Fourier-type monitoring procedures for strict stationarity

TL;DR

This paper introduces new model-free, Fourier-based monitoring procedures using empirical characteristic functions to test for strict stationarity and detect breaks in financial time series.

Contribution

It develops novel L2-type statistics for stationarity testing that do not rely on specific model assumptions.

Findings

Asymptotic properties of the proposed tests are established.

Monte Carlo simulations demonstrate the effectiveness of the methods.

Applied to financial data, the procedures successfully identify stationarity breaks.

Abstract

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector.