Bilineární model pro časové řady

Čorejová, Katarína

Title: A bilinear model for time series Author: Katarína Čorejová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The bilinear model is used to describe the structure of non-linear time series. In this thesis, we discuss the bilinear model BL(P,0,P,1). The main goal is to derive conditions for the first-order and the second-order stationarity, to present its moment and covariance structure, to derive the condition for invertibility and to discuss the method of estimating parameters. The theoretical part of this thesis also presents a test of linearity, which enables to test the presence of the bilinear effect in a given time series. In the following simulation study, we apply the theory to several generated time series from the BL(1,0,1,1) model. Depending on the chosen parameters and length of the generated time series, we examine the accuracy of parameter estimation, the empirical level and the empirical power of the test of linearity. Keywords: time series, bilinear model, stationarity, invertibility, parameter esti- mation, linearity testing. 1

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