In MSE: This is the mean squared
In my assignment I will forecast the third and the fourth quarter revenues of Consolidated Edison Company for the year 1996. The company’s 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 company’s 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 nave, 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 forecaster’s 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 fit to a straight line or to an exponential curve. To be able to get the possible best results I must conduct them all.(Table 6,7)
Having conducted the different procedures it is time to compare them to each other.
MSE MAD MAPE
Naive forecast 1 period ahead 74644.33 254.56 17.45%
Moving Average 3quarter 37631.92 168.74 11.51%
Moving Average 4quarter 24499.71 136.20 9.23%
Exponential Smoothing a=0.2 29485.20 146.25 9.98%
Exponential Smoothing a=0.4 33731.96 160.62 10.97%
Exponential Smoothing a=0.8 54578.95 213.13 14.59%
Deseasonalisation 7010.50 62.04 4.43%
Double Moving Average 3quarter 71216.02 232.20 15.89%
Linear Regression 23354.74 134.48 9.33%
Exponential Regression 23343.68 132.57 9.12%
From the table it is clearly seen that the values of error terms are the smallest for the deseasonalisation model in all of the three measures of accuracy. In Graph 2 it is seen that the forecasted values closely fit to the past data. This indicates that I have to forecast with this method to be the most effective.
The deseasonalization model operates with splitting the time series into components, which are the trend, the cyclical, the seasonal and the irregular component.
In time series the trend component is the long-term component that represents the growth or decline in the series over a period of time. In the case of the Consolidated Edison Company, this trend effect is a continuous growth, which has started since 1985. This trend effect can be related to the changes in the economy- inflation and the continuously growing consumption.
The cyclical component is the wavelike fluctuation around the trend. Any regular pattern above or below the trend line might be related to the effect of cyclical component. In this case this component strongly affected the year 1985-1987, but after this short period it decreased and has much weaker affect on the revenues.
The seasonal component refers to a pattern of change that repeats itself year after year. This seasonal component causes the fluctuation of revenues in the different quarters. These changes can be considered as the effect of weather changes and any other regular changes in a year time.
The irregular component is the measure of variability of the time series after the other components after the other components have been removed. This component can determine the unpredictable and unexpected factors, which always causes uncertainty for the forecast. In my case this component is filtered out by the averaging procedure.
Since I have already presented the model that I found the best I must complete the original task, the forecast.
Based on the computer output the trend values for the third and the fourth quarter are 1779 and 1792. To reach the forecasts I must multiple these trend values by the seasonal components, which are 1.138 and 0.929.
Before I tell the result of forecast I want to comment these seasonal indexes.
The value of 1.138 means that in each third quarter the revenues are above the trend line by 13.8% on an average. The value of 0.929 means that the revenues in each fourth quarter are 7.1% below the trend line on an average.
Finally the reached results are 2024 for the third quarter and 1666 for the fourth period. These values mean that the revenues are expected to be $2.024 billion in the third quarter of 1996, while the revenues in the fourth quarter are expected to be $1.666 billion in 1996.