Results and Discussion

The exponential smoothing models obtained for each country are reported in Table 3.4. Using SPSS version 19, the Expert Modeller procedure generates optimal (minimum SSE) exponential smoothing models for each exchange rate series. This process compares all previously mentioned (Table 3.3) exponential smoothing models in response of SSE. The Normalised Bayesian Information Criteria (NBIC) are also reported in Table 3.4. NBIC is a general measure of the overall fit of a model that attempts to account for model complexity. It is a score based on the mean squared error. It includes a penalty for the number of parameters in the model and the length of the series. The penalty removes the advantage of models with more parameters, making the statistic easy to compare across different models for the same series (SPSS Inc., 2010).

The estimated values of the parameters α, γ, and δ for all exchange rates are presented in Table 3.4. The Winters’ additive model is optimal for Bangladesh, Mexico and Peru. The α value for Bangladesh, Mexico and Peru are 1.000, 0.999 and 1.000 respectively. These high values of imply that the impact of historical observations dies out quickly. The parameter γ has a very low value for these countries. This indicates to give more weight to historical estimates of this component. Moreover, the estimated value for δ is very high for Mexico (0.999) when compared with Bangladesh (0.001) and Peru (0.001). This implies that the most recent observations have more significant impacts on Mexico-USA exchange rate. Conversely, smaller values of δ give more weight to historical estimates of this component for the country like Bangladesh and Peru.

The simple one parameter model is optimal for China and Trinidad & Tobago. High values of α (1.000) suggests that only the most recent observations significantly affect the Chinese yuan/U.S. dollar and Trinidad & Tobago dollar/U.S. dollar exchange rates. For the Euro area, the simple seasonal model is found to be superior to other models. The estimated parameters i.e. level ( ) and seasonality are 0.999 and 1.000 respectively. These

Table 3.4: Results from exponential smoothing models

Country Model NBIC

Advanced Countries

Australia Damped Trend 1.000 1.000 0.255 --- -6.892 Canada Damped Trend 1.000 1.000 0.201 --- -8.268 Denmark Damped Trend 1.000 1.000 0.300 --- -3.427 Euro area Simple Seasonal 0.999 --- --- 1.000 -7.559 Japan Damped Trend 1.000 1.000 0.300 --- 3.143 Norway Damped Trend 1.000 1.000 0.300 --- -3.726 Singapore Damped Trend 1.000 1.000 0.299 --- -7.204 Sweden Damped Trend 1.000 1.000 0.300 --- -3.608 Switzerland Damped Trend 1.000 1.000 0.300 --- -5.764 UK Damped Trend 1.000 1.000 0.269 --- -8.428

Emerging Countries

Brazil Damped Trend 1.000 0.999 0.299 --- -4.577 Chile Damped Trend 1.000 1.000 0.398 --- 4.382 China Simple 1.000 --- --- --- -3.771 Colombia Damped Trend 1.000 1.000 0.400 --- 6.759 Czech Republic Damped Trend 1.000 1.000 0.298 --- -0.477 Hungary Holt linear 1.000 0.100 --- --- 2.400 India Damped Trend 1.000 0.294 0.627 --- -1.503 Indonesia Damped Trend 1.000 1.000 0.200 --- 12.274 Malaysia Simple Seasonal 0.999 --- 0.001 -5.516 Mexico Winters' Additive 0.999 3.23x 10-7 --- 0.999 -3.204 Peru Winters' Additive 1.000 0.100 --- 0.001 -6.444 Philippines Damped Trend 1.000 1.000 0.341 --- -0.908 Poland Damped Trend 1.000 1.000 0.300 --- -4.950 Russia Damped Trend 0.999 0.273 0.860 --- -0.512 South Africa Damped Trend 1.000 1.000 0.301 --- -3.285 South Korea Damped Trend 1.000 1.000 0.500 --- 6.864 Taiwan Damped Trend 1.000 0.711 0.496 --- -1.894 Thailand Damped Trend 1.000 1.000 0.299 --- 0.122 Turkey Damped Trend 1.000 1.000 0.400 --- -6.221

Frontier Countries

Bangladesh Winters' Additive 1.000 0.001 --- 0.001 -1.499 Bhutan Damped Trend 1.000 0.294 0.627 --- -1.503 Botswana Damped Trend 1.000 1.000 0.242 --- -4.615 Brunei Damped Trend 1.000 1.000 0.299 --- -7.203 Croatia Damped Trend 1.000 0.421 0.738 --- -3.007 Estonia Damped Trend 1.000 1.000 0.300 --- -2.226 Jamaica Damped Trend 0.986 0.374 0.810 --- -1.214 Kazakhstan Damped Trend 0.874 0.999 0.641 --- 1.912 Kenya Damped Trend 0.999 0.989 0.396 --- 0.591 Lao PDR Damped Trend 0.900 1.000 0.513 --- 10.737 Mauritius Damped Trend 1.000 0.960 0.422 --- -2.377 Myanmar Damped Trend 0.999 0.069 0.924 --- -4.226 Nepal Damped Trend 0.999 0.901 0.400 --- -0.634 Nigeria Damped Trend 0.887 0.250 0.563 --- 2.378 Pakistan Damped Trend 1.000 1.000 0.401 --- -1.434 Romania Holt linear 1.000 0.100 --- --- -5.892 Sri Lanka Holt linear 1.000 0.001 --- --- -0.603 Trinidad & Tobago Simple 1.000 --- --- --- -4.798 Tunisia Damped Trend 1.000 1.000 0.296 --- -7.954 Vietnam Damped Trend 1.000 1.000 0.200 --- 11.501 α: level smoothing weight, γ: trend smoothing weight, φ: damped trend smoothing weight and δ: season smoothing weight. NBIC: Normalised Bayesian Information Criteria.

indicate that a constant seasonal effect is present in Euro/dollar series. A similar result is observed in the case of Malaysian ringgit/dollar. Holt’s linear model is found to be optimal in the cases of Hungary, Romania and Sri Lanka. The estimated values of α for these countries is 1.000, but the values for estimated trend smoothing parameter ( ) are 0.100 for Hungary and Romania and 0.001 for Sri Lanka. According to this model, the exchange rates of these countries follow a linear trend with no seasonal effect.

Surprisingly enough, the damped trend model is found to be superior for 39 countries cases out of 49. This result supports the findings of McKenzie and Gardner (2010), who argued that over the past twenty years, damped trend exponential smoothing models have performed well in numerous empirical studies and it is now well established as highly accurate forecasting method. Fildes et al. (2008) reported that the damped trend can reasonably claim to be a benchmark forecasting method for all others to beat. Armstrong (2006) also recommended that the damped trend as a well-established forecasting method that should improve accuracy in practical applications. Theoretically, the damped trend model is appropriate for series with a linear trend that is dying out and which possess no seasonality. The results show that the values are very high (equal to 1) in majority of the cases. This indicates that the most recent observation has significant impacts on future exchange rates of these countries. The values of estimated damped trend ( ) parameter is less than 0.4 in all cases except India (0.627), Russia (0.860), South Korea (0.500), Bhutan (0.627), Croatia (0.738), Jamaica (0.810), Kazakhstan (0.641), Lao PDR (0.513), Myanmar (0.924) and Nigeria (0.563). Large values for φ give more weight to recent estimates of the damped trend components, with smaller values giving more weight to historical estimates of this component for determining the future exchange rates of these countries.

The MAPE values (static) for all series are presented in the fourth column of Appendix 8. The results show that the MAPE values are less than 5% in all cases except Peru (6.96%). The optimal model for each series is then used to produce monthly ex post forecast for 2008M1 to 2010M4 inclusive (hold back period) for each series. Dynamic MAPE values are presented in the fifth column of Appendix 8. The dynamic MAPE values are less than 10% in all cases except Australia, Japan, Sweden and UK in the advanced markets group. By contrast, MAPE values are less than 10% for all emerging markets except Hungary,

India, Philippines, Poland, Russia, South Africa, South Korea and Turkey. In the frontier markets group, MAPE values are higher than 10% is the cases of Bhutan, Botswana, Kenya, Nepal, Nigeria, Pakistan and Romania. Overall, the analyses show that the exponential smoothing models generate highly accurate forecasts (MAPE < 10%; Lewis, 1992) for 32 countries out of 49. These indicate that the exponential smoothing model is equally as good as other time series models as far as exchange rate forecasting is concerned. The results are in line with some recent studies, e.g. Borhan and Hussain (2011), Li (2010), Yu et al. (2007) and Dheeriyaa and Raj (2000), who noted that the exponential smoothing models generate better forecasts of exchange rates. Therefore, the current findings add to a growing body of literature on the application of exponential smoothing models to forecast exchange rate series. The next section discusses the application of Naїve models for forecasting exchange rates.