Analysis of Seasonal Time Series with Missing Observations of Fish Harvesting in Lake Victoria, Kenya

Abstract

Time series is a measured observation recorded with time. 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. The most commonly used approaches to estimate missing values include the use of autoregressive-moving 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 paper 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 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 analyzed produced a SARIMA model (0, 1, 1) (2, 0, 0)12 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 the strong positive relationship indicating high level of accuracy on predictability of the model used.

Keywords: Stationary and Stochastic process, Auto-covariance and Autocorrelation Function, Partial Autocorrelation Function, correlogram, Moving Average process, Autoregressive process.