Mean and variance equation dynamics: Time deformation, GARCH, and a robust analysis of the London housing market

• DOI: http://doi.org/10.1002/ijfe.1589
• Date: 01 October 2017
• Author: Steve Cook,Duncan Watson
• Published date: 01 October 2017

Received: 17 September 2015 Revised: 15 March 2017 Accepted: 24 August 2017

DOI: 10.1002/ijfe.1589

RESEARCH ARTICLE

Mean and variance equation dynamics: Time deformation,

GARCH, and a robust analysis of the London housing market

Steve Cook1Duncan Watson2

1Accounting and Finance, Swansea

University, BayCampus, Swansea, SA1

8EN, UK

2Economics, University of East Anglia,

Norwich, UK

Correspondence

Steve Cook, Economics, University of

Wales Swansea,Singleton Park, Swansea

SA2 8PP,United Kingdom.

Email: s.cook@swan.ac.uk

Abstract

The potential relationship between time deformation and generalized autore-

gressive conditional heteroscedasticity (GARCH) is examined. Despite time

deformation and GARCH being mean and variance equation phenomena,

respectively, they are argued herein to share a common motivation relating to

the examination of changes in the temporal evolution of time-series processes.

Via extensive simulation analysis, a close connection between the two concepts

is established. It is found that the presence of GARCH can result in the spuri-

ous detection of time deformation, particularly when examining the heavy-tailed

distributions and volatile data typically considered in empirical finance. It is

shown that although the application of heteroskedasticity corrected covariance

matrix estimators often increases, rather than corrects, the detected oversizing

of the tests of time deformation, the application of GARCH filters does provide a

solution to size distortion. The findings of the experimental analysis are drawn

upon to provide a robust empirical examination of the London housing market

where evidence of overwhelming and widespread nonlinearity is detected in the

form of time deformation. The implications of these findings for the conduct of

future, and the interpretation of previous, research are discussed.

KEYWORDS

GARCH, house prices, nonlinearity, time deformation, volatility

1INTRODUCTION

Changes in the nature of the evolution of financial and

economic variables have long been of interest to empiri-

cists in both finance and economics. Following Engle

(1982), Bollerslev (1986), and Taylor (1986), the notions

autoregressive conditional heteroscedasticity (ARCH) and

generalized ARCH (GARCH) have come to occupy promi-

nent positions within finance as means of examining such

changes in the form of movements in the volatility of

a series. Within economics, consideration of changes in

the evolution of variables has often occurred in connec-

tion with the business cycle where a long history exists

depicting, typically, a contrast between the rapid move-

ment of series during cyclical downturns and their slow

steady growth during recovery periods (see Burns and

Mitchell, 1946; Hicks, 1950; and Keynes, 1936). A par-

ticular example of this form of analysis is provided by

the studies of Stock (1987, 1988) where the notion of

time deformation has been introduced to consider the

possibility that variables evolve on an operational time

scale rather than the calendar timescale from which

observations are drawn, thereby permitting the capture

of potentially differing speeds of evolution of a series

through time. The resulting diagnostic tests associated

with this concept consider the relationship between the

304 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/ijfe Int J Fin Econ. 2017;22:304–318.