Forecasting Essays - Time Series Analysis, Exponential Smoothing

Forecasting In my assignment I will forecast the third and the fourth quarter revenues of Consolidated Edison Company for the year 1996. The companys main fields are electricity, gas and steam supplying. In the case of every company it is important to forecast the future revenues to be able to calculate the companys expected profits. That is the situation in this case as well, so I must do my job as perfect as I can. I got the past eleven years data, from which I can analyse the whole situation and which I can use to predict for the future. To make the forecast more accurate I can use the actual quarterly revenues. Quarterly revenues for Consolidated Edison Company ($ million), 1985-1995 Year March 31. June 30. September 30. December 31. 1985 1441 1209 1526 1321 1986 1414 1187 1411 1185 1987 1284 1125 1493 1192 1988 1327 1102 1469 1213 1989 1387 1218 1575 1371 1990 1494 1263 1613 1369 1991 1479 1330 1720 1344 1992 1456 1280 1717 1480 1993 1586 1396 1800 1483 1994 1697 1392 1822 1461 1995 1669 1460 1880 1528 1996 1867 1540 Source:The Value Line Investment Survey (New York: Value Line, 1990, 1993, 1996) p.170. There are several different methods, which can be used by forecasters. For this case I will test the na?ve, the moving averages, the exponential smoothing, the double moving averages, the deseasonalisation, the linear regression and the exponential regression models. After having conducted the procedures, the forecasters task is to evaluate the models. This is not an easy task because there are a lot of measures, based on which the person has to decide. The measure coefficients test the difference between the observed and the forecasted values, which then used for comparison. These measures are as follows: MSE: This is the mean squared error, which sum and square all of the errors and take their average. MAD: This is the mean absolute deviation, which sum the absolute errors and take their averages. MAPE: This is the mean average percentage error, which shows the difference in percentages. As I mentioned, all of these measures test the errors, and when the values of measures are the smallest in a method, that method seems to be the most accurate one. Now, I will conduct the different methods one by one. The first technique is the naive approach. The essence of this approach is that it uses the value of the current period as the forecast for the next period. This model is rarely the best one because it does not take the seasonality and the economic changes into consideration.(Table I) The next method I have conducted is the moving averages. This technique uses several past time periods as the forecast for the next period. I averaged three and four quarters to get the possible best one, but it has turned up that the three quarter one has overestimated, while the four quarter one has underestimated the values a bit. From the graph we can see that the four quarter moving average method does not take the seasonality into consideration, therefor it calculates only average values.(Table 2) After the moving averages procedure I conducted the exponential smoothing method, which uses a weighted average of past time series values to get a smoothed forecast. This model decreases the effects of past data and this way creates more accurate forecasts for the future. I used three different weights; the value of 0.2 and the 0.4 and the 0.8. Among them the model weighted by 0.2 was the most accurate one.(Table 3) The double moving average model is an improved variation of the moving averages models. Although a better result was hoped from this technique I must say that the result was worse than the previous ones. It is seen in the graph that this method is continually overestimating. It can be related to the wrong model building. It would be interesting to test the four quarter one as well.(Table 4) It is said that usually the best procedure is the deseasonalisation technique, because this method splits the components of the time series up into parts and analysed separately. After, the components are rebuilt and the forecast is made.(Table 5) The regression models (linear and exponential) use the built in regression of Excel to forecast the values. The different types are needed because the values of data may be