Part 1: The Statistical Analysis of Cointegration

1 Introduction

2 The Vector Autoregressive Model

3 Basic Definitions and Concepts

4 Cointegration and Representation of Integrated Variables

5 The I(1) Models and their Interpretation

6 The Statistical Analysis of I(1) Models

7 Hypothesis Testing for the Long-Run Coefficients β

8 Partial Systems and Hypotheses on α

9 The I(2) Model and a Test for I(2)

PART II: The Probability Analysis of Cointegration

10 Probability Properties of I(1) Processes

11 The Asymptotic Distribution of the Test for Cointegrating Rank

12 Determination of Cointegrating Rank

13 Asymptotic Properties of the Estimators

14 The Power Function of the Test for Cointegrating Rank under Local Alternatives

15 Simulations and Tables

PART III Appendices

A Some Mathematical Results

A.1 Eigenvalues and eigenvectors
A.2 The binomial formula for matrices
A.3 The multivariate Gaussian distribution
A.4 Principal components and canonical correlations

B Weak Convergence of Probability Measures on RP and C[0,1]

B.l Weak convergence on RP
B.2 Weak convergence on C[0, 1]
B.3 Construction of measures on C[0, 1]
B.4 Tightness and Prohorov's theorem
B.5 Construction of Brownian motion
B.6 Stochastic integrals with respect to Brownian motion
B.7 Some useful results for linear processes

References
Subject Index
Author Index