The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison.

Giray Gozgor,Ahmet Faruk Aysan,Ibrahim Guney,Nicoleta Isac,Asad ul Islam Khan

doi:10.1371/journal.pone.0259994

Abstract

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

Highlights

The concept of cointegration was firstly proposed by [1]
The aim of this paper is twofold: comparison of tests on basis of the probability of Type I error, known as size of test using asymptotic critical values or distributions developed by the respective authors, controlling the probability of Type I error around the assumed nominal probability of Type I error and comparison of tests based on probability of Type II error when the probability of Type I error is controlled around a nominal level
Considering two different kinds of variables say Zt and Wit, 8 i = 1, 2, – –, k where both of these kinds of variables are integrated of order one i.e. I(1). [11] proposed the estimation of Ordinary Least Squares (OLS) regression first, i.e

Summary

Introduction

The concept of cointegration was firstly proposed by [1]. If two or more than two integrated of order one variables possess a long run relationship, it is termed as existence of cointegration among them. Soon after the development of concept of “cointegration”, a huge variety of tests were proposed to test it like [3,4,5] and many more Most of these tests proposed were testing the null of no cointegration. These tests have been widely and frequently used in economics and finance to assess the long run relationship between a set of time series. Some of these studies are but not limited to; [6,7,8,9,10]. In their pioneered paper, [11] proposed first test assessing the null of cointegration

Objectives

Methods

Conclusion