STATISTICAL MODELS FOR FORECASTING TOURISTS’ ARRIVAL IN KENYA
Albert Orwa Akuno1 Charles Wambugu Mwangi2 Lawrence Areba Bichanga3 Michael Oduor Otieno4
Department of Mathematics, Egerton University, Egerton Kenya.
Abstract
In this paper, an attempt has been made to forecast tourists’ arrival using statistical time series modeling techniques-Double Exponential Smoothing and the Auto-Regressive Integrated Moving Average (ARIMA). It is common knowledge that forecasting is very important in making future decisions such as ordering replenishment for an inventory system or increasing the capacity of the available staff in order to meet expected future service delivery. The methodology used is given in section 2 and the results, discussion and conclusion…show more content… It incorporates three smoothing equations; first for the level, second for trend and third for seasonality.
II Auto-Regressive Integrated moving Average (ARIMA MODEL)
(i) Model identification
According to Box and Jenkins two graphical procedures are used to access the correlation between the observations within a single time series data. According to [3], these devices are called an estimated autocorrelation functions and the estimated partial autocorrelation function. These two procedures measures statistical relationships within the time series data. Summarization of statistical correlation within the time series data is the other step in the identification. Box and Jenkins suggests a whole family of ARIMA models from which we may choose.
In choosing the model that seems appropriate we use the estimated ACF and PACF. This is due to the basic idea that every ARIMA model will have unique ACF and PACF associated with it. Thus we select the model whose theoretical ACF and PACF resembles the anticipated ACF and PACF of the time series data [4].
(ii)…show more content… No. Year Observed Tourist arrival (‘000) Forecast of Tourists arrival Double exponential model
1 2009 1490.4 1560.934
2 2010 1609.1 1660.592
3 2011 1822.9 1760.25
4 2012 1873.8 1859.908
MAPE 3.027711
RMSE 54.1861
(ii) ARIMA model
The stationary check of the data based on Figure 1 revealed that it is non – stationary. The data was made stationary by taking the first order difference ( ). The time plot of the differenced data is shown in Fig 2.
Fig 2: Plot of differenced tourists’ arrival data
Table 3: Forecast of tourists arrival in Kenya ARIMA (1, 1, 1) models
Sl. No. Year Observed Tourist arrival (‘000) Forecast of Tourists arrival ARIMA(1,1,1) model
1 2006 1600.7 1534.95
2 2007 1816.8 1579.84
3 2008 1203.2 1627.01
4 2009 1490.4 1673.71
MAPE 16.95
RMSE 282.26
Using R – language for different values of and , various ARIMA models were fitted and the best model was chosen on the basis of minimum value of the selection criteria, that is, minimum Akaike Information Criteria (AIC) whose formula is given in Equation (4). In this way, ARIMA (1, 1, 1) was found to be the best model. The fitted model is given