LARGE-SAMPLE PROPERTIES OF LEAST-SQUARES ESTIMATORS OF HARMONIC COMPONENTS IN A TIME SERIES WITH STATIONARY RESIDUALS. I. INDEPENDENT RESIDUALS

1968 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Large Sample ◽  
Least Squares Estimators ◽  
Harmonic Components

scholarly journals Bootstrapping periodically autoregressive models

2017 ◽  
Vol 21 ◽  
pp. 394-411
Author(s):  
Gabriela Ciołek ◽  
Paweł Potorski
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Autoregressive Models ◽  
Wild Bootstrap ◽  
Autoregressive Time Series ◽  
Least Squares Estimators ◽  
Theoretical Considerations

The main objective of this paper is to establish the residual and the wild bootstrap procedures for periodically autoregressive models. We use the least squares estimators of model’s parameters and generate their bootstrap equivalents. We prove that the bootstrap procedures for causal periodic autoregressive time series with finite fourth moments are weakly consistent. Finally, we confirm our theoretical considerations by simulations.

On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle

1991 ◽  
Vol 7 (3) ◽  
pp. 269-306 ◽  
Author(s):  
P. Jeganathan
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Least Squares ◽  
Unit Circle ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Ar Model ◽  
Convergence In Distribution ◽  
Least Squares Estimators ◽  
The Given

Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order p, p ≥ 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions.Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.

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