Imputation of incomplete non- stationary seasonal time series data

Abstract

Missing observations in time series data is a common problem that occurs due to many reasons. In order to estimate missing observation accurately, it is necessary to select an appropriate model depending on the type and nature of the data being handled so as to obtain the best possible estimates of missing observations.  The objective of the study was to examine and compare the appropriateness of Box Jenkins models and direct linear regression in imputing missing observation in non stationary seasonal time series data. The study examined Box Jenkins techniques SARIMA and ARIMA models in imputing non stationary seasonal time series specifically in situations where missing observation are encountered towards the end of the series. Besides that,  direct linear regression have also been proposed in  imputing missing observations when seasonality has been relaxed by rearranging the time series data in periods and grouping observations which corresponds to each other from each period  together and then analyze each as a single series. From the study it was observed that it is easy to impute missing observations using direct linear regression in non-stationary time series data when seasonality has been relaxed by rearranging the data in periods compared to traditional Box Jenkins models SARIMA and ARIMA models. Also direct linear regression proved, more accurate and reliable compared to Box-Jenkins techniques. So Based on the finding, the proposed direct linear regression approach can be used in imputing missing observations for non stationary series with seasonality by first rearranging the data in periods.

KEYWORDS: Imputation, SARIMA, ARIMA models and Direct Linear regression (L.REG).