Odhady parametrů useknutých časových řad

Flimmel, Samuel

In some situations we cannot observe the original time series and instead, we record only binary data which express whether the values of the original series exceeded a certain threshold or not. The thesis deals with estimation of characteristics of the original series constructed from the binary (so called clipped or hard-limited) data, in particular in Gaussian ARMA models. We summarize some basic characteristics of the clipped series and describe their relation to the original ones. Some practical examples are provided as well. The estimation of parameters in AR(p) model is shown for the case of zero threshold. Using a similar approach, an estimator of the MA(1) model parameter is proposed and its properties are studied with emphasis on asymptotic variance. Subsequently, we propose an estimation procedure for AR(p) and MA(1) models with unknown (non-zero) threshold. The behaviour of our estimators is investigated in a simulation study, which provides a comparison with estimators constructed from the original data. Finally, a real data analysis is presented for an illustration. Powered by TCPDF (www.tcpdf.org)

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