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PARAMETRIC AND NON‐PARAMETRIC MODELLING OF TIME SERIES — AN EMPIRICAL STUDY
Author(s) -
CHEN GEMAI,
ABRAHAM BOVAS,
BENNETT GREG W.
Publication year - 1997
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/(sici)1099-095x(199701)8:1<63::aid-env238>3.0.co;2-b
Subject(s) - parametric statistics , parametric model , autoregressive integrated moving average , computer science , mars exploration program , multivariate adaptive regression splines , semiparametric model , time series , smoothing spline , series (stratigraphy) , mathematics , regression analysis , statistics , machine learning , nonparametric regression , physics , astronomy , computer vision , bilinear interpolation , spline interpolation , paleontology , biology
Time series modelling methods can be loosely classified as (i) parametric methods and (ii) non‐parametric methods. Within a usually quite flexible but well structured family of models, the parametric modelling process typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. On the other hand, within a much less structured framework, different non‐parametric smoothing techniques are usually used to bring out the features of the observed time series, however, few serious and systematic attempts have been made to model time series non‐parametrically. We concentrate on a non‐parametric method based on multivariate adaptive regression splines (MARS). Parallel to the parametric modelling process, we systemize a non‐parametric modelling process as (i) model perception (where a very large spline expansion of a very large family of models is specified), (ii) model search (forward plus backward search to come up with a model), (iii) model diagnostic checking, and (iv) forecasting. The major difference between the MARS and the parametric methods is that the potential models for the MARS method form a family which is much larger than any family of parametric time series models, and the local structures found in the data are used to guide the search for a fitted model. Also, unlike most non‐parametric methods, MARS time series models can be analytically written down. In this paper, we present the results of an empirical comparison of parametric (ARIMA) and non‐parametric (MARS) time series modelling methods. Eight environmental time series are used for the comparison. © 1997 by John Wiley & Sons Ltd.