Chapter 7 compares the performance of the different analytic models developed in Chapter 5 and Chapter 6 and concludes upon the aims and objectives of the thesis.
5.5 BSM Forecasting for the 13 Countries to the 31 Chinese Provinces
Number of forecasts <10% 49 Number of forecasts >10% <20% 61 Number of forecasts >20% <30% 66 Number of forecasts >30% <50% 124 Number of forecasts >50% 94
5.5
BSM Forecasting for the 13 Countries to the 31 Chinese
Provinces
5.5.1
Introduction
The basic structural time-series (BSM) technique has been widely used in more recent years. The structural time-series model can also represent causal relationships among variables, using independent variables, causal structural modelling (CSM) is sometimes referred to as structural time series modelling (STSM). Here the term CSM will be used below. Turner and Witt (2001a) compared BSM and CSM models to examine the relationships between a set of explanatory variables for disaggregated tourist flows (holidays, business visits and VFR). Their study showed the potential for both models to forecast tourism arrivals accurately.
A study by Black et al., (2006) on forecasting of tourism in Scotland has demonstrated the ways in which an integrated model, combining the structural time- series model (CSM) and quantifiable forecasts from a computable general equilibrium (GGE) model, can be used to examine combinations of the events and forecasting future tourism demand. It was noted by Blake et al., (2006), that the CSM has an established tradition of providing forecasts of tourism demand at both the sub-
national and national levels (for example, Gonzalez and Moral, 1996, Greenidge, 2001, Papatheodorou and Song, 2005).
Preez and Witt (2003) noted that in previous research in tourism forecasting where the accuracy of short-term forecasts generated by multivariate models (incorporating explanatory variables) is compared with the accuracy of forecasts generated by univariate models, that the extra complexity of multivariate tourism forecasting models does not necessarily lead to an improvement in performance. For example, the univariate ARMA model (Garcia-Ferrer and Queralt, 1997) is shown to outperform the causal structural time series model (CSM); and the ‘no change’ (random walk) model (Song and Witt, 2000, Kulendran and Witt, 2001) has outperformed the error correction model. However, the study by Smeral and Wǜger (2005), in the case of Austria, concludes that complexity does matter in designing short-term tourism forecast modelling, and that variations in tourism demand can be influenced by the combination of complex data adjustment methods, and adequate model structures will significantly improve forecast results, and the simpler approaches are decidedly outperformed by complex methods.
The BSM was introduced by Harvey and Todd (1983). The model assumes that a time-series possesses some structure, which is the sum of independent trend, seasonal and irregular components. The BSM is well-know in the literature of tourism demand forecasting for its approach in decomposing the data into components and using the Kalman filter to evaluate the function. Often the components of a time series are not fixed but are stochastic by nature and the basic structural model consists of components including stochastic trend, cyclical change, seasonality and an error term. The trend component changes from the previous period by the amount of the slope, where the slope allows for stochastic changes from period to period. The model can allow for seasonal change but can also be used on non-seasonal data. The model manages the issue of non-stationarity without the need for differencing.
As explained by Harvey and Todd (1983), the main identification tools in the Box- Jenkins approaches are the functions of autocorrelation and partial auto correlation. However, these counterparts are not always very informative, in particular when dealing with small samples. Furthermore, a series with differencing adds additional
difficulties and the risk of over-differencing. Consequently, they suggested formulating models directly in terms of trend cycle, seasonal and irregular components.
Turner and Witt (2001b) argue that univariate structural time series models are capable of providing reasonably accurate forecasts. However, their study could not show improvement in the accuracy of BSM when extended to include explanatory variables (CSM).
The BSM is represented as yt =µt+πt+ct +αt where = µ is the stochastic trend component, πt the seasonal component, ct the cyclical component, and αt the error term.
The trend component changes from the previous period by the amount of the slope
1 − t β such that: t t t t µ 1 β 1 α1 µ = −+ − + ,
Where β the slope, is also stochastic and changes from period t to t−1as follows: t
t
t β 1 α2
β = − + .
The seasonal component πis additive and totals to zero over s seasons in the year as follows: . 1 1 t j t s j t π ω π = − − + −
∑
.The parameters αt,α1t,α2t and ωt are all stochastic, independent, white noise error terms with expected values of zero.
In this study the BSM forecasts were obtained using STAMP software. The cyclical component comprises a damping factor p in the range 0<p>1, λas the frequency in (radians) in the range 0≤λ≤π and two mutually uncorrelated disturbances K with zero mean and a common variance. There may be two additional cycles of the same form incorporated into the model.
A first-order auto regressive AR (1) process is also available. The auto regressive component acts as a limiting case on the stochastic cycle whenλis equal to φor .π It is not a limiting case in CSM modelling.
5.5.2
Results of BSM Forecasting for the 13 Countries to the 31
Chinese Provinces
Each BSM model has the slope, level and irregular components tested using the q- ratio of the variance of each component to the largest variance of these components. The component with the largest variance will have a q-ratio of unity. Components with no variance will have q-ratio of zero, indicating absence of that component in the data.
The independence of the error term is tested, using the Q statistic which follows the χ2 distribution for:
0
H : Independent error terms,
1
H : Error terms are not independent.
The cycle is tested by comparison of the amplitude of the cycle with the level of the trend. This gives an indication of its relative importance. When the cycle is deterministic, but stationary, a joint significance χ2 test which is the same as the seasonal test is also reported.
Table 5.1.9 shows that Japan has the lowest overall MAPE average of 28.3%, and Russia has the highest overall MAPE average of 48.7%. Total MAPE average for the 13 source countries to the 31 Chinese regions is 35.6%.
Table 5.1.9 MAPE for BSM forecast for all countries to the 31 Chinese provinces 2006 - 2007
Jap Kor M'sia S'pore Thai USA Can UK Fra G'many Rus Aust Phi T/A Beijing 16.4 9.3 15.6 32.9 18.1 20.8 35.5 9.9 13.7 28.9 15.3 18.9 51.3 22.0 Tianjin 12.4 40.5 NC 17.6 97.4 9.8 NC 11.4 18.3 8.6 82.1 21.1 NC 31.9 Hebei 9.4 9.7 49.2 70.3 61.6 51.1 32.6 55.7 61.1 34.0 16.5 54.8 62.9 43.8 Shanxi 72.0 12.1 48.8 43.1 74.4 69.7 76.8 64.0 63.6 61.4 56.5 73.0 85.8 61.6 Inner Mongolia 36.3 47.2 30.2 68.5 NC 22.6 24.9 44.8 74.9 NC 8.2 34.8 86.0 43.5 Liaoning 4.0 21.6 11.4 2.2 10.8 15.7 23.5 28.6 30.2 13.2 69.8 17.5 25.3 21.1 Jilin 14.3 56.2 NC 52.0 67.8 9.8 157.5 NC 40.5 66.7 49.0 15.4 68.2 54.3 Helongjiang 88.6 27.6 33.7 13.1 62.1 9.5 18.9 48.1 33.0 27.5 60.8 25.7 50.7 38.4 Shanghai 28.8 23.6 12.6 15.5 48.6 39.2 4.9 4.4 18.8 48.3 14.7 19.7 35.7 24.2 Jiangsu 11.9 32.3 31.7 7.0 40.8 16.8 14.7 23.5 14.0 27.0 62.6 29.8 41.9 27.2 Zhejiang 5.0 31.1 18.3 8.8 35.9 1.8 36.1 5.7 9.4 27.5 46.8 11.2 3.9 18.6 Anhui 18.0 42.1 19.4 13.3 31.4 13.8 20.4 41.1 15.0 3.5 68.6 31.6 46.1 28.0 Fujian 9.8 67.4 1.5 16.5 84.7 23.9 39.7 13.8 2.4 27.1 9.3 11.7 11.3 24.5 Jiangxi 7.9 22.6 32.7 37.9 43.6 45.3 NC NC 9.2 37.7 44.1 14.0 54.7 31.8 Shandong 8.9 17.6 3.9 14.4 11.5 34.4 27.4 13.3 24.1 12.2 58.4 31.9 44.5 23.3 Henan 16.3 53.9 15.2 54.4 20.8 36.3 29.7 37.8 57.5 83.1 20.0 20.0 7.6 34.8 Hubei 3.5 65.9 38.4 58.2 42.9 6.3 41.5 5.1 33.9 4.2 74.9 66.2 54.7 38.1 Hunan 55.7 59.2 72.8 75.4 43.3 41.8 71.3 64.7 16.0 78.5 57.4 19.0 50.2 54.2 Guangdong 18.7 10.0 37.0 23.2 40.2 21.3 49.7 9.5 59.1 33.7 52.0 47.7 31.8 33.4 Guangxi 13.6 23.2 71.7 21.7 61.9 35.7 57.7 60.9 10.1 42.1 9.7 51.5 51.6 39.3 Hainan 16.6 6.2 NC 52.3 18.0 12.3 28.7 28.6 9.9 13.8 88.8 47.0 61.8 32.0 Chongqing 27.7 57.8 36.6 44.4 43.1 29.9 15.8 76.0 51.2 6.7 36.5 42.2 36.6 38.8 Sichuan 28.2 14.9 NC 17.6 22.8 9.8 26.9 34.7 23.8 18.7 34.1 22.7 48.4 25.2 Guizhou 52.0 8.8 55.0 61.8 23.6 57.4 25.1 45.0 43.3 39.7 NC 5.9 23.2 36.7 Yunnan 40.7 13.8 11.5 26.4 39.6 28.9 24.6 31.6 16.8 10.6 15.9 21.5 52.0 25.7 Tibet 63.5 65.8 80.8 80.5 76.1 33.6 73.0 44.2 40.6 33.3 82.8 55.0 28.3 58.3 Shaanxi 37.3 22.0 NC 48.5 24.9 60.1 57.4 69.7 74.1 71.7 79.6 32.2 59.2 53.1 Gansu 17.2 47.4 21.9 23.3 14.7 17.9 22.9 11.3 22.4 40.5 74.8 95.9 32.7 34.1 Qinghai 85.4 50.1 50.4 34.3 51.9 46.9 56.1 29.4 26.0 33.2 52.5 27.4 43.5 45.2 Ningxia 16.2 12.1 20.0 20.1 58.2 36.3 33.9 9.9 15.8 57.4 80.2 66.8 NC 35.6 Xinjiang 41.9 8.0 18.6 9.5 11.9 26.2 15.7 20.8 30.7 23.0 40.4 52.1 17.6 24.3 MAPE Overall 28.3 31.6 32.3 34.3 42.8 28.5 39.4 32.5 30.9 33.8 48.7 35.0 43.7 35.6 Note: NC means not calculable for values over 100.
Table 5.1.10 Summary MAPE counts for BSM forecast for all countries to the 31 Chinese provinces Number of forecasts <10% 47 Number of forecasts >10% <20% 131 Number of forecasts >20% <30% 123 Number of forecasts >30% <50% 69 Number of forecasts >50% 32
The results of the BSM analysis are not highly accurate for any province and the overall error exceeds 30% (35.6%), and when compared with the previous analyses Holt (Average MAPE of 33.9%) and the Exponential Smoothing model (Average MAPE of 34.1%) shows the most accurate overall forecast result is the Naïve (Average MAPE of 25.3%). However, the number of results below 30% error far exceeds to exponential smoothing and Holt results and exceeds the results for the Naïve model.