### 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 ε 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 θ_{Q}. The second-order asymptotic approximation of M(θ̂_{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(θ̂_{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.

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 |

### Fingerprint

### 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

*Journal of Forecasting*,

*20*(8), 543-564. https://doi.org/10.1002/for.807

**Misspecified prediction for time series.** / Choi, In Bong; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Journal of Forecasting*, vol. 20, no. 8, pp. 543-564. https://doi.org/10.1002/for.807

}

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 -