An Optimality Property of the Least-Squares Estimate of the Parameter of the Spectrum of a Purely Nondeterministic Time Series

Consider, initially, a time series regression model of the simplest kind, namely Assume that x(t) is second-order stationary with zero mean and absolutely continuous spectrum with density f(ω) so that The y(t) are taken to be part of a sequence generated entirely independently of x(t) and will be treated as constants. Let β N be the least squares estimate of β and Call the numerator and denominator of b(N), respectively, c(N), d(N). We shall use K for a positive finite constant, not always the same one. We have the following result, which is Menchoff's inequality [3].

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Rates of convergence for time series regression

Advances in Applied Probability ◽

10.2307/1426656 ◽

1978 ◽

Vol 10 (4) ◽

pp. 740-743 ◽

Cited By ~ 8

Author(s):

E. J. Hannan

Keyword(s):

Time Series ◽

Regression Model ◽

Least Squares ◽

Continuous Spectrum ◽

Rates Of Convergence ◽

Absolutely Continuous Spectrum ◽

Time Series Regression ◽

Absolutely Continuous ◽

Least Squares Estimate ◽

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Consider, initially, a time series regression model of the simplest kind, namely Assume that x(t) is second-order stationary with zero mean and absolutely continuous spectrum with density f(ω) so that The y(t) are taken to be part of a sequence generated entirely independently of x(t) and will be treated as constants. Let βN be the least squares estimate of β and Call the numerator and denominator of b(N), respectively, c(N), d(N). We shall use K for a positive finite constant, not always the same one. We have the following result, which is Menchoff's inequality [3].

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A novel recursive modal parameter estimator for operational time-varying structural dynamic systems based on least squares support vector machine and time series model

Computers & Structures ◽

10.1016/j.compstruc.2019.106173 ◽

2020 ◽

Vol 229 ◽

pp. 106173 ◽

Cited By ~ 1

Author(s):

Jie Kang ◽

Li Liu ◽

Si-Da Zhou ◽

Da-Yu Wang ◽

Yuan-Chen Ma

Keyword(s):

Time Series ◽

Support Vector Machine ◽

Least Squares ◽

Dynamic Systems ◽

Support Vector ◽

Time Varying ◽

Modal Parameter ◽

Parameter Estimator ◽

Structural Dynamic ◽

Operational Time

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On eliminating the asymptotic bias in the quasi-least squares estimate of the correlation parameter

Journal of Statistical Planning and Inference ◽

10.1016/s0378-3758(98)00180-3 ◽

1999 ◽

Vol 76 (1-2) ◽

pp. 145-161 ◽

Cited By ~ 47

Author(s):

N.Rao Chaganty ◽

Justine Shults

Keyword(s):

Least Squares ◽

Asymptotic Bias ◽

Correlation Parameter ◽

Least Squares Estimate

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Identification of an unstable ARMA equation

Mathematical Problems in Engineering ◽

10.1155/s1024123x01001557 ◽

2001 ◽

Vol 7 (1) ◽

pp. 97-112 ◽

Cited By ~ 5

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.

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