MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS

2008 ◽  
Vol 24 (3) ◽  
pp. 677-695 ◽  
Author(s):  
M. Zarepour ◽  
S.M. Roknossadati
Keyword(s):  
Autoregressive Model ◽  
Domain Of Attraction ◽  
Ordinary Least Squares ◽  
Infinite Variance ◽  
Regularity Conditions ◽  
Vector Autoregressive Model ◽  
Stable Law ◽  
Limiting Behavior ◽  
Vector Autoregressive ◽  
Multivariate Autoregression

We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases.

M-ESTIMATION FOR A SPATIAL UNILATERAL AUTOREGRESSIVE MODEL WITH INFINITE VARIANCE INNOVATIONS

2010 ◽  
Vol 26 (6) ◽  
pp. 1663-1682 ◽  
Author(s):  
S.M. Roknossadati ◽  
M. Zarepour
Keyword(s):  
Simulation Study ◽  
Unit Root ◽  
Autoregressive Model ◽  
Domain Of Attraction ◽  
Infinite Variance ◽  
Stable Law ◽  
Limiting Behavior ◽  
Asymptotically Normal ◽  
M Estimation ◽  
Unit Root Models

We study the limiting behavior of the M-estimators of parameters for a spatial unilateral autoregressive model with independent and identically distributed innovations in the domain of attraction of a stable law with index α ∈ (0, 2]. Both stationary and unit root models and some extensions are considered. It is also shown that self-normalized M-estimators are asymptotically normal. A numerical example and a simulation study are also given.

On the First-Order Autoregressive Process with Infinite Variance

1989 ◽  
Vol 5 (3) ◽  
pp. 354-362 ◽  
Author(s):  
Ngai Hang Chan ◽  
Lanh Tat Tran
Keyword(s):  
Strong Consistency ◽  
Domain Of Attraction ◽  
Unit Roots ◽  
Autoregressive Process ◽  
Ordinary Least Squares ◽  
Seasonal Difference ◽  
Infinite Variance ◽  
Stable Law ◽  
First Order ◽  
Heavy Tailed

For a first-order autoregressive process Yt = βYt−1 + ∈t where the ∈t'S are i.i.d. and belong to the domain of attraction of a stable law, the strong consistency of the ordinary least-squares estimator bn of β is obtained for β = 1, and the limiting distribution of bn is established as a functional of a Lévy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the ∈t'S are heavy-tailed.

scholarly journals A Spatial Panel Structural Vector Autoregressive Model with Interactive Effects and Its Simulation

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 883
Author(s):  
Yaqing Liu ◽  
Hongbing Ouyang ◽  
Xiaolu Wei
Keyword(s):  
Autoregressive Model ◽  
Common Factors ◽  
Interactive Effects ◽  
Vector Autoregressive Model ◽  
Finite Sample ◽  
Vector Autoregressive ◽  
Spatial Panel ◽  
The Common ◽  
Structural Vector Autoregressive Model ◽  
Structural Vector

The existing spatial panel structural vector auto-regressive model can effectively capture the time and spatial dynamic dependence of endogenous variables. However, the hypothesis that the common factors have the same effect for all spatial units is unreasonable. Therefore, incorporating time effects, spatial effects, and time-individual effects, this paper develops a more general spatial panel structural vector autoregressive model with interactive effects (ISpSVAR) that can reflect the different effects of common factors on different spatial units. Additionally, based on whether or not the common factors can be observed, this paper proposes procedures to estimate ISpSVAR separately and studies the finite sample properties of estimators by Monte Carlo simulation. The simulation results show the effectiveness of the proposed ISpSVAR model and its estimation procedures.

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