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.

In situations that the predictors are correlated with the error term, we propose a bridge estimator in the two-stage least squares estimation. We apply this estimator to overcome the multicollinearity and sparsity of the explanatory variables, when the endogeneity problem is present.The proposed estimator was applied to modify the Durbin-Wu-Hausman (DWH) test of endogeneity in the presence of multicollinearity. To compare our modified test with the existing DWH for detection of an endogenous problem in multi-collinear data, some numerical assessments are carried out. The numerical results showed that the proposed estimators and the suggested test perform better for the multi-collinear data. Finally, a genetical data set is applied for illustration the our results by estimating the coefficients parameters in the presence of endogeneity and multicollinearity.