Forecasting Monthly Rainfall In Malaysia Using Exponential Smoothing, Holt’s Method And Winter’s Method

Data Source

For the purpose of this project time series data has been collected from world bank. The data on average monthly rainfall in Malaysia for the 9-year period from 2007 to 2015 has been collected for this study. A total of 108 data points are available for the analysis. The analysis has been conducted using the statistical software SPSS version 20.

The original time series is plotted in figure 1. From the figure, it can be seen clearly that the average monthly rainfall follows a seasonal fluctuation every year.

By seasonal fluctuations it is meant that there is a periodic movement in a time series where the period is not longer than 1 year. A periodic movement in time series is one which recurs or repeats at regular intervals of time (or periods) (Montgomery, Jennings and Kulahci 2015).

C.C. Holt first suggested this this method of forecasting in 1958. This method is usually used to forecast values which do not have any systematic trend and follows non-seasonal time series data. In reality, the data that are obtained do not usually follow any seasonal pattern. The non-seasonal effects are measurable and can be removed and thus, the developed and revised model will be stationary.

In exponential smoothing technique of forecasting, data which is older is given lesser priority and the data which are new are given more priority. This method is also known as averaging and is used to forecast values for a shorter term (Ramtirthkar et al. 2016).

The forecast using the simple exponential smoothing method for the year 2016 is given in table 2.1.

This method is an extension of the simple exponential smoothing method and has been developed by Holt in 1957. Hence the name. This method allows the forecasting data along with a trend. Thus, there are more than one equations involved in this type of forecasting. One of them is the forecasting equation and two others are smoothing equations (Box et al. 2015).

The forecast using the Holt’s method for the year 2016 is given in table 2.2.

 Winter’s Method

The holt’s method of forecasting was extended by Winters in 1960 to capture the seasonality in the forecast. Thus, in this case, along with the three equations that explains the forecasting and the smoothing, another extra smoothing equation has been introduced. This method has two types of variations. The additive method is used when there are roughly constant seasonal variations. The multiplicative model is useful when the changes in the seasonal variations are proportional to the level of the series. The seasonal component is supposed to add up to be zero within a year (Brockwell and Davis 2016).

Seasonal Fluctuations in Monthly Rainfall

The forecast using the Winter’s method for the year 2016 is given in table 2.3.

It can be easily observed from the three different types of forecasting methods that the Winter’s method of forecasting shows the most accurate forecast as the value of r square is the highest in this method as can be seen from table 2.6. This indicates that the developed Winter’s model will explain the variability in the trend by 74.3 percent. This also indicates that the error is minimum in this model.

It can be seen from the developed ACF that there are spikes at lags 1, 5, 6, 11, 12 and 13. All the lags are significant. Thus, it can be said that there is no existence of autocorrelation in the model developed. The ACF measures are given in table 3.1. The values also sum up to be zero.

The partial autocorrelation shows the correlation between any two of the lags (Granger and Newbold 2014). It can be seen from the results that the partial autocorrelation at each of the lags are quite high, it is positive at some lags and negative at some other lags. The partial correlations sum up to be zero.

A regression model has been developed for the forecasting purpose. Regression has been performed on the Winter’s model as that model is the best fitted model. From the results of the regression, it can be seen that the R Square value is 0.053, which indicates that the seasonal dummies can represent only 5.3 percent of the variations in the rainfall measures. It can also be said from the coefficients that with the increase in the years and months, the average monthly rainfall decreases by 0.474.

Conclusions

Analysis has been done in this project on the monthly rainfall of Malaysia. The methods of prediction that has been used here are Exponential Smoothing, Holt’s Method and Winter’s Method. It has been observed from the analysis that the Winter’s Method has been the most appropriate method of prediction as the error in variation has been the minimum in this model fit. On prediction with the help of this model, it has been seen that the error in prediction is high and the average monthly rainfall decreases with time.

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M., 2015. Time series analysis: forecasting and control. John Wiley & Sons.

Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. springer.

Granger, C.W.J. and Newbold, P., 2014. Forecasting economic time series. Academic Press.

Montgomery, D.C., Jennings, C.L. and Kulahci, M., 2015. Introduction to time series analysis and forecasting. John Wiley & Sons.

Ramtirthkar, M., Gupta, A., Sonawane, R. and Kolhatkar, A., 2016. Forecasting yield of coarse cereals in India using ARIMA model. AgricINTERNATIONAL, 3(1), pp.117-127.

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