Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Gill, Ryan

Committee Co-Chair (if applicable)

Tone, Cristina

Committee Member

Tone, Cristina

Committee Member

Han, Dan

Committee Member

Kulasekera, Karunarathna

Author's Keywords

cross-validation; autoregressive models; time series; order selection; model selection


There are no set rules for choosing the lag order for autoregressive (AR) time series models. Currently, the most common methods employ AIC or BIC. However, AIC has been proven to be inconsistent and BIC is inefficient. Racine proposed an estimator based on Shao's work which he hypothesized would also be consistent, but left the proof as an open problem. We will show his claim does not follow immediately from Shao. However, Shao offered another consistent method for cross validation of linear models called APCV, and we will show that AR models satisfy Shao's conditions. Thus, APCV is a consistent method for choosing lag order. Simulations also show that APCV performs as well, and in some cases, performs better than AIC, AICc, and BIC.