Nonparametric Statistical Inference for Ergodic Processes

TL;DR

This paper introduces nonparametric statistical tests for stationary ergodic processes, enabling reliable analysis of time series data for goodness-of-fit, classification, and change point detection without assuming specific data distributions.

Contribution

It develops asymptotically accurate tests for classical statistical problems using empirical distributional distance estimates under minimal ergodic assumptions.

Findings

Tests are asymptotically consistent for stationary ergodic processes.

Applicable to goodness-of-fit, classification, and change point problems.

Provides a nonparametric framework for time series analysis.

Abstract

In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, three problems are considered: goodness-of-fit (or identity) testing, process classification, and the change point problem. For each of the problems a test is constructed that is asymptotically accurate for the case when the data is generated by stationary ergodic processes. The tests are based on empirical estimates of distributional distance.