~16~ International Journal of Statistics and Applied Mathematics 2017; 2(6): 16-22 ISSN: 2456-1452 Maths 2017; 2(6): 16-22 © 2017 Stats & Maths www.mathsjournal.com Received: 03-09-2017 Accepted: 04-10-2017 Catherine Nyaboke Jomo Kenyatta University of Science and Technology, P.o Box 62,000-00200, Nairobi, Kenya George Otieno Orwa Jomo Kenyatta University of Science and Technology, P.o Box 62,000-00200, Nairobi, Kenya Mungatu Joseph Jomo Kenyatta University of Science and Technology, P.o Box 62,000-00200, Nairobi, Kenya Correspondence Catherine Nyaboke Jomo Kenyatta University of Science and Technology, P.o Box 62,000-00200, Nairobi, Kenya Time series modelling with application to Kenya’s inflation data comparison of ARIMA and ARCH models Catherine Nyaboke, George Otieno Orwa and Mungatu Joseph Abstract Throughout the world, most central bank policy initiatives have been aimed at achieving and maintaining price stability and the Central Bank of Kenya is no exception to this rule. This study attempts to find the best model that can be used to forecast inflation by comparing the ARIMA and ARCH models. The main focus of the study is compare the forecast performance of ARIMA and GARCH models in order to find the best fit model that can be used to model and forecast Kenya’s monthly inflation rates for the inflat ion data spanning from January 2005 to June 2017.This study used the Box-Jenkins methodology and GARCH approach in analysing the inflation rates data. The best model for ARIMA and GARCH were selected based on model selection criteria AIC, AICc and BIC. The one with the least AIC and BIC was selected as the best model. A comparison was then made between ARIMA (1, 1, 12) and GARCH (1, 1) models in order to determine which better to use in similar situation. The accuracy of GARCH and ARIMA models was compared using different statistical forecast evaluation criteria MAE, MSE, and MAPE efficiency. Results proved that the concluded that the forecast performance from GARCH (1, 1) model was greater than that from ARIMA (1, 1, 12) model. It was concluded that the ARIMA (1, 1, 12) model performs better than GARCH (1, 1) thus the ARIMA (1, 1, 12) is a better forecast model for inflation rate. The analysis of this study is carried out with the assist of R software. Presentation and explanations of results were aided by the use of graphs and tables. Keywords: Inflation, ARIMA, GARCH Introduction Inflation is the general rise in the average level of a group of prices in a country. Inflation creates a problem because the purchasing power of money falls as the price level rises. It imposes an opportunity cost on holders of money. Inflation retards economic growth because the economy needs a certain level of savings to finance investments which boosts economic growth. Inflation causes global concerns because it can distort economic patterns and can result in the redistribution of wealth when not anticipated. Inflation can also discourage investors within and without the country by reducing their confidence level in investments. This is because investors expect high possibility of returns so that they can make good financial decisions. The maintenance of price stability is one of the macroeconomic challenges that the Kenyan government has been facing since its independence which is now 54 years ago. Inflation Rate in Kenya averaged 10.44 percent from 2005 until 2016, reaching an all-time high of 45.98% in 1993, 31.50% in May of 2008 and a record low of -0.1 in 1964 (KNBS,2016). Inflation modelling is one of the most important research area in monetary planning. According to Kohn, (2005):“Nothing is more important to the conduct of monetary policy than understanding and predicting inflation. Achieving and maintaining price stability will be more efficient and effective the better we understand the causes of inflation and the dynamics of how it evolves”. Financial and economic models are heavily influenced by time, through both time resolution and time horizon. The resolution concept that signifies how densely data are recorded varying from seconds to years and time horizon looks at the length of time the data spans. Financial analysis usually involves a study of price movement, usually given over time, hence financial