Least Tail-Trimmed Squares for Infinite Variance Autoregressions

2012 ◽  
Author(s):  
Jonathan B. Hill
Keyword(s):  
Infinite Variance

scholarly journals A Shortcut to LAD Estimator Asymptotics

1991 ◽  
Vol 7 (4) ◽  
pp. 450-463 ◽  
Author(s):  
P.C.B. Phillips
Keyword(s):  
Asymptotic Expansion ◽  
Regression Model ◽  
Taylor Series ◽  
Asymptotic Theory ◽  
Random Variables ◽  
Generalized Functions ◽  
Infinite Variance ◽  
Series Expansions ◽  
Linear Functionals ◽  
Taylor Series Expansions

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (02) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators β i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(β i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi (N).

scholarly journals On the law of the iterated logarithm in the infinite variance case

1980 ◽  
Vol 30 (1) ◽  
pp. 5-14 ◽  
Author(s):  
R. A. Maller
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Infinite Variance ◽  
Iterated Logarithm ◽  
The Law ◽  
Necessary And Sufficient ◽  
Independent And Identically Distributed

AbstractThe main purpose of the paper is to give necessary and sufficient conditions for the almost sure boundedness of (Sn – αn)/B(n), where Sn = X1 + X2 + … + XmXi being independent and identically distributed random variables, and αnand B(n) being centering and norming constants. The conditions take the form of the convergence or divergence of a series of a geometric subsequence of the sequence P(Sn − αn > a B(n)), where a is a constant. The theorem is distinguished from previous similar results by the comparative weakness of the subsidiary conditions and the simplicity of the calculations. As an application, a law of the iterated logarithm general enough to include a result of Feller is derived.

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