Estimation of a dynamic threshold panel time series regression with cross-sectional dependence - with Lulu Wang (Southampton) and Zudi Lu (Southampton)

The idea of dynamic threshold has been popular in nonlinear time series modelling. Although this idea has been extended to panel data analysis, it basically assumes a cross-sectional independence over the panel in the literature, which cannot facilitate, e.g., financial analysis of the impact of climate on the panel of stocks in a financial market. In this paper, we therefore propose a dynamic threshold panel time series regressive model which allows the panel data to be cross-sectionally dependent. To facilitate the inference, we have established the asymptotic distribution theory for the suggested least squares based estimators of the model parameters. Under the time series length T and cross-sectional size n tending to infinity, we show that the estimated coefficients are asymptotically normal with a convergence rate of root-nT, and its asymptotic variance matrix is derived in a form that is different from that under cross-sectional independence. The estimated threshold parameters are further shown to have a non-standard asymptotic distribution which allows the threshold effects diminishing at different rates in T and n. Monte Carlo simulations with different cases of fixed effects and dependencies demonstrate the finite sample performance of our estimators, which particularly display that the variances of our estimators would be significantly underestimated if the panel’s cross-sectional dependency was ignored or mistaken as cross-sectional independence. An empirical application to financial study of the effect of precipitation on the panel of stocks in the FTSE100 confirms that our methods offer a useful tool to facilitate a climate financial analysis.