ECONOMETRIC MODELS VERSUS DEEP LEARNING FOR STOCK RETURN FORECASTING: EVIDENCE FROM THE KAZAKHSTAN STOCK EXCHANGE

АННОТАЦИЯ

Целью исследовательской работы данной диссертации является сравнительная оценка моделей ARIMA, SARIMAX и LSTM для одношагового прогноза доходности семи акций, обращающихся на Казахстанской фондовой бирже (KASE) в период с 2020 по 2025 год. Методология включает walk-forward валидацию с разделением на тестовую и обучающую выборки в пропорциях 80:20 и девять технических индикаторов в качестве экзогенных регрессоров SARIMAX. Результаты показывают, что SARIMAX достигает наименьших RMSE и MAE для шести из семи активов и наивысшую направленческую точность (среднее DA=0,811) для всех семи. Тестом Диболда-Мариано подтверждается статистическое превосходство SARIMAX над LSTM (p<0,001). Выводы: эконометрические модели с экзогенными переменными формируют точные и легко интерпретируемые прогнозы в развивающихся рынках, где предоставлено очень ограниченное количество данных.

ABSTRACT

This research evaluates ARIMA, SARIMAX, and LSTM models for predicting one-step-ahead smoothed log-returns of seven stocks listed on the Kazakhstan Stock Exchange (KASE) over 2020-2025. The methodology employs walk-forward validation with an 80/20 split; SARIMAX model includes nine technical indicators as exogenous regressors. Results show that SARIMAX achieves the lowest RMSE and MAE for six of seven equities and the highest directional accuracy (mean DA = 0.811) for all seven. The Diebold-Mariano test validates the statistical advantage of SARIMAX compared to LSTM (p < 0.001). These results indicate that econometric models enhanced with structured exogenous variables deliver precise and comprehensible forecasts in data-limited emerging markets.

Ключевые слова: прогнозирование фондового рынка, ARIMA, SARIMAX, LSTM, направленческая точность, KASE, развивающиеся рынки.

Keywords: stock market forecasting, ARIMA, SARIMAX, LSTM, directional accuracy, KASE, emerging markets.

Введение

Forecasting equity returns remains one of the most challenging tasks in financial time-series analysis. Stock prices exhibit non-stationarity, volatility clustering, structural breaks, and characteristically low signal-to-noise ratios, all of which render accurate prediction exceptionally difficult [15]. Despite decades of research, no universally superior forecasting model has emerged-particularly for emerging markets, where lower liquidity, thinner order books, and idiosyncratic market microstructure further complicate the prediction problem [5], [12].

ARIMA models constitute the traditional baseline for financial time-series forecasting. However, their purely autoregressive structure constrains them to exploiting only the internal temporal dependence of the target series, potentially missing predictive signals embedded in complementary market indicators. In practice, equity returns are influenced by momentum, trend strength, volatility regimes, and trading activity-factors that can be quantified through well-established technical indicators and incorporated as exogenous regressors within the SARIMAX framework [21], [23].

Concurrently, deep learning architectures-particularly Long Short-Term Memory (LSTM) networks-have attracted substantial attention owing to their capacity to model complex nonlinear temporal dependencies [11], [20]. Nevertheless, the empirical evidence on their superiority over classical statistical models is mixed. Deep learning models typically require large datasets, substantial computational resources, and extensive hyperparameter tuning; in data-scarce environments, they may overfit or fail to generalize [12], [16]. Moreover, the majority of comparative studies focus exclusively on developed market equities, employ standard accuracy metrics without formal statistical testing, and neglect directional accuracy-a metric with direct relevance to trading signal generation.

A critical gap persists in the literature: few studies systematically compare econometric and deep learning models for emerging market equities under a consistent methodological framework that includes walk-forward validation, exogenous feature engineering, and rigorous statistical significance testing. In particular, the Kazakhstan Stock Exchange (KASE) has received virtually no attention in the forecasting competition literature, despite its growing importance as Central Asia’s principal equity market.

The goal of this study is to conduct a comprehensive comparative evaluation of ARIMA, SARIMAX, and LSTM for one-step-ahead prediction of smoothed log-returns for seven major KASE equities over the period 2020-2025. The specific objectives are: (1) to apply a strict walk-forward validation protocol with a time-ordered 80/20 split; (2) to evaluate forecasts using RMSE, MAE, and Directional Accuracy; (3) to test statistical significance via the Diebold-Mariano test. The following hypotheses are tested:

H1: The SARIMAX model achieves statistically significantly lower forecast errors (RMSE, MAE) than the ARIMA and LSTM models.

H2: The SARIMAX model demonstrates higher Directional Accuracy than the ARIMA and LSTM models across all examined equities.

H3: The observed performance differences between SARIMAX and LSTM are statistically significant as confirmed by the Diebold-Mariano test.

Financial time-series forecasting has evolved substantially over the past three decades. The earliest approaches relied on autoregressive stochastic processes-AR, ARMA, and ARIMA models [1], [21], [23]. However, financial time series frequently exhibit nonlinear dynamics, volatility clustering, and structural breaks [9], [15]. Nonlinear extensions have achieved improvements [5], [13], yet remain constrained by rapid regime transitions. Decomposition and hybrid models combining EMD with autoregressive components have outperformed standalone linear models [4], [6-7]. Machine learning algorithms-tree-based ensembles, boosting, and SVMs-have expanded the toolkit [2], [14], [16], though overfitting remains a concern [2], [7], [9], [15]. Deep learning, particularly LSTM networks, has been widely applied [3], [5], [8-10], but imposes substantial data and computational requirements that may not be met in emerging markets [12], [16]. This study addresses these gaps with a rigorous comparison under a unified walk-forward framework, focusing on KASE-an emerging market that has received negligible attention in the literature.

Materials and Methods

This study uses daily historical market data for seven equities listed on KASE: Air Astana (AIRA), Bank TsentrKredit (CCBN), Kaspi.kz (KSPI), Kazakhstanskaya Kompaniya (KEGC), Kazakhtelekom (KZTK), KazMunayGaz (KMGZ), and KazTransOil (KZTO). The sample period spans 2020-2025. Each dataset includes Date, Open, High, Low, Close, and Volume. After cleaning and feature construction, the final dataset comprises 8,090 observations. A time-ordered 80/20 split yields 1,620 out-of-sample test observations [5].

Table 1

Sample of raw KASE price data

Log-returns are computed as . The forecasting target is the three-period smoothed log-return  Nine technical indicators serve as exogenous features: log_return, SMA_5, SMA_10, EMA_10, volatility_10, RSI_14, MACD, MACD_signal, and Volume_change. Standardization uses a StandardScaler fitted on the training segment only.

Figure 1. Methodology Pipeline

ARIMA serves as the univariate baseline with order (2, 0, 4) selected via AIC grid search. SARIMAX extends ARIMA with the nine technical indicators as exogenous regressors (). The LSTM architecture consists of two stacked layers (64 and 32 units), Dropout (0.2), Adam optimizer (lr = 5×10⁻⁴), Huber loss (δ = 0.5), up to 50 epochs with early stopping (patience = 10), and a rolling window of w = 40 days.

A one-step-ahead walk-forward protocol is adopted: ARIMA and SARIMAX are refit at each step; LSTM is trained once. Performance is measured by RMSE, MAE, and Directional Accuracy (DA). The Diebold-Mariano (DM) test with Newey-West HAC standard errors and Harvey-Leybourne-Newbold correction tests statistical significance of forecast differences.

Results and Discussion

Tables 2 and 3 present out-of-sample RMSE and MAE. SARIMAX achieves the lowest values for six of seven equities; ARIMA ranks first only for CCBN. Mean RMSE: ARIMA 0.0233, SARIMAX 0.0168, LSTM 0.0347. Mean MAE: ARIMA 0.0147, SARIMAX 0.0116, LSTM 0.0252. SARIMAX reduces mean RMSE by 28% relative to ARIMA and 52% relative to LSTM.

Table 2.

Out-of-sample RMSE (one-step-ahead, walk-forward)

Table 3.

Out-of-sample MAE (one-step-ahead, walk-forward)

Figure 2. Actual vs Predicted Values for all seven KASE equities

Figure 3. Model Performance Metrics: RMSE, MAE, and Directional Accuracy

Table 4 presents Directional Accuracy. SARIMAX attains the highest DA for all seven equities (0.774-0.846). Mean DA: ARIMA 0.694, SARIMAX 0.811, LSTM 0.565. The SARIMAX mean DA of 0.811 indicates ~81% of next-day return signs are correctly predicted.

Table 4.

Directional Accuracy (DA)

Figure 4. RMSE Heatmap by Ticker and Model

Figure 5. Directional Accuracy Heatmap by Ticker and Model

The Diebold-Mariano test (Table 5) rejects equal predictive accuracy for all seven equities (p < 0.001). All DM statistics are negative (-9.679 to -5.167), confirming SARIMAX incurs lower squared-error loss than LSTM.

Table 5.

Diebold-Mariano test: SARIMAX vs. LSTM

SARIMAX surprasses ARIMA by using exogenous regressors to capture trend, momentum, volatility, and volume dynamics. The only exception is CCBN (SARIMAX RMSE 0.0525 vs. ARIMA 0.0521), which is probably due to extremely low liquidity. SARIMAX’s DA dominance (mean 0.811 vs. 0.565 for LSTM) indicates robust directional forecasting skill, while LSTM’s DA slightly exceeds the random baseline of 0.50.

Several factors explain LSTM’s underperformance: (1) limited data (~1,500 observations per equity); (2) non-stationarity and regime shifts including the COVID-19 disruption; (3) asymmetric retraining-econometric models are refit at each step while LSTM is trained once; (4) low signal-to-noise ratio in daily returns. These findings are consistent with the broader literature suggesting model complexity should match data volume [2], [8].

Limitations include: DM test applied only with squared-error loss; asymmetric retraining protocol favoring SARIMAX; absence of strict close-to-close temporal alignment; non-exhaustive LSTM hyperparameter search; and exclusion of macroeconomic variables and transaction costs.

Conclusion

This study demonstrates that SARIMAX achieves the best out-of-sample accuracy for six of seven KASE equities (H1), the highest directional accuracy for all seven (H2, mean DA = 0.811), and statistically significant superiority over LSTM confirmed by the Diebold-Mariano test for all equities at p < 0.001 (H3). Mean RMSE is reduced by 28% relative to ARIMA and 52% relative to LSTM.

The inclusion of structured exogenous regressors provides substantial incremental predictive value beyond univariate autoregressive models. From a practical standpoint, parsimonious econometric models augmented with technical indicators offer a viable, interpretable, and computationally efficient alternative to deep learning in data-constrained emerging markets.

Future research should implement expanding-window retraining for LSTM, systematic Bayesian hyperparameter optimization, strict close-to-close temporal alignment, macroeconomic and commodity feature expansion, and formal trading simulation with transaction costs and risk-adjusted returns.

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