scholarly journals Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method

2014 ◽  
Vol 490 ◽  
pp. 012040
Author(s):  
Cyril Voyant ◽  
Wani Tamas ◽  
Christophe Paoli ◽  
Aurélia Balu ◽  
Marc Muselli ◽  
...  
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Modeling ◽  
Multi Layer Perceptron ◽  
Damped Least Squares

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.

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