On the estimation of a harmonic component in a time series with stationary dependent residuals
- 1 August 1973
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 5 (2) , 217-241
- https://doi.org/10.2307/1426034
Abstract
Let observations (X1, X2, …, 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.Keywords
This publication has 6 references indexed in Scilit:
- On the estimation of a harmonic component in a time series with stationary independent residualsBiometrika, 1971
- Non-linear time series regressionJournal of Applied Probability, 1971
- Asymptotic properties of the periodogram of a discrete stationary processJournal of Applied Probability, 1967
- Some asymptotic results for the periodogram of a stationary time seriesJournal of the Australian Mathematical Society, 1965
- Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-seriesJournal of the Australian Mathematical Society, 1964
- The simultaneous estimation of a time series harmonic components and covariance structureTrabajos de Estadistica, 1952