Robust estimation in time series, unit root test based on ranks and counting process
Valdério A. Reisen (UFES)
In this talk the following research topics will be discussed.
Robust estimation: It is well-known that the sample autocovariance is not
robust to the presence of additive outliers. Hence, the definition of an autocovariance estimator which is robust to additive outlier can be very useful for
time-series modeling. The robust autocovariance estimator proposed by Ma
and Genton (2000) is studied and applied to time series with different correlation structures such as short and long memory. Based on the robust autocorrelation function, a robust estimator of the parameter d in ARFIMA(p, d, q)
is proposed. Some simulations are used to support the use of this method
when a time series has additive outliers.
DF unit root test based on ranks: In this subject, the classical Dickey-Fuller
(DF) test will be studied in the context of unit root time series with outliers.
Based on the ranks of the observations, a robust DF test is proposed. The test
is robust against outliers observations. The asymptotic distribution of the
test is obtained.
Counting process: The Integer-valued Autoregressive Moving Average (INARMA) models have suggested modeling observed count time series. This
research is concerned with the problem of modeling INAR processes under
seasonal, unit root and long memory properties.