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

The present research aims to test the weak-form efficiency of the French ETF market through a LSTAR model with ANSTGARCH errors, by using semiparametric maximum likelihood where the innovation distribution is replaced by a nonparametric estimate based on the kernel density function. 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, we show that the price fluctuations appear as the result of transitory shocks and the predictions provided by the LSTAR-ANLSTGARCH 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 a not weak form of an efficient market for the entire period because its successive return is nonlinearly dependent and does not generate randomly. bispectrum estimates by exploiting its asymptotic distribution. The numbers in the parenthesis are critical probabilities. 𝐹 𝑇𝑠𝑎𝑦4 is the Tsay Ori-F test for neglected non-linearities in an autoregression. We test more specifically against STAR using 4 lags.