Modeling Stock High-Low Price Range: Fractional Cointegrating VAR Approach (FCVAR)

Document Type : Research Paper

Author

Assistant Prof., Department of Economics and Social Sciences, Nahavand Higher Education Complex, Bu-Ali Sina University, Hamedan, Iran.

Abstract

Objective
This paper seeks to employ fractional cointegration methodology to model high and low stock prices, as well as the range series, indicating the difference between high and low stock prices. Additionally, it tries to examine the regime-switching characteristic in the cointegrating relationship between price series.
 
Methods
The study utilizes the Fractionally Cointegrated Vector Autoregressive (FCVAR) approach to explore the cointegrating relationships among six key indices of the Tehran Stock Exchange - TEPIX, First Market index, Second Market index, Industry index, Mali index, and Fara Bourse overall index - across various time frequencies from August 14, 2007, to August 15, 2022. To test for the fractional unit root in each price series, the GPH and ELW methods are also employed. Furthermore, the Qu (2011) method is employed to test the true long memory against spurious long memory on the range series. Finally, the threshold effect in the cointegrating relationship between the high and low price series is analyzed by the two regimes' Self-Exciting Threshold Autoregressive approach (SETAR).
 
Results
In most indices, the estimated fractional parameter of the range series is lower than that of the high and low stock price indices. Moreover, the high and low prices and the range series are affected by regime changes or a smoothly varying trend. The high and low stock price indices are fractionally cointegrated, in the two levels of stationary and non-stationary ranges. Further, the fractional cointegration approach gives a lower measure of dependency in price range series than the fractionally integrated approach. These findings are robust to different time frequencies, including daily, weekly, and monthly. Finally, the results affirm the time-varying cointegrating relationship between high and low stock prices. Thus, the FCVAR framework should be generalized to adjust according to this characteristic.
 
 
Conclusion
The empirical results show that, unlike the return, which is stationary and unpredictable, the range prices have characteristics of the long-memory processes, falling into non-stationary and stationary levels with mean-reverting behavior. Accordingly, one can obtain a non-stationary range-based volatility estimator, which is more efficient than a stationary return-based realized volatility estimator. These results imply that traders, investors, and policymakers could predict the future extreme prices of the market indices from past values and exploit such predictions to design investment strategies. The cointegration between high and low prices of indices implies limited arbitrage opportunities for the investors and traders in the Tehran Stock Exchange and Iran Fara Bourse Co. Furthermore, the efficiency of these markets is shown to be unstable across indices. Still, there are robust long-run relationships between the high and low stock price indices. Thus, to design hedge fund strategies containing combinations of the stocks from these markets, the behavior and long-run relations of the indices must be considered. Moreover, to design portfolio allocation and diversification strategies, one should mix assets that haven’t short-term behavior with indices that show long-term relationships. This conclusion is derived from the notion that mispricing and over-hedging may occur in the absence of cointegrating relationships between price series.

Keywords

Main Subjects

References

 
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Financial Research Journal
Volume 26, Issue 1
2024
Pages 159-184

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