Title: Properties of change point estimates for short time series with missing data
Authors: Daniela Jaruskova - Czech Technical University, Faculty of Civil Engineering (Czech Republic) [presenting]
Abstract: A time series of independent normally distributed random variables or vectors is observed and its mean shifts from one unknown value to a different unknown value at an unknown time point. For a confidence intervals construction an asymptotic distribution is usually applied. There exist two formulations of the problem. In the first, the change point is an integer and its estimator maximizes a certain two-sided random walk. In the second, the change point is modelled as a fraction of time and the size of the change tends to zero at a certain rate. Sometimes in applications the studied series are relatively short. The first question may be which of these two approaches is more accurate. Moreover, in multiple time series analysis we often encounter a situation where in several components the data are missing while they are present in the remaining components. One may ask whether it is better to cut off a time interval where the data are missing or to replace them by a constant, e.g. by an average. The answers obtained from a simulation study are rather unexpected.