Robustness of Zero Crossing Estimator

Abstract

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.

Re-Evaluation of World Population Figures: Politics and Forecasting Mechanics

“…In this study, ARMA/ARIMA is developed and also examines the performance of the model using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) (Ben Amor, Boubaker, & Belkacem, 2018;Goto & Taniguchi, 2019). As postulated by Box and Jenkins in the second half of the 1970s (Zhang et al, 2018), time series model had an autoregressive and moving average part (Gonçalves Mazzeu, Veiga, & Mariti, 2019).…”