High Persistence and Nonlinear Behavior in Financial Variables: A More Powerful Unit Root Testing in the ESTAR Framework

Tolga Omay,Esra Hasdemir,Aysegul Corakci

doi:10.3390/math9202534

Tolga Omay, Esra Hasdemir + Show 1 more

Open Access

https://doi.org/10.3390/math9202534

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Abstract

In this study, we consider the hybrid nonlinear features of the Exponential Smooth Transition Autoregressive-Fractional Fourier Function (ESTAR-FFF) form unit root test. As is well known, when developing a unit root test for the ESTAR model, linearization is performed by the Taylor approximation, and thereby the nuisance parameter problem is eliminated. Although this linearization process leads to a certain amount of information loss in the unit root testing equation, it also causes the resulting test to be more accessible and consistent. The method that we propose here contributes to the literature in three important ways. First, it reduces the information loss that arises due to the Taylor expansion. Second, the research to date has tended to misinterpret the Fourier function used with the Kapetanios, Shin and Snell (2003) (KSS) unit root test and considers it to capture multiple smooth transition structural breaks. The simulation studies that we carry out in this study clearly show that the Fourier function only restores the Taylor residuals of the ESTAR type function rather than accounting forthe smooth structural break. Third, the new nonlinear unit root test developed in this paper has very strong power in the highly persistent near unit root environment that the financial data exhibit. The application of the Kapetanios Shin Snell- Fractional Fourier (KSS-FF) test to ex-post real interest rates data of 11 OECD countries for country-specific sample periods shows that the new test catches nonlinear stationarity in many more countries than the KSS test itself.

Highlights

Stochastic properties of financial variables are examined in many studies
The main aim of this study is to introduce an alternative method to increase the power of the ESTAR type unit root test, which is based on using the fractional Fourier function
The main contribution of [11] to the literature is developing a new unit root test statistic designed to be more robust against stationary ESTAR processes

Summary

Introduction

Stochastic properties of financial variables are examined in many studies. Existing research has established that financial variables exhibit state-dependent nonlinearity and high persistence. KSS compute the first-order Taylor expansion of the ESTAR (1) function and obtain an auxiliary regression to test for the unit root null. [16] criticized [15] on the over filtration problem of the integer frequency Fourier function This over filtration problem may, in turn, cause misinterpretations about structural breaks and state-dependent nonlinearity. [15] utilizes the integer frequency Fourier function to test the structural break and state-dependent nonlinearity. [19] concludes that model misspecification disappears if fractional frequency Fourier function is used instead of the integer frequency Fourier function Another contribution of this study to the literature is obtaining the asymptotic distributions of the newly proposed test that prevents model misspecification. The KSS-FF test that we propose in this study can account for state-dependent nonlinearity and high persistence properties of financial data much better.

Theoretical Background

Small Sample Properties of the Proposed Tests

Limits of the Fourier Function in the Framework of the ESTAR Unit Root Test

Empirical Analysis

Conclusions