10

Fractional Integration and

Cointegration: An Overview and an

Empirical Application

Luis A. Gil-Alana and Javier Hualde

Abstract

In this chapter we first review the theoretical and empirical work on fractional integration and
cointegration, placing special emphasis on the estimation procedures for fractionally cointegrated
systems. An empirical application is then carried out using some of the more recently developed
techniques in this area. In particular, we investigate the purchasing power parity hypothesis for
four bivariate price series, the US (“domestic”) versus the “foreign” countries Australia, Canada,
Italy and the UK. Fractional cointegration is found in the US–UK relationship.

10.1 Introduction 434
10.2 Fractional integration 436
10.2.1 Concept and modelization 436
10.2.2 Empirical evidence of fractional integration 438
10.2.2.1 Applications to macroeconomics 439
10.2.2.2 Applications to exchange rates 440
10.2.2.3 Applications to interest rates 440
10.2.2.4 Applications to stock markets 441
10.2.2.5 Applications to geophysics and other sciences 441
10.2.2.6 Applications using seasonal and cyclical FI models 441
10.3 Fractional cointegration 442
10.3.1 The concept and modelization of fractional cointegration 442
10.3.2 Estimation methods for fractional cointegration 446
10.3.3 Empirical evidence of fractional cointegration 450
10.3.3.1 Applications to exchange rates 451
10.3.3.2 Applications to financial series 453
10.3.3.3 Applications to interest rates 455
10.3.3.4 Applications to electricity prices 455
10.3.3.5 Applications to political studies 455
10.4 The empirical investigation: the PPP hypothesis 456

10.1 Introduction

One characteristic of many economic and financial time series is its non-stationary
nature. There exists a great variety of models to describe such non-stationarity.

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