Comparing the applicability of box-jenkins arima methodology and arch/garch methodology among real data sets

Abstract

The main objective of this research is to compare the applicability of Box-Jenkins ARIMA methodology and ARCH/GARCH methodology among two real data sets. This study addresses the question of how to analyze time series data, identify structures, explain behaviours, model the identified structures and using the insight gained, to analyze and forecast values for the specific time series. For the purpose of this study the time series data included, the total kurakkan yield obtained from the Census department of Sri Lanka and the Money series obtained from the International Financial Statistics data source of Central bank of Sri Lanka. Each of the time series has its own characteristics and different methodologies were needed to require a deeper understanding of the time series data. The analysis of time series constitutes an important area of statistics. The kurakkan yield data set consisted of a few missing values. Three different approaches namely deterministic, stochastic and state space method were used to estimate these missing values. Out of the three approaches the state space method gave the best estimates. Once the missing values were fitted The complete series was used to analyze and then forecast values. To build the models and perform the analysis a statistical software called "Minitab" and the software package called "E-views" was used. The best model obtained was a seasonal ARIMA model with 2 non-seasonal AR terms and 2 non-seasonal MA terms with one seasonal differencing. The model was used to forecast values and the accuracy measure MAPE was 1.65% for the ARIMA model fitted, which.was the minimum value of MAPE for all the en-bloc methods mentioned above. The errors of this model were independent and identically distributed and followed a normal distribution. The main difference between the two time series data sets used for this study is that the money series obtained is a high-volatile data series which includes heteroscedasticity. For this data series the ARIMA methodology cannot be used since the data will not become stationary to fit a model. Therefore the ARCH/GARCH methodology was used to deal with the money data series. To build models for this series the software package called "E-views" has been used. Different ARCH models and GARCH models were fitted to this data set and the parameters were chosen so that the kurtosis value was closer to three. The best model was, a logarithmic transformation of the money series with one GARCH term and no ARCH terms. This model yielded a kurtosis value of 3.09. The main model for this data set did not include any AR or MA terms. However a very large number of data points are required to model the series with AR and MA terms in the main model. iii