Model validity tests for non-linear signal processing applications

Abstract

Time series model validity tests based on general correlations are presented in this paper. It is shown that the tests Φ_{xi xi}(τ), Φ _{xi xi} ²(τ) and Φ _{xi xi xi}(τ₁, t₂) can only detect a subset of any possible unmodelled terms in the residuals, whereas Φ _{xi 2 xi 2}(τ) detects all possible terms. These basic results are then extended to include functions of process or residual terms as entries in the correlation. Simulation studies are included to demonstrate the effectiveness of the tests when applied to estimated models of both simulated and real data sequences.