Evaluating the Performance of Unit Root Tests in Single Time Series Processes

Sampson Twumasi-Ankrah,Jonathan Kwaku Afriyie,Doris Arthur,Kwasi Baah Gyamfi,Wilhemina Adoma Pels

doi:10.13189/ms.2020.080605

Abstract

Unit root tests for stationarity have relevancy in almost every practical time series analysis. Deciding on which unit root test to use is a topic of active interest. In this study, we compare the performance of the three commonly used unit root tests (i.e., Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski Phillips Schmidt and Shin (KPSS)) in time series. Based on literature, these unit root tests sometimes disagree in selecting the appropriate order of integration for a given series. Therefore, the decision to use a unit root test relies essentially on the judgment of the researcher. Suppose we wish to annul the subjective decision. In that case, we have to locate an objective basis that unmistakably characterizes which test is the most appropriate for a particular time series type. Thus, this study seeks to unravel this problem by providing a guide on which unit root tests to utilize when there is a disagreement between them. A simulation study of eight (8) univariate time series models with eight (8) different sample sizes, three (3) differencing orders, and nine different parameter values were performed. It was observed from the results that the performance of the three tests improved as the sample size increased. Based on comparing the overall performance, the KPSS was the

Highlights

A time series is a sequence of ordered data from a family of random variables, say ... , xt−1, xt, xt+1 Tebbs [1].Time series modeling aims to study past observations of a series to develop an appropriate model that explains the series Adhikari [2]
Kwiatkowski Phillips Schmidt and Shin (KPSS) test is broadly utilized in empirical work as an accompaniment to standard unit root tests Hadri[12], and it is not affected by seasonal dummies Phillips[13]
The results from the simulation study are presented in terms of the performance of the individual tests in selecting the appropriate order of integration, the effect of the order of the model on the three conventional unit root tests, the impact of sample size on the three unit root tests, and the overall performance of the unit root tests

Summary

Introduction

A time series is a sequence of ordered data from a family of random variables, say ... , xt−1 , xt , xt+1 Tebbs [1].Time series modeling aims to study past observations of a series to develop an appropriate model that explains the series Adhikari [2]. A time series is a sequence of ordered data from a family of random variables, say ... A time series process is said to be weak stationary if its mean, variance, and covariance do not change over time Test [3]. A time series is characterized as integrated of order (d) if their stationarity is achieved by differencing the series "d times" Fedorov'a [4]. The importance of stationarity cannot be underestimated since many statistical tests and forecasts in time series depend on it. It is necessary to ensure that a time series data is stationary before building a model. Non-stationary time series exhibits trends, seasonal variations from which these models' forecasts are not reliable Twumasi-Ankrah [5]

Methods

Results

Conclusion