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Applied Time Series Modelling and Forecasting


Applied Time Series Modelling and Forecasting provides a relatively non-technical introduction to applied time series econometrics and forecasting involving non-stationary data. The emphasis is very much on the why and how and, as much as possible, the authors confine technical material to boxes or point to the relevant sources for more detailed information.

This book is based on an earlier title Using Cointegration Analysis in Econometric Modelling by Richard Harris. As well as updating material covered in the earlier book, there are two major additions involving panel tests for unit roots and cointegration and forecasting of financial time series. Harris and Sollis have also incorporated as many of the latest techniques in the area as possible including: testing for periodic integration and cointegration; GLS detrending when testing for unit roots; structural breaks and season unit root testing; testing for cointegration with a structural break; asymmetric tests for cointegration; testing for super-exogeniety; seasonal cointegration in multivariate models; and approaches to structural macroeconomic modelling. In addition, the discussion of certain topics, such as testing for unique vectors, has been simplified.

Applied Time Series Modelling and Forecasting has been written for students taking courses in financial economics and forecasting, applied time series, and econometrics at advanced undergraduate and postgraduate levels. It will also be useful for practitioners who wish to understand the application of time series modelling e.g. financial brokers.

Data sets and econometric code for implementing some of the more recent procedures covered in the book can be found on the following web site

Richard Harris is a Professor in the Department of Economics and Finance at the University of Durham. His areas of research are in the field of applied econometrics and he has published widely in numerous journals.

Robert Sollis is a Lecturer in the Department of Economics and Finance at the University of Durham. His research interests are in time series econometrics with particular focus on nonlinear models for macroeconomic and financial time series.


1. Introduction and Overview.

Some Initial Concepts.


Outline of the Book.

2. Short- and Long-run Models.

Long-run Models.

Stationary and Non-stationary Time Series.

Spurious Regressions.


Short-run Models.


3. Testing for Unit Roots.

The Dickey–Fuller Test.

Augmented Dickey–Fuller Test.

Power and Level of Unit Root Tests.

Structural Breaks and Unit Root Tests.

Seasonal Unit Roots.

Structural Breaks and Seasonal Unit Root Tests.

Periodic Integration and Unit Root-testing.

Conclusion on Unit Root Tests.

4. Cointegration in Single Equations.

The Engle–Granger (EG) Approach.

Testing for Cointegration with a Structural Break.

Alternative Approaches.

Problems with the Single Equation Approach.

Estimating the Short-run Dynamic Model.

Seasonal Cointegration.

Periodic Cointegration.

Asymmetric Tests for Cointegration.

Conclusion s.

5. Cointegration in Multivariate Systems.

The Johansen Approach.

Testing the Order of Integration of the Variables.

Formulation of the Dynamic Model.

Testing for Reduced Rank.

Deterministic Components in the Multivariate Model.

Testing of Weak Exogeneity and VECM with Exogenous I (l) Variables.

Testing for Linear Hypotheses on Cointegration Relations.

Testing for Unique Cointegration Vectors.

Joint Tests of Restrictions on α and β Seasonal Unit Roots.

Seasonal Cointegration.


Appendix 1: Programming in SHAZAM.

6. Modelling the Short-run Multivariate System.


Estimating the Long-run Cointegration Relationships.

Parsimonious VECM.

Conditional PVECM.

Structural Modelling.

Structural Macroeconomic Modelling.

7. Panel Data Models and Cointegration.


Panel Data and Modelling Techniques.

Panel Unit Root Tests.

Testing for Cointegration in Panels.

Estimating Panel Cointegration Models.

Conclusion on Testing for Unit Roots and Cointegration in Panel Data.

8. Modelling and Forecasting Financial Times Series.



Multivariate GARCH.

Estimation and Testing.

An Empirical Application of ARCH and GARCH Models.


Asymmetric GARCH Models.

Integrated and Fractionally Integrated GARCH Models.

Conditional Heteroscedasticity, Unit Roots and Cointegration.

Forecasting with GARCH Models.

Further Methods for Forecast Evaluation.

Conclusions on Modelling and Forecasting Financial Time Series.

Appendix: Cointegration Analysis Using the Johansen Technique: A Practitioner’s Guide to PcGive 10.1.

Statistical Appendix.