The general solution to an autoregressive law of motion
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917375442419712 |
|---|---|
| author | Beare, Brendan K. Franchi, Massimo Howlett, Phil |
| author_facet | Beare, Brendan K. Franchi, Massimo Howlett, Phil |
| contents | We provide a complete description of the set of all solutions to a vector autoregressive law of motion. Every solution is shown to be the sum of three components, each corresponding to a directed flow of time. One component flows forward from the arbitrarily distant past; one flows backward from the arbitrarily distant future; and one flows outward from time zero. The three components are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive coefficient matrix according to whether they are inside, outside or on the unit circle. We establish a one-to-one correspondence between the set of all solutions and a finite-dimensional space of initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The general solution to an autoregressive law of motion Beare, Brendan K. Franchi, Massimo Howlett, Phil Econometrics We provide a complete description of the set of all solutions to a vector autoregressive law of motion. Every solution is shown to be the sum of three components, each corresponding to a directed flow of time. One component flows forward from the arbitrarily distant past; one flows backward from the arbitrarily distant future; and one flows outward from time zero. The three components are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive coefficient matrix according to whether they are inside, outside or on the unit circle. We establish a one-to-one correspondence between the set of all solutions and a finite-dimensional space of initial conditions. |
| title | The general solution to an autoregressive law of motion |
| topic | Econometrics |
| url | https://arxiv.org/abs/2402.01966 |