On the first-order bilinear time series model

1981 ◽  
Vol 18 (03) ◽  
pp. 617-627 ◽  
Author(s):  
Tuan Dinh Pham ◽  
Lanh Tat Tran
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Model ◽  
First Order ◽  
Strongly Consistent

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

On the first-order bilinear time series model

1981 ◽  
Vol 18 (3) ◽  
pp. 617-627 ◽  
Author(s):  
Tuan Dinh Pham ◽  
Lanh Tat Tran
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Model ◽  
First Order ◽  
Strongly Consistent

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

scholarly journals Identification of an unstable ARMA equation

2001 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Yulia R. Gel ◽  
Vladimir N. Fomin
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Infinite Order ◽  
Time Series Model ◽  
Identification Algorithm ◽  
Data Handling ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Strongly Consistent ◽  
Minimal Phase

Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.

On the estimation of a harmonic component in a time series with stationary dependent residuals

1973 ◽  
Vol 5 (02) ◽  
pp. 217-241 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Harmonic Component ◽  
Asymptotic Distributions ◽  
Finite Variance ◽  
Rigorous Derivation ◽  
Image Position ◽  
Vector Valued ◽  
Special Case

Let observations (X 1, X 2, …, Xn ) be obtained from a time series {Xt } such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu (θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu (θ) = 0 for u > 0, the parameter θ thus being absent.

Consistency for the least squares estimator in a transfer function model

1984 ◽  
Vol 21 (01) ◽  
pp. 88-97
Author(s):  
Victor Solo
Keyword(s):  
Time Series ◽  
Transfer Function ◽  
Least Squares ◽  
Time Series Model ◽  
Least Squares Estimator ◽  
Transfer Function Model ◽  
Function Model ◽  
Mild Conditions ◽  
Function Time

The consistency is developed under mild conditions for the least squares estimator of the parameters of a transfer function time series model.

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