The Effect of Tick Size on Testing for Nonlinearity in Financial Markets Data

Heather Mitchell,Michael Mckenzie

doi:10.4236/jmf.2011.11001

Abstract

The discrete nature of financial markets time-series data may prejudice the BDS and Close Returns test for nonlinearity. Our estimation results suggest that a tick/volatility ratio threshold exists, beyond which the test results are biased. Further, tick/volatility ratios that exceed these thresholds are frequently observed in financial markets data, which suggests that the results of the BDS and CR test must be interpreted with caution.

Highlights

A body of literature has evolved which considers the implications of discreteness for: 1) trading behaviour [1]; 2) technical trading strategies [2,3]; 3) model estimation [4,5]; and most importantly in the current context, 4) tests of the statistical properties of financial market data
Tick/volatility ratios that exceed these thresholds are frequently observed in financial markets data, which suggests that the results of the BDS and CR test must be interpreted with caution
For sample sizes of less than 500 observations a tick/volatility ratio equal to the test neighbourhood size marks a threshold beyond which the proportion of rejections of the null hypothesis for the BDS test declines

Summary

Introduction

A body of literature has evolved which considers the implications of discreteness for: 1) trading behaviour [1]; 2) technical trading strategies [2,3]; 3) model estimation [4,5]; and most importantly in the current context, 4) tests of the statistical properties of financial market data. Crack and Ledoit [9] discuss how the presence of the compass rose pattern may distort the null distribution for the Brock, Dechert and Scheinkman (BDS) test for nonlinearity. The purpose of this paper is to provide further evidence of the impact of discreteness on tests of the properties of financial markets data. The BDS test of Brock, Dechert and Scheinkman [11] and the Close Returns (CR hereafter) tests of nonlinearity are considered. The results suggest that both the CR and BDS test are sensitive to data discreteness, only in sample sizes of less than 500 observations for the latter

The BDS and Close Returns Test

Random Data and the BDS and Close Returns Test

Discrete Data and the BDS and Close Returns Test

Conclusions