Norming rates and limit theory for some time-varying coefficient autoregressions

A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random-walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its AR coefficient....

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Main Authors: LIEBERMAN, Offer, Peter C. B. PHILLIPS
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Language:English
Published: Institutional Knowledge at Singapore Management University 2014
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Online Access:https://ink.library.smu.edu.sg/soe_research/1835
https://ink.library.smu.edu.sg/context/soe_research/article/2834/viewcontent/NormingRatesLimitTheoryTime_varyingCoefficientAutoregressions_pp.pdf
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spelling sg-smu-ink.soe_research-28342020-01-15T02:54:58Z Norming rates and limit theory for some time-varying coefficient autoregressions LIEBERMAN, Offer Peter C. B. PHILLIPS, A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random-walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its AR coefficient. Consistency of the quasi-maximum likelihood estimator of the parameters in this model is established, the behaviours of the score and Hessian functions are analysed and test statistics are suggested. A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian function standardization. A large family of unit root models with stationary and explosive alternatives is characterized within the similarity class through the asymptotic negligibility of a certain quadratic form that appears in the score function. A variant of the stochastic unit root model within the class is studied, and a large-sample limit theory provided, which leads to a new nonlinear diffusion process limit showing the form of the drift and conditional volatility induced by sustained stochastic departures from unity. The findings provide a composite case for time-varying coefficient dynamic modelling. Some simulations and a brief empirical application to data on international Exchange Traded Funds are included. Copyright (c) 2014 Wiley Publishing Ltd 2014-11-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/1835 info:doi/10.1111/jtsa.12083 https://ink.library.smu.edu.sg/context/soe_research/article/2834/viewcontent/NormingRatesLimitTheoryTime_varyingCoefficientAutoregressions_pp.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Autoregression Consistency Nonlinear diffusion Non-stationarity Similarity Small-sigma approximation Stochastic unit root Time-varying coefficients Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Autoregression
Consistency
Nonlinear diffusion
Non-stationarity
Similarity
Small-sigma approximation
Stochastic unit root
Time-varying coefficients
Econometrics
spellingShingle Autoregression
Consistency
Nonlinear diffusion
Non-stationarity
Similarity
Small-sigma approximation
Stochastic unit root
Time-varying coefficients
Econometrics
LIEBERMAN, Offer
Peter C. B. PHILLIPS,
Norming rates and limit theory for some time-varying coefficient autoregressions
description A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random-walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its AR coefficient. Consistency of the quasi-maximum likelihood estimator of the parameters in this model is established, the behaviours of the score and Hessian functions are analysed and test statistics are suggested. A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian function standardization. A large family of unit root models with stationary and explosive alternatives is characterized within the similarity class through the asymptotic negligibility of a certain quadratic form that appears in the score function. A variant of the stochastic unit root model within the class is studied, and a large-sample limit theory provided, which leads to a new nonlinear diffusion process limit showing the form of the drift and conditional volatility induced by sustained stochastic departures from unity. The findings provide a composite case for time-varying coefficient dynamic modelling. Some simulations and a brief empirical application to data on international Exchange Traded Funds are included. Copyright (c) 2014 Wiley Publishing Ltd
format text
author LIEBERMAN, Offer
Peter C. B. PHILLIPS,
author_facet LIEBERMAN, Offer
Peter C. B. PHILLIPS,
author_sort LIEBERMAN, Offer
title Norming rates and limit theory for some time-varying coefficient autoregressions
title_short Norming rates and limit theory for some time-varying coefficient autoregressions
title_full Norming rates and limit theory for some time-varying coefficient autoregressions
title_fullStr Norming rates and limit theory for some time-varying coefficient autoregressions
title_full_unstemmed Norming rates and limit theory for some time-varying coefficient autoregressions
title_sort norming rates and limit theory for some time-varying coefficient autoregressions
publisher Institutional Knowledge at Singapore Management University
publishDate 2014
url https://ink.library.smu.edu.sg/soe_research/1835
https://ink.library.smu.edu.sg/context/soe_research/article/2834/viewcontent/NormingRatesLimitTheoryTime_varyingCoefficientAutoregressions_pp.pdf
_version_ 1770572937819062272