Testing the weak form efficiency of the French ETF market with the LSTAR-ANLSTGARCH approach using a semiparametric estimation

Abstract

In this paper, we consider the daily Xtrackers CAC 40 UCITS from 2009 to 2020 for the analysis as it is supposed to capture more information compared to other French stock markets. After application of different statistical tests including BDS test, Hinich bispectrum test, Tsay test for linearity, long memory test and automatic serial correlation tests, we try to test the weak form efficiency of French ETF market through a logistic smooth transition AR model with nonlinear asymmetric logistic smooth transition GARCH errors using semiparametric maximum likelihood where the innovation distribution is replaced by a nonparametric estimate based on the kernel density function. After analyzing the forecasting results, we show that the price fluctuations appear as the result of transitory shocks and the predictions provided by the LSTAR-ANSTGARCH model are better than those of other models for some time horizons. The predictions from this model are also better than those of the random walk model; accordingly, the XCAC 40 price is not weak form of efficient market for the entire period because its successive return are nonlinearly dependent and doesn't generate randomly.