Modelling Tea Production in Kenya using the Linear Regression with GARCH error term

Abstract

Tea is a popular drink globally and contributes to 4% of Kenya’s annual GDP. The continued variation
in Tea production has prompted numerous research. Some researchers have linked the variation to climatic changes while others to soil fertility dynamics. In the present research, we link the tea production changes to climatic variables. Thus, we attempt to establish the linear regression equation modeling relationship between trends of tea production and climatic variables, namely NDVI, minimum humidity, maximum humidity, rainfall, minimum temperature, maximum temperature, and solar radiation between January 2007 and December 2015. We have also presented the effect of volatility and seasonality of climatic variables on tea production in Kenya. The effect of volatility and seasonality is investigated via the GARCH model, which is used to estimate linear regression error terms for tea production using data from major tea zones in Kenya, namely Embu, Kakamega,
Kericho, Kisii, Meru, and Nyeri. The demonstration in the research via the already established GARCH model is based on a combination of garchorder(2,2) and armaorder(1,1) that seasonality affects tea production with climatic variables as independent variables. We compared the analysis results among the data obtained from different major tea zones in Kenya. The results summarized in tables show that in the presence of seasonality larger error term exists than in the absence of seasonality for most tea zones. The AIC and BIC in most of the tables are lower in cases of deseasonalized data. The loglikelihood in most cases is also higher in cases on deseasonalized data. Comparison of deviation between tea production value estimated using data and constructed tea production based
on linear regression equation shows that the seasonal data exhibits higher deviation than deseasoned data in most cases. The effect of seasonality on serial correlation is also evident. There exists serial correlation for most cases of deseasoned data compared to when the data has seasonality. A future study may consider estimating linear regression error terms amidst volatility effect on seasonal data for different GARCH models