Information quantity evaluation of nonlinear time series processes and applications

Among several models proposed in the time series literature, the Self-Exciting Threshold Autoregres-sive (SETAR) model is non-linear and considers threshold values to model time series affected by regimes. Beyond the linear models, the computation of information and dependence metrics in non-linear time series is of great interest to compare processes and test non-linearity. This paper considers the stationary marginal density of a SETAR(2;1,1) process to compute explicit differential entropy and Kullback-Leibler and Jeffrey's divergences. In addition, an asymptotic homogeneity test for statistical significance of the disparity between two SETAR(2;1,1) processes was built. Numerical illustrations and applications to fish condition factor and Chilean economic perception time series are presented to illustrate the proposed methodology. Besides, a numerical algorithm based on Riemann-Stieltjes integral definition is implemented to calculate information measures based on stationary cumulative density functions of other types of nonlinear stationary stochastic processes, such as the first-order double autoregressive bilinear threshold moving average and threshold autoregressive moving average processes.(c) 2022 Elsevier B.V. All rights reserved.