Modelling Consumer Price Index (CPI) in Kenya for the Period 2000 to 2017 Using Autoregressive Integrated Moving Averages--ARIMA(p, d, q)

ABSRACT

The Kenyan CPI data for the period January 2000 to December 2017, obtained from the KNBS website, was the variable of interest, modelled as a time series variable. R was the package used for analysis. Descriptive statistics such as the mean, median, ACF, PACF, time series plots, histograms, lagged scatter plots and qqplots were employed to assess the non-stationarity of CPI after which appropriate smoothing techniques such as differencing were made use of to detrend the data. Formally, Augmented Dickey-Fuller test and Ljung-Box algorithm were used to test the hypothesis of stationarity. The tests conducted at 95% confidence level found the CPI to be non-stationary at lag one, thus necessitating smoothing. The CPI was smoothed by log transformation and then twice differenced to remain with white noise. Maximum Likelihood, AIC, BIC were the methods invoked to establish the parsimonious parameters of the model. The study fit a time series Box-Jenkins (ARIMA) model to the CPI for the period and provided 95% and 99% confidence interval for CPI forecasts for the next 12 years. Ljung-Box as the diagnostic test of goodness of fit was used to evaluate the fitted model ARIMA (1,2,2). The study found that in January 2030, the CPI will be 292.7646 on average. The 95% confidence interval is (214.2001, 371.3290) and the 99% confidence interval is (189.5134, 396.0158). The twelve-year prediction, chosen to coincide with Kenya Vision 2030, is of crucial use both to the government and policy makers as it will give insight into the future behaviour of inflation, one of the most important uses of CPI.

Keywords: ARIMA(p,d,q), ACF, PACF, ADF, Differencing, Maximum Likelihood, AIC, BIC, log-transformation, forecasting.