Short range vs long range dependence. An hyppothesis test based on Fractional Iterated Ornstein--Uhlenbeck processes

TL;DR

This paper introduces a new hypothesis test based on Fractional Iterated Ornstein-Uhlenbeck processes to distinguish short memory from long memory in time series, demonstrating superior performance in certain scenarios.

Contribution

The paper develops a novel hypothesis test leveraging Fractional Iterated Ornstein-Uhlenbeck processes to effectively differentiate short and long memory in time series data.

Findings

The new test outperforms existing tests under the null hypothesis.

It exhibits maximum power against specific alternatives.

The test is based on asymptotic properties of parameter estimators.

Abstract

In this work, which is based on the family of Fractional Iterated Ornstein Uhlenbeck processes, we propose a new hypothesis test to contrast short memory versus long memory in time series. This family includes short memory and long memory processes, and has the ability to approximate a long memory processes by a short memory processes. Based on the asymptotic results of the estimators of its parameters, we will present the test and show how it can be implemented. Also, we will show a comparison with other tests widely used under both short memory and long memory scenarios. The main conclusion is that this new test is the one with best performance under the null hypothesis, and has the maximum power in some alternatives.