Abstract
Let [Xt] 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 fθ(λ), θ ε Θ, is fitted to g(λ). Then, constructing the best linear predictor based on fθ(λ), we can evaluate the prediction error M(θ) Since θ is unknown we estimate it by a quasi-MLE θQ. The second-order asymptotic approximation of M(θ̂Q)is given. This result is extended to the case when Xt 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(θ̂Q) 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.
| Original language | English |
|---|---|
| Pages (from-to) | 543-564 |
| Number of pages | 22 |
| Journal | Journal of Forecasting |
| Volume | 20 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2001 Dec |
| Externally published | Yes |
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Keywords
- Best linear predictor
- Conjectured spectral density
- Long-memory process
- Misspecified prediction
- Multistep prediction
- Quasi-MLE
- Spectral density
- Stationary process
- Time series regression model
ASJC Scopus subject areas
- Management of Technology and Innovation
- Strategy and Management
- Development
- Safety, Risk, Reliability and Quality
Cite this
Misspecified prediction for time series. / Choi, In Bong; Taniguchi, Masanobu.
In: Journal of Forecasting, Vol. 20, No. 8, 12.2001, p. 543-564.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Misspecified prediction for time series
AU - Choi, In Bong
AU - Taniguchi, Masanobu
PY - 2001/12
Y1 - 2001/12
N2 - Let [Xt] 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 fθ(λ), θ ε Θ, is fitted to g(λ). Then, constructing the best linear predictor based on fθ(λ), we can evaluate the prediction error M(θ) Since θ is unknown we estimate it by a quasi-MLE θQ. The second-order asymptotic approximation of M(θ̂Q)is given. This result is extended to the case when Xt 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(θ̂Q) 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.
AB - Let [Xt] 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 fθ(λ), θ ε Θ, is fitted to g(λ). Then, constructing the best linear predictor based on fθ(λ), we can evaluate the prediction error M(θ) Since θ is unknown we estimate it by a quasi-MLE θQ. The second-order asymptotic approximation of M(θ̂Q)is given. This result is extended to the case when Xt 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(θ̂Q) 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.
KW - Best linear predictor
KW - Conjectured spectral density
KW - Long-memory process
KW - Misspecified prediction
KW - Multistep prediction
KW - Quasi-MLE
KW - Spectral density
KW - Stationary process
KW - Time series regression model
UR - http://www.scopus.com/inward/record.url?scp=0035676994&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035676994&partnerID=8YFLogxK
U2 - 10.1002/for.807
DO - 10.1002/for.807
M3 - Article
AN - SCOPUS:0035676994
VL - 20
SP - 543
EP - 564
JO - Journal of Forecasting
JF - Journal of Forecasting
SN - 0277-6693
IS - 8
ER -