Comment on "Regression with slowly varying regressors and nonlinear trends" by P.C.B. Phillips

Mynbaev, Kairat (2007): Comment on "Regression with slowly varying regressors and nonlinear trends" by P.C.B. Phillips.

Abstract

Standardized slowly varying regressors are shown to be $L_p$-approximable. This fact allows one to relax the assumption on linear processes imposed in central limit results by P.C.B. Phillips, as well as provide alternative proofs for some other statements.

• Item Type: MPRA Paper
• Language: English
• Keywords: slowly varying regressors; central limit theorem; $L_p$-approximability
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Aljan\v{c}i\'{c}, S., R. Bojani\'{c} \& M. Tomi\'{c} (1955) Deux th\'{e}or\`{e}mes relatifs au comportement asymptotique des s\'{e}ries trigonom\'{e}triques. \textit{Zbornik Radova Matemati\v{c}ki Institut SANU} 43, 15--26.

Mynbaev, K.T. (2001) $L_{p}$-approximable sequences of vectors and limit distribution of quadratic forms of random variables. \textit{Advances in Applied Mathematics} 26, 302--329.

Mynbaev, K.T. (2007) Tools for econometrician's toolbox: Working with deterministic regressors (unpublished).

Phillips, P.C.B. (2007) Regression with slowly varying regressors and nonlinear trends. \textit{Econometric Theory} 23, 557--614.

Seneta, E. (1985) Pravil$^{\prime}$no menyayushchiesya funktsii. (Russian) [Regularly varying functions] With appendices by Shiganov and Zolotarev. ``Nauka'', Moscow.