TY - JOUR
T1 - Robustness of Zero Crossing Estimator
AU - Goto, Yuichi
AU - Taniguchi, Masanobu
N1 - Funding Information:
The authors are grateful to the editor and two referees for their instructive comments and kindness. The first author Y.G. thanks Professor Haruyoshi Mita and Doctor Fumiya Akashi for their encouragements and comments. The first author Y.G. also grateful to Professor Hans Rudolf Künsch for sharing dataset with us. The second author M.T. was supported by the Research Institute for Science & Engineering of Waseda University and JSPS Grant-in-Aid: Kiban(S)(18H05290).
Publisher Copyright:
© 2019 John Wiley & Sons Ltd
PY - 2019
Y1 - 2019
N2 - Zero crossing (ZC) statistic is the number of zero crossings observed in a time series. The expected value of the ZC specifies the first-order autocorrelation of the processes. Hence, we can estimate the autocorrelation by using the ZC estimator. The asymptotic consistency and normality of the ZC estimator for scalar Gaussian processes are already discussed in 1980. In this article, first, we derive the joint asymptotic distribution of the ZC estimator for ellipsoidal processes. Next, we show the variance of the ZC estimator does not attain the Cramer–Rao lower bound (CRLB). However, it is shown that the ZC estimator has robustness when the process is contaminated by an outlier. In contrast with this, we observe that the quasi-maximum likelihood estimator (QMLE) attains the CRLB. However, we can see that QMLE is sensitive for the outlier.
AB - Zero crossing (ZC) statistic is the number of zero crossings observed in a time series. The expected value of the ZC specifies the first-order autocorrelation of the processes. Hence, we can estimate the autocorrelation by using the ZC estimator. The asymptotic consistency and normality of the ZC estimator for scalar Gaussian processes are already discussed in 1980. In this article, first, we derive the joint asymptotic distribution of the ZC estimator for ellipsoidal processes. Next, we show the variance of the ZC estimator does not attain the Cramer–Rao lower bound (CRLB). However, it is shown that the ZC estimator has robustness when the process is contaminated by an outlier. In contrast with this, we observe that the quasi-maximum likelihood estimator (QMLE) attains the CRLB. However, we can see that QMLE is sensitive for the outlier.
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U2 - 10.1111/jtsa.12463
DO - 10.1111/jtsa.12463
M3 - Article
AN - SCOPUS:85065032944
VL - 40
SP - 815
EP - 830
JO - Journal of Time Series Analysis
JF - Journal of Time Series Analysis
SN - 0143-9782
IS - 5
ER -