Estimating the Return Distribution of Tehran Stock Exchange Companies Using Random Matrix Approach for Taking Non-stationary into Account

To assess the financial market risks, the correlations between the prices of the individual stocks are of crucial importance. They change significantly in time due to trader's market expectation changes and the relation between business units' changes .This means the volatility of financial time series is non-stationary and fluctuate quickly. Non-stationary can lead many challenges for estimating the covariance estimation, which is main parameter in risk assessing. In addition, the impact of large event shows that we cannot easily assume normal distribution for financial time series especially when we observe large event frequently in the case of crises. In fact, non-stationary leads heavy tails distribution and this can affect the quantities we wish to measure. In this regard, we review the changes of covariance matrices of returns related to companies listed on the Tehran Stock Exchange during the period of 2011-2019 and obtain the multivariate distribution of returns, in terms of taking into account non-stationary and using the method of random matrices. The results show that the theoretical distribution obtained from the random matrix method with two approaches, heterogeneous and homogeneous covariance matrix, can well describe the experimental distribution of returns of Tehran Stock Exchange companies.