growth and development in the country.