Comparing the Intensity of Long-Memory Symmetry in the Returns of the Capital Market Index and Bahar Azadi Coin: An ARFIMA–FIGARCH Approach
Keywords:
Iranian financial markets, EGARCH, FIGARCH, ARFIMA, Long-term memoryAbstract
Objective: The study aims to compare the structure of long memory in the returns and volatility of the Tehran Stock Exchange Price Index (TEPIX) and the Bahar Azadi gold coin.
Methodology: Using daily data from December 2008 to September 2025, the study employs the ARFIMA model to analyze long memory in returns and the FIGARCH model to assess long memory in volatility. To capture asymmetric reactions to positive and negative news, the EGARCH model is estimated. Stationarity was evaluated using ADF and PP tests, and fractional differencing parameters (d) were computed to measure long-memory persistence in both markets.
Findings: The results indicate significant long-memory behavior in both markets’ returns and volatility; however, the long-memory intensity is stronger in the gold coin market. In the ARFIMA model, the fractional parameter d was 0.25 for TEPIX and 0.38 for the coin. In the FIGARCH model, d equaled 0.31 for TEPIX and 0.47 for the coin, implying more persistent volatility in the gold market. EGARCH estimation revealed a significant negative γ coefficient for the coin market, indicating stronger asymmetric reactions to negative shocks, whereas TEPIX exhibited relatively symmetric responses.
Conclusion: The findings confirm that the gold coin market retains the impact of past shocks more persistently than the stock market, with more pronounced asymmetric volatility reactions. These results highlight essential behavioral differences between the two markets and offer useful implications for risk management and investment strategy.
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