We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an L2 space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.
- Diffusion process
- Goodness-of-fit test
- Nonlinear time series
- Weak convergence in Hilbert space
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty