| Preface |
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1 | (7) |
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Motivation and Results of the Research |
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1 | (4) |
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5 | (1) |
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Exploration of Different Approaches |
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6 | (1) |
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7 | (1) |
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8 | (8) |
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Co-trending in the Non-parametric Approach |
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9 | (1) |
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Co-trending in the Parametric Approach |
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10 | (3) |
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13 | (1) |
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Co-trending and Co-breaking |
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13 | (1) |
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A Survey on the Direct and the Indirect Modelling of Trend |
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14 | (2) |
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Statistics from the Data Covariance Matrix |
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16 | (9) |
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Three-way Decomposition of the n-Dimensional Space |
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17 | (1) |
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18 | (1) |
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19 | (2) |
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21 | (2) |
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23 | (1) |
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Plan for the Rest of the Book |
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23 | (2) |
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25 | (3) |
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26 | (1) |
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Group 2, i = n -- r + 1,...,n -- r1, r2 > 0 |
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27 | (1) |
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Group 1, i = n -- r1 + 1,...,n, r1 > 0 |
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27 | (1) |
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28 | (11) |
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Univariate Unit Root Test |
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29 | (2) |
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Group : The Case Where B η ,i is not a Cointegration Vector |
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31 | (1) |
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Group : The Case Where B η ,i is a Cointegration Vector |
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31 | (1) |
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Group 2: The Case Where r2 = 1, and Group 1 |
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32 | (1) |
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Multivariate Unit Root Test |
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33 | (2) |
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Group 2: The Case Where r2 ≥ 2 |
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35 | (1) |
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Mistaken Constituents of Groups |
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35 | (2) |
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Supplement on the Martingale Covariance |
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37 | (2) |
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39 | (16) |
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Discrimination Between Group 1 and Group with B η ,i as a Cointegration Vector |
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40 | (1) |
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Failure of the Standard Trend Tests in Discriminating Groups and 2 |
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40 | (1) |
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Test Statistic and Limit Distribution for the Discrimination Between Group 2 and Group with B η ,i not in the Cointegrating Space |
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41 | (2) |
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Reduced Rank Regression of X on S H |
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43 | (1) |
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A Finite Sample Analysis of the Reduced Rank Regression |
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44 | (3) |
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Asymptotic Analyses of the Reduced Rank Regression |
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47 | (2) |
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Data-Dependent Critical Value |
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49 | (2) |
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Mistaken Constituents of the Groups and 2 |
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51 | (4) |
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55 | (9) |
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55 | (2) |
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57 | (1) |
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Tests of a Grouping Method |
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57 | (2) |
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Justification of the Sequential Decision Rule |
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59 | (2) |
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61 | (3) |
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64 | (13) |
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64 | (3) |
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Details of the Trend Test for I(O) |
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67 | (1) |
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A Table of Asymptotic Probabilities |
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67 | (5) |
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Results of Simulation Studies |
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72 | (3) |
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75 | (2) |
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77 | (21) |
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Mathematical Proofs of Propositions and Lemmas in Chapter 2 |
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77 | (1) |
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Mathematical Proofs of Propositions and Lemmas in Chapter 3 |
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77 | (5) |
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Mathematical Proofs of Propositions and Lemmas in Chapter 4 |
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82 | (1) |
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Mathematical Proofs of Propositions and Lemmas in Chapter 5 |
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83 | (9) |
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Mathematical Proofs of Propositions and Lemmas in Chapter 6 |
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92 | (6) |
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B OLS Inference on the Matrix B |
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98 | (7) |
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99 | (2) |
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101 | (1) |
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Estimation of the VAR, (B.3) |
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102 | (1) |
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Estimation of C(1), Λ, and C*(1) |
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103 | (1) |
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104 | (1) |
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C Determination of the Co-breaking Rank |
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105 | (6) |
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The Number of Common Breaks |
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105 | (1) |
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Detrended Covariance Matrix |
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106 | (1) |
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107 | (1) |
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108 | (1) |
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109 | (2) |
| Notes |
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111 | (3) |
| References |
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114 | |
