Analysis of seasonal time series with Missing observations: A case of harvesting of fish in Lake Victoria Kenya.

Abstract

ABSTRACT Time series is a measured observation recorded with time. This statistical procedure is applicable in many fields of study including engineering and economics. The process of collecting data sometimes faces a lot of challenges that may arise due to defective working tools, misplaced or lost records and errors that are prone to occur. These problems can be addressed by estimating the missing values so as to enable one to proceed with the analysis and forecasting. The most commonly used approaches include the use of autoregressivemoving average models developed by Box Jenkins, use of extrapolation or interpolation under regression analysis and use of state space models where data is considered as a combination of level, trend and seasonal components. This project intends to use the most appropriate method of estimating missing values by using the direct method of imputation. Incomplete secondary data obtained from the Ministry of fisheries and Development, together with the Kenya Marine and Fisheries Research Institute are to be used to estimate the gap left just before, during and immediately after the post election violence of the year 2007/2008, a time when data could not be obtained and/or recorded. The original time series data when analysed produced a SARIMA model (0,1,1)(2,0, 0h2 as the best candidate for the lower segment. SARIMA (0,1,2)(0,0,1)12 was produced for the upper segment using autoarima function in R package. The missing data were estimated using forecast from the lower segment which was extended to the in sample forecast in the upper segment. The regression test between predicted and the original values in upper segment proves strong positive relationship indicating high level of accuracy on predictability of the model used.