IID Time Series Testing

TL;DR

This paper introduces a comprehensive omnibus test for identifying i.i.d. properties in time series, including heteroscedastic data, and provides a flexible framework for developing various i.i.d. tests.

Contribution

It presents a novel omnibus testing framework that combines multiple tests for i.i.d. properties, extending beyond traditional autocorrelation-based methods.

Findings

The omnibus test effectively detects heteroscedasticity in simulated data.

The framework allows for creating diverse i.i.d. tests tailored to different data characteristics.

Application to simulated data demonstrates the test's robustness and versatility.

Abstract

Traditional white noise testing, for example the Ljung-Box test, studies only the autocorrelation function (ACF). Time series can be heteroscedastic and therefore not i.i.d. but still white noise (that is, with zero ACF). An example of heteroscedasticity is financial time series: times of high variance (financial crises) can alternate with times of low variance (calm times). Here, absolute values of time series terms are not white noise. We could test for white noise separately for original and absolute values, for example using Ljung-Box tests for both. In this article, we create an omnibus test which combines these two tests. Moreover, we create a general framework to create various i.i.d. tests. We apply tests to simulated data, both autoregressive linear and heteroscedastic.