Estimation of missing data by using the filtering process in a time series modeling

Abstract

This paper proposed a new method to estimate the missing data by using the filtering process. We used datasets without missing data and randomly missing data to evaluate the new method of estimation by using the Box - Jenkins modeling technique to predict monthly average rainfall for site 5504035 Lahar Ikan Mati at Kepala Batas, P. Pinang station in Malaysia. The rainfall data was collected from the $1^{st}$ January 1969 to $31^{st}$ December 1997 in the station. The data used in the development of the model to predict rainfall were represented by an autoregressive integrated moving - average (ARIMA) model. The model for both datasets was ARIMA$(1,0,0)(0,1,1)_s$. The result checked with the Naive test, which is the Thiel's statistic and was found to be equal to $U=0.72086$ for the complete data and $U=0.726352$ for the missing data, which mean they were good models.