AR(1)-GARCH(1,1) MORTALITY MODEL

• Main Author: Dara Nurina Firdaus, Fika
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/34871
• Institution: Institut Teknologi Bandung

Mortality is an event that could affect the size of population. The number of mortality is different every year. The changes in the number of mortality can be measured by mortality rate. Central Death Rate (CDR) is a mortality rate which can be used to determine the changes in the size of a population. In modeling log CDR, there are two considerations, which are the behavior of log CDR and the behavior of log CDR volatility. Based on that, AR(1)-GARCH(1,1) model, which can capture the dynamics of log CDR and log CDR volatility, was chosen. To analyze the ability of AR(1)-GARCH(1.1) model in capturing the behavior of log CDR, the empirical properties of log CDR will be determined. The empirical properties of log CDR are autocorrelation, kurtosis, volatility clustering and persistence of volatility. Moreover, prediction of log CDR and VaR of log CDR will be carried out by using a model AR(1)-GARCH(1.1) and the accuracy test will also be carried out. The Log CDR data of the United States, Japan, Sweden, Belgium, Portugal and the Czech Republic ages 35, 45, and 55 years with the time period 1950 to 2012 was chosen for this thesis. The country selected due to the respect to the ranking index of GDP. The United States and Japan represent the country with high GDP index, Sweden and Portugal represent the country with intermediate GDP index, and Belgium and the Republic of Czech represent a country with low GDP index. As for the results, AR(1)-GARCH(1.1) model showed a good ability to capture the behavior of autocorrelation and volatility clustering of log CDR from the countries with intermediate GDP index. AR(1)-GARCH (1.1) model could also captured fairly the behavior of kurtosis of the log CDR from the countries with intermediate and low GDP index. Persistence of volatility measure was decreased along with the increase in the lag time for all log CDR data. Prediction of log CDR through AR(1)-GARCH(1.1) model was fairly accurate since the value of Mean Square Error (MSE) was small. VaR log CDR prediction was also fairly accurate according to the coverage probability and backtesting methods. Therefore, AR(1)-GARCH(1.1) model was good enough to model the log CDR data.