Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series

Ing, Ching‐Kang

doi:10.1214/009053606000001550

Cited by 58 publications

(50 citation statements)

References 31 publications

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“…This expression provides the first exact evaluation of the impacts of nonstationarity, model complexity and model misspecification on the corresponding MSPE. It not only gives a nontrivial extension of Ing and Wei's (2005) Theorem 3, but also forms the theoretical foundation for a companion paper by Ing et al (2007), which shows that the asymptotic efficiency (see (32)) of AIC and a two-stage information criterion of Ing (2007) in various stationary time series models can carry over to nonstationary cases. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 70%

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Ing¹,

Sin²,

Yu³

2009

Econom. Theory

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Assume that observations are generated from a nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.

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Section: Introductionmentioning

confidence: 70%

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Ing¹,

Sin²,

Yu³

2009

Econom. Theory

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“…For results on asymptotically-optimal model selection for AR models, see, e.g., Ing [24] and Ing et al [25]. We here compare forecast combination methods.…”

Section: Simulation Settingsmentioning

confidence: 99%

Forecast Combination under Heavy-Tailed Errors

2015

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Forecast combination has been proven to be a very important technique to obtain accurate predictions for various applications in economics, finance, marketing and many other areas. In many applications, forecast errors exhibit heavy-tailed behaviors for various reasons. Unfortunately, to our knowledge, little has been done to obtain reliable forecast combinations for such situations. The familiar forecast combination methods, such as simple average, least squares regression or those based on the variance-covariance of the forecasts, may perform very poorly due to the fact that outliers tend to occur, and they make these methods have unstable weights, leading to un-robust forecasts. To address this problem, in this paper, we propose two nonparametric forecast combination methods. One is specially proposed for the situations in which the forecast errors are strongly believed to have heavy tails that can be modeled by a scaled Student's t-distribution; the other is designed for relatively more general situations when there is a lack of strong or consistent evidence on the tail behaviors of the forecast errors due to a shortage of data and/or an evolving data-generating process. Adaptive risk bounds of both methods are developed. They show that the resulting combined forecasts yield near optimal mean forecast errors relative to the candidate forecasts. Simulations and a real example demonstrate their superior performance in that they indeed tend to have significantly smaller prediction errors than the previous combination methods in the presence of forecast outliers.

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“…Indeed, using arguments similar to those presented in Ing (2001) and Yu, Lin and Cheng (2012), we can link the second-order MSPE of the least squares predictor to the Fisher information matrix, n−1 j=1 x j x j , and express (47) and (49) in a unified way:…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Predictor Selection for Positive Autoregressive Processes

Ing

Yang²

2014

Journal of the American Statistical Association

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Let observations y 1 , • • • , y n be generated from a first-order autoregressive (AR) model with positive errors. In both the stationary and unit root cases, we derive moment bounds and limiting distributions of an extreme value estimator,ρ n , of the AR coefficient. These results enable us to provide asymptotic expressions for the mean squared error (MSE) ofρ n and the mean squared prediction error (MSPE) of the corresponding predictor,ŷ n+1 , of y n+1 . Based on these expressions, we compare the relative performance ofŷ n+1 (ρ n ) and the least squares predictor (estimator) from the MSPE (MSE) point of view. Our comparison reveals that the better predictor (estimator) is determined not only by whether a unit root exists, but also by the behavior of the underlying error distribution near the origin, and hence is difficult to identify in practice. To circumvent this difficulty, we suggest choosing the predictor (estimator) with the smaller accumulated prediction error and show that the predictor (estimator) chosen in this way is asymptotically equivalent to the better one. Both real and simulated data sets are used to illustrate the proposed method.

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Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series

Cited by 58 publications

References 31 publications

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Forecast Combination under Heavy-Tailed Errors

Predictor Selection for Positive Autoregressive Processes

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