Compounding approach for univariate time series with non-stationary variances

TL;DR

This paper investigates a compounding approach to model the long-term statistical behavior of non-stationary univariate time series with changing variances, exemplified by turbulent airflow and foreign exchange rates.

Contribution

It empirically determines the parameter distribution for the compounding method in highly non-stationary univariate time series.

Findings

Identified appropriate parameter distributions for non-stationary systems

Applied the approach to turbulent airflow and forex data

Demonstrated the effectiveness of compounding in modeling non-stationary variance

Abstract

A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model the long-term statistical behavior, we compound the local distribution with the distribution of its parameters. Here we consider two concrete, but diverse examples of such non-stationary systems, the turbulent air flow of a fan and a time series of foreign exchange rates. Our main focus is to empirically determine the appropriate parameter distribution for the compounding approach. To this end we have to estimate the parameter distribution for univariate time series in a highly non-stationary situation.