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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 are given in Section 3. When the forecasts from these models were validated, Double Exponential Smoothing model performed better than the ARIMA model.

Tourism is one of Kenya’s major foreign exchange earners. This greatly depends on the arrival of various groups of tourists. The forecast of tourists’ arrivals is important since it would enable the tourism related industries like airlines, hotels and other stakeholders to adequately prepare for any number of tourists at any future date. In this paper, an attempt has been made to forecast tourists’ arrivals using statistical time series modeling techniques―Double Exponential Smoothing and Auto-Regressive Integrated Moving Average (ARIMA). [

Then data on tourists’ arrival in Kenya were obtained from the Ministry of East African Affairs, Commerce and Tourism, Department of Tourism. Tourists’ arrival for the period 1995 to 2008 was used for model fitting, and data for the remaining periods from 2009 to 2012 were used for model validation. The analysis was carried out using R-language, Excel and Minitab version 16.1.1.

Once the presence of trend is detected in the data, smoothing of the time series data follows. Various smoothing techniques as discussed by [

For the series_{ }

The size of

The form of the model is

where

The pair of

When time series data exhibit seasonality, Triple Exponential Smoothing method is the most recommendable. It incorporates three smoothing equations; first for the level, second for trend and third for seasonality.

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 [

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 [

An estimate of the coefficients of the model is obtained by modified least squares method or the maximum likelihood estimation method suitable to the time series data.

Diagnostic checks help to determine if the anticipated model is adequate. At this stage, an examination of the residuals from the fitted model is done and if it fails the diagnostic tests, it is rejected and we repeat the cycle until an appropriate model is achieved.

The ARIMA model is obtained by taking

Equation (3) is referred to as the ARIMA

Different combinations of AR and MA individually yield different ARIMA models [

where

where

Sl. No. | Year | Observed tourists’ arrival (‘000) |
---|---|---|

1 | 1995 | 973.6 |

2 | 1996 | 1003.0 |

3 | 1997 | 1000.6 |

4 | 1998 | 894.3 |

5 | 1999 | 969.3 |

6 | 2000 | 1036.5 |

7 | 2001 | 993.6 |

8 | 2002 | 1001.5 |

9 | 2003 | 1146.2 |

10 | 2004 | 1360.7 |

11 | 2005 | 1479.0 |

12 | 2006 | 1600.7 |

13 | 2007 | 1816.8 |

14 | 2008 | 1203.2 |

15 | 2009 | 1490.4 |

16 | 2010 | 1609.1 |

17 | 2011 | 1822.9 |

18 | 2012 | 1873.8 |

Source: Ministry of East African affairs, Commerce and Tourism: Department of Tourism (Kenya).

in the number of tourists in the year 2008 followed by an increasing trend from the year 2009 to 2012. For smoothing the data, Holt’s Double Exponential Smoothing was used. Various combinations of

where

Using R-language for different values of

The estimation of the model parameters was done by maximum likelihood estimation technique. The fitted model was then used to forecast tourists’ arrival from 2009 to 2012. The forecast values are shown in

S. No. | Year | Observed tourists’ arrival (‘000) | Forecast of tourists’ arrival |
---|---|---|---|

Double exponential model | |||

1 | 2009 | 1490.4 | 1560.936 |

2 | 2010 | 1609.1 | 1660.595 |

3 | 2011 | 1822.9 | 1760.254 |

4 | 2012 | 1873.8 | 1859.912 |

Sl. No. | Year | Observed tourists’ arrival (‘000) | Forecast of tourists’ arrival |
---|---|---|---|

ARIMA (1, 1, 1) model | |||

1 | 2009 | 1600.7 | 1393.607 |

2 | 2010 | 1816.8 | 1497.643 |

3 | 2011 | 1203.2 | 1566.134 |

4 | 2012 | 1490.4 | 1619.997 |

Sl. No. | Year | Observed tourists’ arrival (‘000) | Forecast of tourists’ arrival | |
---|---|---|---|---|

Double exponential model | ARIMA (1, 1, 1) model | |||

1 | 2009 | 1490.4 | 1560.936 | 1393.607 |

2 | 2010 | 1609.1 | 1660.595 | 1497.643 |

3 | 2011 | 1822.9 | 1760.254 | 1566.134 |

4 | 2012 | 1873.8 | 1859.912 | 1619.997 |

MAPE | 3.028 | 10.263 | ||

RMSE | 54.186 | 195.023 |

Performance evaluation measures MAPE and the RMSE were obtained for the forecasted tourists’ arrivals for the years 2009 to 2012.

The comparison of the two models based on MAPE and RMSE is as given in