Testing the functions defining a nonlinear autoregressive time series
The author considers a stationary random sequence \((X_ n\); \(n\geq 1)\), given by \[ X_{n+1}=T(X_ n)+U(X_ n)\epsilon_{n+1}, \] where T and U are real functions, \(U>0\), and \((\epsilon_ n\); \(n\geq 1)\) is a stationary \(\phi\)-mixing sequence with zero expectation and unit variance. Estimators of T and U of the regressogram type are defined and their consistency is proved. A functional limit theorem related to the estimators is derived. Nonparametric goodness-of-fit tests for T and U are presented. The results are illustrated by numerical simulation.
scientific article; zbMATH DE number 4155717
scientific article