Scientific Monographs, Bank of Finland
No E:27/2004:
On robust ESACF identification of mixed ARIMA models
Heikki Hella ()
Abstract: Statistical data sets often contain observations that
differ markedly from the bulk of the data. These outlying observations,
‘outliers’, have given rise to notable risks for statistical analysis and
inference. Unfortunately, many of the classical statistical methods, such
as ordinary least squares, are very sensitive to the effects of these
aberrant observations, ie they are not outlier robust. Several robust
estimation and diagnostics methods have been developed for linear
regression models and more recently also for time series models.
The
literature on robust identification of time series models is not yet very
extensive, but it is growing steadily. Model identification is a ‘thorny
issue’ in robust time series analysis (Martin and Yohai 1986). If outliers
are known or expected to occur in a time series, the first stage of
modelling the data should be done using robust identification methods.In
this thesis, the focus is on following topics: 1. The development of a
robust version of the extended autocorrelation function (EACF) procedure of
Tsay and Tiao (1984) for tentative identification of univariate ARIMA
models and comparison of non-robust and robust identification results. 2.
Simulation results for the sample distributions of the single coefficients
of the extended sample autocorrelation function (ESACF) table, based on
classic and robust methods, both in outlier-contaminated and outlier-free
time series. 3. Simulation results for two basic versions of the sample
standard error of ESACF coefficients and the results of the standard error
calculated from simulation replications.
Robust designing concerns two
parts of the ESACF method: iterative autoregression, AR(p), and an
autocorrelation function to obtain less biased estimates in both cases.
Besides the simulation experiments, robust versions of the ESACF method
have been applied to single generated and real time series, some of which
have been used in the literature as illustrative examples.
The main
conclusions that emerge from the present study suggest that the robustified
ESACF method will provide a) A fast, operational statistical system for
tentative identification of univariate, particularly mixed ARIMA(p, d, q),
models b) Various alternatives to fit the robust version of AR(p) iteration
into a regression context and use of optional robust autocorrelation
functions to handle both isolated and patchy outliers c) Robust procedures
to obtain more normal-shape sample distributions of the single coefficient
estimates in the ESACF twoway table d) The option of combining OLS with a
robust autocorrelation estimator.
Simulation experiments of robust
ESACF for outlier-free series show that, since the robust MM-regression
estimator is efficient also for outlier-free series, robust ESACF
identification can always be used with confidence. The usefulness of the
method in testing for unit roots is obvious, but requires further
research.
Keywords: robust tentative identification; robust extended autocorrelation function; outliers; robust regression estimation; Monte Carlo simulations; time series models; (follow links to similar papers)
JEL-Codes: C15; C22; (follow links to similar papers)
162 pages, January 1, 2004
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