ANALYSIS OF SPATIAL TIME SERIES BY THE STATE SPACE MODEL AND KALMAN FILTER APPROACH

• Main Author: Rizky Kurniawan, Muhammad
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65340
• Institution: Institut Teknologi Bandung

The GSTARMA (generalised space-time autoregressive moving average) is a model that can be used to model observed values of an endogenous or output variable in several locations if the observed value for a location depends on the observed values and errors of neighbouring locations. This model can be modified to include the effects of an exogenous or input variable to form the GSTARMAX (generalised space-time autoregressive moving average-exogenous) model. As a space-time series model which includes input and output variables at each modelled location, space-time series models are essentially vector time series models, and the GSTARMA-X model is no exception. The GSTARMA-X model can be thought of as a VARMA-X (vector autoregressive moving average-exogenous) model, and therefore be analysed using methods typically used in analysing vector time series, such as the state space model approach and the Kalman filter. In this thesis, an iterative three-stage method to analyse space-time series by treating it as a VARMAX model is proposed. The stages are implemented in analysing both artificially generated data that is known to follow a GSTARMA-X model and real data whose model must first be identified. The artificial data were generated under three types of GSTARMA-X models: stationary and invertible model, stationary and noninvertible model, and nonstationary and invertible model. The real data of interest are the number of active COVID-19 cases in Bandung City between July 22nd, 2021 and March 1st, 2022 under the influence of number of vaccinated people, and the number of confirmed COVID-19 cases in Java Island between January 1st, 2021 and October 31st, 2021 under the influence of the change in workplace mobility. The analysis of the artificial data concluded that the Kalman filter is very good at modelling nonstationary processes, but very poor at forecasting noninvertible processes. The analysis of the real data shown that the number of active COVID-19 cases in Bandung City is modelled equally well by GSTARMA-X(11, 01)-(01, 11) and GSTARMA-X(11, 11)-(01, 11) models, while number of confirmed COVID- 19 cases in Java Island is best modelled by the GSTARMA-X(11, 11)-(01, 21). However, while the errors of the models are relatively small, the errors of each model do not pass diagnostic tests.