Quality & Quantity 37: 151–168, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Advances in the Analysis of Non-stationary Time
Series: An Illustration of Cointegration and Error
Correction Methods in Research on Crime and
and AUGUSTINE BRANNIGAN
Dept. of Sociology and Anthropology, Carleton University, 1125 Colonel by Drive, Ottawa,
Ontario, Canada K1S 5B6;
Dept. of Sociology, The University of Calgary, 2500 University Drive,
IV.W Calgary Alberta, Canada, T2N 1N4
Abstract. Time series data of interest to social scientists often have the property of random walks in
which the statistical properties of the series including means and variances vary over time. Such non-
stationary series are by deﬁnition unpredictable. Failure to meet the assumption of stationarity in the
process of analyzing time series variables may result in spurious and unreliable statistical inferences.
This paper outlines the problems of using non-stationary data in regression analysis and identiﬁes
innovative solutions developed recently in econometrics. Cointegration and error-correction models
have recently received positive attention as remedies to the problems of “spurious regression” arising
from non-stationary series. In this paper, we illustrate the relevant statistical concepts concerning
these methods by referring to similar concepts used in cross-sectional analysis. An historical example
is used to demonstrate how such techniques are applied. It illustrates that “foreign” immigrants to
Canada (1896–1940) experienced elevated levels of social control in areas of high police discretion.
“Foreign” immigration was unrelated to trends in serious crimes but closely related to vagrancy and
drunkenness. The merits of cointegration are compared to traditional approaches to the regression
analysis of time series.
Key words: time series, cointegration, error correction methods, non-stationary time series
In the past decade and a half, the use of regression analysis with time series vari-
ables has become increasingly important in historical criminology and sociology
(Allen and Campbell, 1994; Boritch and Hagan, 1987; Garnier et al., 1989; Gillis,
1989, 1994, 1996; Grant II, 1995; Neilsen and Alderson, 1995; Western, 1995;
Monkkonen, 1981; Lane, 1968, 1980). Prior to this, social scientists in historical
studies used little quantitative data in their research often because such data were
unavailable or because there was a resistance to statistical modelling by researchers
traditionally inclined to rely on non-quantitative archival documents (Stone, 1987).
One advantage of time series techniques over conventional cross-sectional analyses