Adaptive Estimation in Multiple Time Series With Independent Component Errors. (9th September 2016)
- Record Type:
- Journal Article
- Title:
- Adaptive Estimation in Multiple Time Series With Independent Component Errors. (9th September 2016)
- Main Title:
- Adaptive Estimation in Multiple Time Series With Independent Component Errors
- Authors:
- Robinson, P. M.
Taylor, L. - Other Names:
- Subba Rao Tata guestEditor.
Tunnicliffe Wilson Granville guestEditor. - Abstract:
- Abstract : This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N . The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross‐autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non‐identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo‐maximum likelihood estimates of the parameters are typically √ n ‐consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call 'adaptive, ' are asymptotically as first‐order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel‐based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √ n ‐consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing aAbstract : This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N . The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross‐autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non‐identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo‐maximum likelihood estimates of the parameters are typically √ n ‐consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call 'adaptive, ' are asymptotically as first‐order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel‐based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √ n ‐consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing a variety of parameterizations, distributions and choices of N, is reported. … (more)
- Is Part Of:
- Journal of time series analysis. Volume 38:Number 2(2017:Mar.)
- Journal:
- Journal of time series analysis
- Issue:
- Volume 38:Number 2(2017:Mar.)
- Issue Display:
- Volume 38, Issue 2 (2017)
- Year:
- 2017
- Volume:
- 38
- Issue:
- 2
- Issue Sort Value:
- 2017-0038-0002-0000
- Page Start:
- 191
- Page End:
- 203
- Publication Date:
- 2016-09-09
- Subjects:
- Multiple time series -- independent component analysis -- efficient semiparametric estimation -- adaptive estimation -- stationary processes -- forecast error
Time-series analysis -- Periodicals
519.232 - Journal URLs:
- http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9892 ↗
http://onlinelibrary.wiley.com/ ↗ - DOI:
- 10.1111/jtsa.12212 ↗
- Languages:
- English
- ISSNs:
- 0143-9782
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5069.400000
British Library DSC - BLDSS-3PM
British Library STI - ELD Digital store - Ingest File:
- 15227.xml