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Order selection of time series models, especially with AIC

Parzen (1974) [288] Review of tehory and estimation of stationary time series. Mentions AIC, proposes an alternative order selection approach, which does not assume that true model has finite order.

Jones (1975) [203] Points out an error in some earlier calculations by Bhansali for the use of Akaike's FPE crtiterion.

Shibata (1976) [337] Selecting the order of AR using AIC. Asymptotic distribution of the selected order. MSE of prediction.

Ozaki (1977) [287] Using AIC for selection the order of ARIMA models.

Bhansali and Downham (1977) [38] Asymptotic distribution of the order of an AR process selected by generalization of AIC (constant $\alpha$ instead of 2). Probability of overfitting decreases as $\alpha$ increases, especially for large $T$ and strong AR dependence. Values of $\alpha=1,2,3,4$ examined in simulation.

McClave (1978) [264] Compares Akaike's FPE and a sequential testing method for selecting the order of an AR. Also uses a procedure which allows some lower-order lag coefficients to be set to zero even when higher-order ones are nonzero.

Hannan and Quinn (1979) [177] (Automatic) determination of the order of an autoregression. Seek a consistent procedure with a penalty term of as small an order as possible -- $\mathbf{\log \log N}$ suggested.

Akaike (1979) [9] Order of an AR process. Gives a (fairly vague) Bayesian interpretation to the penalty term of any `generalized' AIC, and suggests a Bayesian approach to model estimation and order selection.

Fine and Hwang (1979) [133] Selection of `system order', illustrated for AR and ARMA. Notes on AIC, BIC etc. Proposes an alternative consistent estimator of order.

Hannan (1980) [175] Estimation of the order of an ARMA($p,q$) process with $p,q$ fixed. BIC and $\phi$ of Hannan and Quinn (1979) [177] are consistent, but AIC is not. Probabilities of overestimation are given for AIC.

Shibata (1980) [338] Selection of the order of an AR process when the true process is of infinite order. Shows that AIC is then asymptotically efficient.

Pötscher (1983) [298] Selecting the order of an ARMA process using a sequence of LM tests. Consistency of the selected order.

Tsay (1984) [370] Properties of AIC, BIC and $\phi$ of Hannan and Quinn (1979) [177] for order selection for nonstationary AR models. Distribution of model selectted by AIC given in Shibata (1976) citeshibata76 still holds. BIC and $\phi(k, 0)$ are consistent.

Paulsen (1984) [290] AR with unit roots (i.e. a particular nonstationary process). Conditions for weak consistency (essentially penalty term $f(n)$ such that $f(n)\rightarrow\infty$ and $f(n)/n\rightarrow\infty$). Probability of underestimation actually reduced from the stationary case. Simulations with AIC, BIC and $\phi$.

Pötscher (1989) [299] Order selection for `general stochastic linear regression models', and, as a special case, nostattionary AR. Conditions for the penalty term under which probability of over- or underestimation tends to zero, consistency when both. Inconsistency of AIC, BIC consistent for some but not all types of nonstationarity.

Chen and Gupta (1997) [77] Considers BIC, but in the spirit of AIC (and in a completely non-Bayesian way). Testing for variance changepoints in a sequence of normal variables with constant mean. Derives a significance test based on BIC and a small-sample modification of BIC.

Faraway and Chatfield (1998) [129] Forecasting in time series analysis. Compare the performance of some neural network models to more traditional time series models. Performance evaluated by data splitting, model choice by AIC and BIC, with BIC preferred by the authors.


next up previous contents
Next: NIC/TIC and other generalisations Up: AIC and related methods Previous: AIC and related methods   Contents
Jouni Kuha 2003-07-16