Forecasting stock market movements has remained a central issue in financial economics due to its implications for investment decision-making, portfolio management, risk assessment, and financial market efficiency. In particular, the ability of time series models to extract predictive information from historical price movements continues to attract significant academic and practical attention. However, financial time series are characterized by non-stationarity, volatility clustering, structural fluctuations, and dynamic dependence patterns, making accurate forecasting inherently challenging.

The Efficient Market Hypothesis (EMH), introduced by Fama (1970), provides an important theoretical foundation for evaluating forecasting performance in financial markets. Under weak-form efficiency, current asset prices fully incorporate all historical price information, implying that future price movements cannot be systematically predicted using past prices alone. Consequently, if sophisticated forecasting models fail to generate economically meaningful improvements over a naïve random walk benchmark, the findings may be interpreted as evidence broadly consistent with weakform market efficiency. Despite these theoretical implications, empirical studies have reported mixed evidence regarding stock market predictability, particularly in emerging markets where information inefficiencies, lower market depth, and evolving institutional structures may create temporary forecasting opportunities. In this context, time series econometric models such as the Autoregressive Positive Science -Economics Integrated Moving Average (ARIMA) and Seasonal ARIMA (SARIMA) frameworks have been widely employed to model and forecast stock market indices. The Box-Jenkins methodology developed by Box (1970), remains one of the most widely applied approaches for capturing linear dependence structures in financial time series data.

The Nepal Stock Exchange (NEPSE), the sole organized securities exchange in Nepal, has experienced substantial structural and behavioral change in recent years. The market has witnessed increased investor participation, expansion of the dematerialized trading system, rapid growth in trading volume, and heightened market volatility. Such developments have intensified interest in understanding the statistical behavior and forecasting dynamics of the NEPSE index. At the same time, the Nepalese stock market remains relatively underexplored in empirical financial econometrics compared to more developed financial markets.

Previous studies on NEPSE forecasting have primarily focused on the application of ARIMAtype models to evaluate short-term predictive performance (Gaire, 2017). Existing literature has also documented the presence of volatility clustering and conditional heteroskedasticity within the Nepalese stock market (G.C., 2009). However, several important limitations remain in the current body of research. First, prior studies have largely emphasized in-sample model fit rather than rigorous out-of-sample forecasting evaluation. Second, relatively limited attention has been paid to rollingwindow forecasting procedures, which have not been systematically compared against a naïve random walk benchmark in terms of forecasting performance within the framework of weak-form market efficiency.

Accordingly, the present study seeks to address these gaps by applying ARIMA/SARIMAbased forecasting techniques to the daily NEPSE closing index using recent market data covering the period from 2001 to 2006. The study employs a rolling-window out-of-sample forecasting framework and evaluates predictive performance relative to a naïve random walk benchmark using standard forecast accuracy measures. In addition, the findings are interpreted within the context of weak-form market efficiency to assess whether historical price information provides a meaningful predictive advantage.

The contribution of this study is threefold. First, it provides updated empirical evidence on NEPSE forecasting using recent post-pandemic market data. Second, it adopts a rolling-window forecasting framework that improves methodological rigor and reduces look-ahead bias relative to conventional in-sample evaluation. Thirdly, the study links forecasting performance with market efficiency interpretations by comparing SARIMA forecasts against a naïve benchmark model.

The Efficient Market Hypothesis (EMH), proposed by Eugene F. Fama, remains one of the foundational theories in financial economics. According to the weak-form version of the hypothesis, current asset prices fully reflect all historical market information, implying that future price movements cannot be systematically predicted using past price behavior alone. Under such conditions, forecasting models based solely on historical prices are expected to generate only limited predictive superiority over naïve benchmark models (Fama, 1970) The random walk theory further supports this perspective by suggesting that stock price changes follow an unpredictable stochastic process in which successive movements are largely independent over time. Consequently, future market behavior should not be consistently forecasted through historical price analysis alone. However, subsequent empirical evidence has challenged the strict assumption of random walk behavior. Lo and MacKinlay (1998) documented serial dependence in stock returns, providing evidence against pure random walk behavior in financial markets. Similarly, Jegadeesh and Titman (1993) identified momentum effects in stock returns, suggesting that certain short-term price continuation patterns may exist within financial markets. Despite these findings, the predictive forecasting value of historical price information remains highly debated. Malkiel (2003) argued that although markets may not be perfectly efficient, achieving economically meaningful and consistently exploitable forecasting gains remains extremely difficult in practice. Brown (2020) further emphasized that the Efficient Market Hypothesis continues to play a central role in understanding investment behavior, market efficiency, and financial forecasting limitations.

The debate surrounding market predictability is particularly relevant in the context of emerging financial markets, where information inefficiencies, lower market depth, and evolving institutional structures may create temporary forecasting opportunities. Nevertheless, even in such markets, forecasting superiority over naïve benchmark models frequently remains economically limited, reinforcing the continuing relevance of weak-form efficiency arguments.

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Time series econometric models have been widely applied in financial forecasting due to their ability to capture temporal dependence structures in sequential data. Among these approaches, the Box-Jenkins ARIMA framework developed by Box (1970) remains one of the most extensively used methodologies for modeling and forecasting non-stationary financial time series. ARIMA models combine autoregressive and moving average processes with different differencing procedures to capture underlying stochastic structures and generate short-term forecasts.

Financial time series, however, it exhibits several complex statistical properties that complicate forecasting performance. These characteristics include non-stationarity, volatility clustering, structural fluctuations, and time-varying variance. Such features often reduce the stability and forecasting accuracy of traditional linear models. Mandelbrot (1963) highlighted that speculative price movements frequently display irregular fluctuations and non-normal behavior, challenging conventional assumptions regarding financial data.

To address volatility behavior in the financial market, Engle (1982) introduced the Autoregressive Conditional Heteroskedasticity (ARCH) framework, which models time-varying variance in financial series. Subsequent developments by Bollerslev et al. (1992) further emphasized the importance of volatility modeling in financial econometrics and demonstrated that financial series commonly exhibit volatility clustering and conditional heteroskedasticity. These findings imply that while ARIMA-type models may adequately capture mean dynamics, volatility processes often remain incompletely modeled within simple linear forecasting frameworks.

Hence, forecasting stock market behavior remains inherently challenging. Even when econometric models identify short-term dependence structures, the presence of volatility persistence and rapidly changing market conditions often limits the economic significance of forecasting improvements.

ARIMA and SARIMA models have been extensively applied in stock market forecasting across both developed and emerging financial markets. Numerous studies report that ARIMA-type models are capable of capturing short-term linear dependence structures and producing relatively accurate short-horizon forecasts. These models are particularly useful in financial series exhibiting recurring trading patterns and periodic structures.

Nevertheless, empirical evidence regarding the forecasting superiority of ARIMA-based models remains mixed. While several studies report improvements in forecast accuracy relative to simple benchmark models, others conclude that the forecasting gains are often economically modest and inconsistent across different evaluation measures. This inconsistency has contributed to ongoing debates regarding the practical usefulness of time series forecasting models in financial markets.

Recent forecasting literature increasingly emphasizes the importance of out-of-sample evaluation and rolling-window forecasting procedures for obtaining a realistic predictive assessment. Bergmeir et al. (2018) argued that appropriate forecasting validation frameworks are essential for avoiding overfitting and obtaining reliable predictive evaluations in autoregressive time series models.

Rolling-window forecasting procedures are therefore considered methodologically superior to purely in-sample evaluation because they better approximate a real-world forecasting environment and reduce look-ahead bias.

In addition to statistical forecasting accuracy, several researchers emphasize the importance of evaluating whether predictive improvements are economically meaningful. Leitch and Tanner (1991) argued that conventional forecast error measures alone may not fully capture the practical usefulness of forecasting models in financial decision-making. These developments suggest that forecasting evaluation should not focus solely on statistical fit, but also on whether forecasting models meaningfully outperform naïve benchmark specifications under realistic out-of-sample conditions.

Empirical evidence from emerging stock markets suggests that forecasting behavior may differ from that observed in highly developed financial markets due to lower informational efficiency, evolving regulatory systems, and changing investor behavior. Emerging markets frequently exhibit greater volatility, speculative trading activity, and temporary market inefficiencies, which may create limited short-term forecasting opportunities.

However, several studies also report that although forecasting models may capture short-run dependence structures within emerging markets, forecasting improvements over naïve benchmark models often remain economically limited. Such findings imply that even in relatively less efficient markets, consistently outperforming random walk benchmarks remains difficult. Overall, the existing literature suggests that although ARIMA-type models may capture certain short-term dependence structures within the NEPSE index, the broader question of whether such models generate economically meaningful forecasting superiority relative to naïve benchmark models remains insufficiently explored. Compared with lower-frequency observation, daily data provides greater sensitivity to short-term market dynamics and improves the ability of time series models to capture temporal dependence structures.

The NEPSE index was selected due to its importance as the benchmark indicator of Nepal's capital market performance. In recent years, the Nepalese market has experienced substantial fluctuations, increased investor participation, and rapid changes in market activity, making it an appropriate context for evaluating forecasting performance and market efficiency.

The study adopts a quantitative time series econometric research design to examine the forecasting behavior of the NEPSE index and evaluate whether historical price information contains meaningful predictive value. The analysis is conducted within the theoretical framework of the Efficient Market Hypothesis (EMH), particularly weak-form efficiency, which suggests that the current market price fully reflects past price information.

Under weak-form efficiency, future price movements should not be systematically predictable using historical market data alone. Consequently, the forecasting performance of the SARIMA Model is evaluated relative to a naïve random walk benchmark economically limited relative to the benchmark; the findings may be interpreted as broadly consistent with weak-form market efficiency.

The empirical framework of the study consists of the following stages: i.

Descriptive statistical analysis of the NEPSE index,

ii.

Stationarity testing using the Augmented Dickey-Fuller (ADF) test, iii.

Model identification using autocorrelation and partial autocorrelation analysis, iv.

Estimation of ARIMA/SARIMA models, v.

Residual diagnostic testing, vi.

Rolling-window out-of-sample forecasting, vii.

Comparative forecast evaluation against a naïve random walk benchmark.

The study applies the Box-Jenkins time series methodology to model the behavior of the NEPSE index using ARIMA and SARIMA specifications. The general ARIMA framework is represented as:

Where, P = Autoregressive Order, d = Degree if differencing is required for stationarity, q = Moving Average Order.

Because stock market series may exhibit recurring short-term trading patterns, seasonal components were additionally considered through the Seasonal ARIMA Framework:

Where,

This inclusion of seasonal structure is economically meaningful in the context of the NEPSE Index due to the five-day weekly trading cycle of the Nepalese stock market.

Stationarity is a fundamental requirement in ARIMA-based time series modeling because nonstationary series may produce misleading statistical inferences and unstable forecasting performance.

To evaluate the stationarity properties of the NEPSE index, the Augmented Dickey-Fuller (ADF) unit root test was employed.

The null hypothesis of the ADF test states that the series contains a unit root and is therefore non-stationary, while the alternative hypothesis suggests stationarity. Where necessary, differencing procedures hypothesis suggests stationarity. Where necessary, differencing procedures were applied to transform the series into a stationary process before model estimation.

Model identification was conducted using a combination of graphical diagnostics and information criteria. The autocorrelation function (ACF) and partial autocorrelation function (PACF)

plots were analyzed to identify potential autoregressive and moving average structures.

The auto. arima () procedure in R was employed to estimate competing ARIMA and SARIMA specifications. Model selection was based primarily on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), where lower values indicate comparatively superior model fit while maintaining model.

In addition to information criteria, residual diagnostic performance and forecasting behavior were considered during final model selection. Seasonal components were evaluated using a five-day seasonal structure corresponding to the weekly trading cycle of the Nepal Stock Exchange.

Following model estimation, diagnostic tests were conducted to evaluate the adequacy of the fitted SARIMA specification.

The Ljung-Box test was employed to assess the presence of residual autocorrelation. The null hypothesis of the test states that the residuals are independently distributed and exhibit no serial correlation. Failure to reject the null hypothesis suggests that the model adequately captured the linear dependency structure of the series.

In addition, the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test was applied to examine whether the residuals exhibit time-varying volatility. Significant ARCH effects indicate the presence of conditional heteroskedasticity and suggest that volatility dynamics remain unmodeled within the conditional mean specification.

To evaluate forecasting performance under realistic market conditions, the study employs a rolling-window out-of-sample forecasting framework. This approach is better because it better approximates real-world forecasting environments and reduces look-ahead bias.

The forecasting exercise was conducted using a 120-day rolling forecast horizon. An initial estimation sample was first used to estimate the SARIMA model, after which one-step-ahead forecasts were recursively generated for the subsequent trading observation. Following each forecast iteration, the estimation window was expanded by one observation, and the model was re-estimated using the updated information set.

Forecast performance was then compared with a naïve random walk benchmark model, where the forecasted value for the next trading day equals the current observed value of the index. The naïve benchmark serves as an important reference model within the framework of weak-form market efficiency because it represents the hypothesis that future price movements cannot be systematically predicted from historical information.

Forecasting accuracy was evaluated using three commonly applied statistical performance Comparative evaluation of these measures between the SARIMA model and the naïve random walk benchmark provides insight into whether the SARIMA specification generates economically meaningful predictive improvement.

Descriptive The standard deviation of 370.431 indicates considerable variability in the index movements over the sample period, reflecting the volatile nature of the Nepalese stock market. Similarly, the coefficient of variation of 15.468% suggests moderate relative dispersion in the index values.

The Jarque-Bera statistic of 100.721 with a p-value below 0.05, indicates the rejection of the null hypothesis of normal distribution. These findings suggest that the NEPSE index series does not follow a normal distribution and exhibits characteristics commonly observed in financial time series data. Such behavior is consistent with the findings of Mandelbrot (1963), who argued that financial market series frequently display irregular fluctuations and non-normal distributional properties. Table 2 presents the descriptive statistics of NEPSE log returns, indicating a mean daily return of 0.000129 and a standard deviation of 0.0138, suggesting relatively small average returns with a noticeable short-term volatility. The return distribution exhibits positive skewness of 0.490, indicating a slight asymmetry toward positive returns. Similarly, the kurtosis value of 5.047 exceeds the normal benchmark value of 3, implying leptokurtic behavior and the presence of heavier tails in the distribution.

These findings indicate that the NEPSE return series does not follow a normal distribution and exhibits characteristics commonly observed in financial time series data (Mandelbrot, 1963).

Augmented Dickey Fuller (ADF) Test

Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) Similarly, the PACF plot displayed several significant spikes at lower lags, indicating the possible presence of autoregressive components in the series. In addition, repeating lag patterns around the five-trading-day interval suggested the existence of weekly seasonal dependence within the NEPSE index. 5 reports that based on the model identification process, SARIMA (3,1,0) (2,0,0) [5] was selected as the final forecasting specification. The model incorporates both non-seasonal autoregressive terms and seasonal autoregressive components with a five-day trading cycle.

The estimated coefficients indicate the presence of short-term dependence within the NEPSE index series. Among the estimated parameters, the non-seasonal autoregressive terms demonstrated relatively stronger contributions to the model, while the seasonal autoregressive components exhibited comparatively smaller effects. In particular, the first seasonal autoregressive coefficient was relatively weak compared to its standard error, suggesting limited seasonal influence at that lag.

The selected model produced an AIC value of 11397.15 and a BIC value of 11427.47, indicating an acceptable balance between model fit and parsimony. Overall, the SARIMA specification was considered appropriate for capturing the short-term and seasonal dynamics present in the NEPSE index series.

This study examined the forecasting performance of the NEPSE daily closing index using an ARIMA/SARIMA-based time series framework and evaluated the predictive capability of the selected model against a naïve random walk benchmark. The empirical analysis identified SARIMA (3,1,0)

(2,0,0) [5] as the most suitable forecasting specification based on stationarity transformation, seasonal structure, model selection criteria, and diagnostic adequacy.

The rolling-window forecasting evaluation revealed that the SARIMA model generated only marginal improvements over the naïve benchmark across the forecasting error measures. Although the model demonstrated limited short-term predictive capability, the forecasting gains remained economically modest. Consequently, the findings are broadly consistent with weak-form market efficiency, where historical price information provides limited forecasting advantage.

The study further identified the presence of remaining volatility clustering within the residual series, indicating that future studies may benefit from integrating ARIMA/SARIMA models with GARCH-type volatility frameworks for improved modeling of market variance behavior.

Overall, the study contributes to the growing literature on NEPSE forecasting by applying rolling-window out-of-sample forecasting and benchmark comparison within a seasonal time series framework. The findings provide useful insights into the forecasting behavior of the Nepalese stock market and may serve as a foundation for future forecasting and volatility modeling research.