آیا بازار سهام ایران کارا است؟ آزمون‌ باقیمانده- محور هم‌انباشتگی با رویکرد بیزی جزیی

Introduction: After making economic theories, the main goal of researchers in economics is to measure economic relations more accurately. For this purpose, various methods are used in economics to provide a better insight into the functions of economics. The evolution of knowledge in different approaches and methods of measuring economic relations is, thus, happening very fast.
After the US withdrawal from the Barjam nuclear deal between Iran and the P5 + 1 countries in early 2018, relatively long turbulent waves occurred in the Iranian foreign exchange market. The overflow of these turbulent waves, in a short time, disturbed some markets, including financial markets, gold, currency and housing. The stock market, as a major financial market in Iran, did not show strong evidence of currency turbulence overflow at the beginning of these developments. Gradually, over time, the growth of the average stock market index along with the stagnation of transactions in a market such as the housing market showed the possibility of a long-term relationship between foreign exchange market movements and the stock market. The existence of empirical and accurate knowledge of such relationships leads to improved turbulence control by stabilizing the country's financial markets. On the other hand, the development of Iran's economy depends on improving the efficiency of financial markets, which necessitates such knowledge. The short-term relationship between the foreign exchange market and the stock market does not pose a problem in terms of financial theories. However, the long-run relationship, referred to in the economic literature as co-integration, is at odds with Market Efficient Hypothesis. This hypothesis states that dealers in the so-called markets behave rational and use all available information to discover the future trend of stock prices. Hence, stock price movement is random, and the long-term relationship between the foreign exchange market and the stock market violates the Efficient Market Hypothesis; such a relationship can be used for future stock market trends.
Methodology: In financial economics, the co-integration of non-stationery variables is very important. This is because, despite the unpredictability of certain time series, their linear composition is predictable and can be deduced through standard methods. The empirical results suggest that the relationship between the exchange market and the stock market is inconsistent. Various factors lead to such a contradiction addressed in the present study. Here, using some empirical facts about unconditional distribution of financial data, a new Bayesian Method which involves the Partial Bayesian Residual-based Test is introduced and applied. This approach was proposed as an alternative to classical testing methods so as to estimate long-term parameters. There are also alternative methods to the OLS method, which provides only one co-integration relationship. These alternatives offer a consistent and efficient estimate of the long-run relationship. In this case, we can refer to the Dynamic Ordinary Least Squares method (DOLS) and the Fully Modified Ordinary Least Squares method (FMOLS), which were proposed by Stock and Watson (1993) and Phillips and Hansen (1990), respectively. In the present investigation, the FMOLS method has been used to make an efficient estimate of the regression coefficients of the long-run relationship, Inder (1993) used Monte Carlo simulations to show that the estimation of the long-run relationship using the FMOLS method is more appropriate than the OLS method, especially in large samples. This is because the bias of the parameter estimation reduces in long-run relationship significantly. It leads to the creation of residuals that more accurately reflect the structure of their generating process, which is very effective in the performance of the Partial Bayesian Test used in this study; the financial data are not normally distributed, contrary to the classical approach of co-integration tests. This study uses a Residual-based Co-integration Test that explains the behavior of financial data more accurately than a normal distribution approach. It is worth mentioning that this test considers the mentioned test as a special case of normal distribution. In this respect, it has a more general preference for modeling in our investigation.
Results and Discussion: The test was conducted using simulated data in different simulation quantities for two processes. The results confirmed the existence of co-integration between these two processes. It is worth noting that, to estimate the posterior distribution of the parameters of a Bayesian model, it is necessary to calculate the Marginal Likelihood Function of the parameters obtained through integration. However, when the Bayesian model has no mixed-scale normal distributions based on that inference Bayesian model, the integral cannot solve the problem by using analytical methods. In this case, a method such as the MCMC (Markov Chain Monte Carlo) Simulation must be used. Since the correlation hypothesis test in this study was not a co-integrated vector, the MCMC method was used to estimate the real exchange rate and the stock price data. The test results obtained with the Partial Bayesian method show a positive long-run relationship between exchange rates and stock prices. The indication of a co-integration between the stock market and the foreign exchange market means that the future trends of the stock market in combination with the foreign exchange market are predictable.
Conclusion: Based on the results, the long-run relationship between the exchange rate and the stock price index is positive. It is indicated that a one-unit increase in the exchange rate will lead to a 2.5-unit increase in the stock price index. This means that a linear combination of stock prices with the exchange rate is predictable and, thus, contradictive of the Efficient Markets Hypothesis about the stock market in Iran. In other words, the Efficient Markets Hypothesis about the Iranian stock market is rejected.