Working Paper BETA #2019-06

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Title : Testing Nonlinearity through a Logistic Smooth Transition AR Model with Logistic Smooth Transition GARCH Errors

Author(s) : Mohamed Chikhi, Claude Diebolt

Abstract : This paper analyzes the cyclical behavior of CAC 40 by testing the existence of nonlinearity through a logistic smooth transition AR model with logistic smooth transition GARCH errors. We study the daily returns of CAC 40 from 1990 to 2018. We estimate several models using nonparametric maximum likelihood, where the innovation distribution is replaced by a nonparametric estimate for the density function. We find that the rate of transition and the threshold value in both the conditional mean and conditional variance are highly significant. The forecasting results show that the informational shocks have transitory effects on returns and volatility and confirm nonlinearity.

Key-words : LSTAR model, LSTGARCH model, nonparametric maximum likelihood, nonlinearity, informational shocks, time series analysis.

JEL Classification : C14, C22, C58, G17.