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Deterministic Parameter Change Models in Continuous and Discrete Time
Author(s) -
Chambers Marcus J.,
Taylor A. M. Robert
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12456
Subject(s) - discrete time and continuous time , mathematics , discrete time stochastic process , autoregressive model , discrete choice , extant taxon , continuous modelling , discrete modelling , function (biology) , econometrics , statistics , discrete system , algorithm , mathematical analysis , stochastic differential equation , continuous time stochastic process , evolutionary biology , biology
We consider a model of deterministic one‐time parameter change in a continuous time autoregressive model around a deterministic trend function. The exact discrete time analogue model is detailed and compared to corresponding parameter change models adopted in the discrete time literature. The relationships between the parameters in the continuous time model and the discrete time analogue model are also explored. Our results show that the discrete time models used in the literature can be justified by the corresponding continuous time model, with a only a minor modification needed for the (most likely) case where the changepoint does not coincide with one of the discrete time observation points. The implications of our results for a number of extant discrete time models and testing procedures are discussed.