## Dynamic Model Analysis: Advanced Matrix Methods and Unit-Root Econometrics Representation TheoremsThis second edition sees the light three years after the first one: too short a time to feel seriously concerned to redesign the entire book, but sufficient to be challenged by the prospect of sharpening our investigation on the working of econometric dynamic models and to be inclined to change the title of the new edition by dropping the “Topics in” of the former edition. After considerable soul searching we agreed to include several results related to topics already covered, as well as additional sections devoted to new and sophisticated techniques, which hinge mostly on the latest research work on linear matrix polynomials by the second author. This explains the growth of chapter one and the deeper insight into representation theorems in the last chapter of the book. The rôle of the second chapter is that of providing a bridge between the mathematical techniques in the backstage and the econometric profiles in the forefront of dynamic modelling. For this purpose, we decided to add a new section where the reader can find the stochastic rationale of vector autoregressive specifications in econometrics. The third (and last) chapter improves on that of the first edition by re- ing the fruits of the thorough analytic equipment previously drawn up. |

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### Contents

1 | |

6 | |

13 Empty Matrices | 18 |

Classic and Newly Found Results | 19 |

15 Useful Matrix Decompositions | 30 |

Zeroes Roots and poles | 38 |

17 The Laurent Form of a MatrixPolynomial Inverse about a UnitRoot | 51 |

18 Matrix Polynomials and Difference Equation Systems | 62 |

24 Integrated and Cointegrated Processes | 145 |

25 Casting a Glance at the Backstage of VAR Modelling | 151 |

A Convenient Reparametrization of a VAR Model and Related Results | 155 |

Integrated Processes Stochastic Trends and Role of Cointegration | 159 |

Econometric Dynamic Models From Classical Econometrics to Time Series Econometrics | 161 |

32 Basic VAR Specifications and Engendered Processes | 167 |

33 A Sequential Rank Criterion for the Integration Order of a VAR Solution | 172 |

34 Representation Theorems for Processes I 1 | 179 |

19 The Linear Matrix Polynomial | 74 |

110 Index and Rank Properties of Matrix Coefficients vs Pole Order in Matrix Polynomial Inversion | 84 |

111 ClosedForms of Laurent Expansion Coefficient Matrices First Approach | 97 |

112 ClosedForms of Laurent Expansion Coefficient Matrices Second Approach | 111 |

The Statistical Setting | 127 |

22 Principal Multivariate Stationary Processes | 130 |

23 The Source of Integration and the Seeds of Cointegration | 142 |

35 Representation Theorems for Processes 2 | 189 |

36 A Unified Representation Theorem | 203 |

212 | |

Notational Conventions Symbols and Acronyms | 215 |

List of Definitions | 217 |

### Other editions - View all

Dynamic Model Analysis: Advanced Matrix Methods and Unit-Root Econometrics ... Mario Faliva,Maria Grazia Zoia No preview available - 2008 |

Dynamic Model Analysis: Advanced Matrix Methods and Unit-Root Econometrics ... Mario Faliva,Maria Grazia Zoia No preview available - 2010 |

### Common terms and phrases

A=BC algebraic analytic arbitrary autocovariance bearing in mind block block matrix by-product C±SJ Campbell and Meyer characteristic polynomial detA(z closed-form coefficient matrices cointegration columns companion-form Corollary 2.1 defined Definition deleted neighbourhood denote deterministic trends Drazin inverse expression Faliva full column-rank matrices full row-rank ind(A integrated process integration and cointegration integration order isomorphism lag operator Laurent expansion Lemma light linear matrix polynomial matrix function matrix of order matrix polynomial A(z nilpotent non-singular matrix null row null row-space obtained orthogonal complement partitioned matrix permanent component post-multiplying process yt Proof The proof Proposition random walk rank factorization Rao and Mitra Remark representation theorem respectively rewritten right-hand side role roots Schur complement second order pole Sect series econometrics simple pole singular matrix specified square matrix stationary process stochastic process stochastic trend unit circle unit-root vector autoregressive VMA process ΓΓΓΓ εεεε ηηηη τ τ