Evaluating the Predictive Performance of the MIDAS Model for Weekly Returns on the Tehran Stock Exchange Overall Index Compared with Same-Frequency Models

Abstract

The main objective of this study is to compare the performance of mixed-data sampling regression and autoregressive distributed lag models in forecasting weekly returns on the Tehran Stock Exchange (TSE) overall index. Daily and weekly data on overall index returns, the exchange rate, the world gold price, and the world oil price were used for the period 2016–2025. Descriptive statistics and the Dickey–Fuller test were used to identify the statistical properties of the series, and the ARCH-LM test was used to examine heteroskedasticity. The GARCH(1,1) model was selected as the baseline specification for extracting the conditional variances of the exchange rate and gold prices. This choice was based on the principle of parsimony, the widespread use of this specification in modeling volatility clustering, and its ability to capture the effects of both new shocks and past volatility. After the presence of ARCH effects was confirmed, GARCH(1,1) models were estimated for the exchange rate and gold to extract their conditional volatility. Subsequently, a baseline MIDAS model, a MIDAS model incorporating conditional volatility, and a MIDAS model incorporating daily index returns were estimated, and their performance was compared with that of a same-frequency ARDL time-series model. The results showed that daily data exhibit greater volatility and information content than weekly data, while weekly aggregation smooths some short-term fluctuations. Stationarity tests indicated that index returns and conditional volatility are stationary, whereas the price levels of the exchange rate, gold, and oil are nonstationary. ARCH effects and volatility clustering were also confirmed in the foreign exchange and gold markets. The MIDAS estimates indicated that the exchange rate has a positive effect and the world gold price has a negative and statistically significant effect on weekly index returns. Adding the conditional volatility of the exchange rate and gold increased the coefficient of determination from .43 to .51 and reduced forecast errors. Furthermore, the final MIDAS model incorporating daily index returns achieved the best performance, with R^{2}=.58, an RMSE of 2.06, an MAE of 1.47, and a MAPE of 1.28%, whereas the corresponding error measures for the ARDL model were 2.94, 2.13, and 1.87, respectively. The Diebold–Mariano test also confirmed the statistically significant superiority of the MIDAS models over the same-frequency model and the advantages of their extended specifications. Overall, the findings indicate that, by retaining daily information, accounting for conditional volatility, and incorporating daily index returns, MIDAS provides a more accurate tool for forecasting weekly TSE returns than same-frequency time-series models.