Analysis of market efficiency and fractal feature of NASDAQ stock exchange: Time series modeling and forecasting of stock index using ARMA-GARCH model

Abstract The multi-fractal analysis has been applied to investigate various stylized facts of the financial market including market efficiency, financial crisis, risk evaluation and crash prediction. This paper examines the daily return series of stock index of NASDAQ stock exchange. Also, in this study, we test the efficient market hypothesis and fractal feature of NASDAQ stock exchange. In the previous studies, most of the technical analysis methods for stock market, including K-line chart, moving average, etc. have been used. These methods are generally based on statistical data, while the stock market is in fact a nonlinear and chaotic system which depends on political, economic and psychological factors. In this research we modeled daily stock index in NASDAQ stock exchange using ARMA-GARCH model from 2000 until the end of 2016. After running the model, we found the best model for time series of daily stock index. In next step, we forecasted stock index values for 2017 and our findings show that ARMA-GARCH model can forecast very well at the error level of 1%. Also, the result shows that a correlation exists between the stock price indexes over time scales and NASDAQ stock exchange is efficient market and non-fractal market.