𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Misspecified prediction for time series

✍ Scribed by In-Bong Choi; Masanobu Taniguchi

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
205 KB
Volume
20
Category
Article
ISSN
0277-6693

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let {X~t~} be a stationary process with spectral density g(λ).It is often that the true structure g(λ) is not completely specified. This paper discusses the problem of misspecified prediction when a conjectured spectral density f~θ~(λ), θ∈Θ, is fitted to g(λ). Then, constructing the best linear predictor based on f~θ~(λ), we can evaluate the prediction error M(θ). Since θ is unknown we estimate it by a quasi‐MLE $\hat{\theta}_{Q}$. The second‐order asymptotic approximation of $M(\hat{\theta}_{Q})$ is given. This result is extended to the case when X~t~ contains some trend, i.e. a time series regression model. These results are very general. Furthermore we evaluate the second‐order asymptotic approximation of $M(\hat{\theta}_{Q})$ for a time series regression model having a long‐memory residual process with the true spectral density g(λ). Since the general formulae of the approximated prediction error are complicated, we provide some numerical examples. Then we illuminate unexpected effects from the misspecification of spectra. Copyright © 2001 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Time-simultaneous prediction band for a
Time-simultaneous prediction band for a time series
✍ Dag Kolsrud 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 297 KB

## Abstract I propose principles and methods for the construction of a time‐simultaneous prediction band for a univariate time series. The methods are entirely based on a learning sample of time trajectories, and make no parametric assumption about its distribution. Hence, the methods are general a

Functional methods for time series predi
Functional methods for time series prediction: a nonparametric approach
✍ Germán Aneiros-Pérez; Ricardo Cao; Juan M. Vilar-Fernández 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 284 KB

## Abstract The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and wi

On multistep prediction error methods fo
On multistep prediction error methods for time series models
✍ Petre Stoica; Arye Nehorai 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 574 KB

Multistep prediction error methods for linear time series models are considered from both a theoretical and a practical standpoint. The emphasis is on autoregressive moving-average (ARMA) models for which a multistep prediction error estimation method (PEM) is developed. The results of a Monte Carlo

Smoothing splines for trend estimation a
Smoothing splines for trend estimation and prediction in time series
✍ Richard Morton; Emily L. Kang; Brent L. Henderson 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 302 KB

## Abstract We consider the use of generalized additive models with correlated errors for analysing trends in time series. The trend is represented as a smoothing spline so that it can be extrapolated. A method is proposed for choosing the smoothing parameter. It is based on the ability to predict

Predictive models for ground ozone and n
Predictive models for ground ozone and nitrogen dioxide time series
✍ Monique Graf-Jaccottet; Marc-Henri Jaunin 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 241 KB 👁 1 views

Predictive models are built for the mean ground concentration of ozone and nitrogen dioxide on data consisting of 5 years of daily averages. We ®nd the smallest averaging time over which a model with a deterministic trend and an autoregressive error distribution passes a number of statistical tests.