Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Gaussian Approximation For Non-stationary Time Series with Optimal Rate and Explicit Construction (2408.02913v2)

Published 6 Aug 2024 in math.ST and stat.TH

Abstract: Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for non-stationary processes only provide an existential proof and thus they are difficult to apply. In this paper, we provide two clear paths to construct such a Gaussian approximation for non-stationary series. While the first one is theoretically more natural, the second one is practically implementable. Our Gaussian approximation results are applicable for a very large class of non-stationary time series, obtain optimal rates and yet have good applicability. Building on such approximations, we also show theoretical results for change-point detection and simultaneous inference in presence of non-stationary errors. Finally we substantiate our theoretical results with simulation studies and real data analysis.

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com