Likelihood-Based Inference in Cointegrated Vector Autoregressive Models (Advanced Texts in Econometrics)

Contents......Page 10
PART I: THE STATISTICAL ANALYSIS OF COINTEGRATION......Page 14
1 Introduction......Page 16
1.1 The vector autoregressive model......Page 17
1.2 Building statistical models......Page 18
1.3 Illustrative examples......Page 20
1.4 An outline of the contents......Page 21
1.5 Some further problems......Page 23
2.1The vector autoregressive process......Page 24
2.2 The statistical analysis of the VAR......Page 30
2.3 Misspecification tests......Page 33
2.4 The illustrative examples......Page 36
3.1 Cointegration and common trends......Page 47
3.2 Exercises......Page 55
4.1 From AR to MA representation for I(1) variables......Page 58
4.2 From MA to AR representation for I(1) variables......Page 68
4.3 The MA representation of I(2) variables......Page 70
4.4 Exercises......Page 75
5.1 The I(1) models for cointegration......Page 83
5.2 The parametrization of the I(1) model......Page 84
5.3 Hypotheses on the long-run coefficients β......Page 85
5.4 Hypotheses on the adjustment coefficients α......Page 90
5.5 The structural error correction model......Page 91
5.6 General hypotheses......Page 92
5.7 Models for deterministic terms......Page 93
5.8 Intervention and seasonal dummies......Page 97
5.9 Exercises......Page 98
6.1 Likelihood analysis of H(r)......Page 102
6.2 Models for the deterministic terms......Page 108
6.3 Determination of cointegrating rank......Page 111
6.4 Exercises......Page 113
7.1 Degrees of freedom......Page 117
7.2 Linear restrictions on β......Page 119
7.3 Illustrative examples......Page 125
7.4 Exercises......Page 133
8.1 Partial systems......Page 134
8.2 Test of restrictions on α......Page 137
8.3 The duality between [omitted] and [omitted]......Page 141
8.4 Exercises......Page 144
9.1 A statistical model for I(2)......Page 145
9.2 A misspecification test for the presence of I(2)......Page 147
9.3 A test for I(2) in the Australian data......Page 150
PART II: THE PROBABILITY ANALYSIS OF COINTEGRATION......Page 152
10.1 Finite sample results......Page 154
10.2 Asymptotic results......Page 156
10.3 Exercises......Page 162
11.1 Testing Π = 0 in the basic model......Page 164
11.2 The limit distribution of the test for cointegrating rank......Page 169
11.3 Asymptotic properties of the test for I(2)......Page 176
11.4 Exercises......Page 177
12 Determination of Cointegrating Rank......Page 180
12.1 Model without constant term......Page 181
12.2 Model with a constant term......Page 183
12.3 Models with a linear term......Page 188
12.4 Exercises......Page 189
13.1 The mixed Gaussian distribution......Page 190
13.2 A convenient normalization of β......Page 192
13.3 Consistency of the estimators......Page 193
13.4 Asymptotic distribution of [omitted] and [omitted]......Page 194
13.5 More asymptotic distributions......Page 200
13.6 Likelihood ratio test for hypotheses on the long-run coefficients β......Page 205
13.7 Exercises......Page 209
14.1 Local alternatives......Page 214
14.2 Properties of the process under local alternatives......Page 215
14.3 The local power of the trace test......Page 219
14.4 Exercises......Page 222
15.1 Simulation of the limit distributions......Page 224
15.2 Simulations of the power function......Page 225
15.3 Tables......Page 227
PART III: APPENDICES......Page 230
A.1 Eigenvalues and eigenvectors......Page 232
A.2 The binomial formula for matrices......Page 241
A.3 The multivariate Gaussian distribution......Page 246
A.4 Principal components and canonical correlations......Page 250
B.1 Weak convergence on R[sup(p)]......Page 252
B.2 Weak convergence on C[0, 1]......Page 254
B.3 Construction of measures on C[0, 1]......Page 257
B.4 Tightness and Prohorov's theorem......Page 258
B.5 Construction of Brownian motion......Page 260
B.6 Stochastic integrals with respect to Brownian motion......Page 261
B.7 Some useful results for linear processes......Page 263
References......Page 268
C......Page 274
G......Page 275
M......Page 276
T......Page 277
W......Page 278
S......Page 279
Y......Page 280