Consider the following forecasting environments. In each case describe the natur

Question

Consider the following forecasting environments. In each case describe the nature of losses from forecast errors. Do you think the loss function is approximately symmetric?

a. Suppose you are a weather forecaster at a TV station for your city. You forecast the probability of rain the following day among other things. You know that people hate to be caught up in rain unprepared. You also know that they feel less irritated than in the former situation if they carried an umbrella based on the day’s forecast but the rain never materialized. And, of course, you do care how your viewers feel about your forecasts, because your job and salary depend on viewers’Page 2 of 2 ratings.

b. Your forecast project involves projecting water flows in a river in order to determine the height of the dam that is going to be built.

c. A person is trying to project his post retirement expenses. Based on that he will determine how much money from his current earnings he will have to set aside.

Explanation / Answer

a. The loss function would be asymmetric in the case of forecasting errors on the probability of rain. The loss function becomes symmetric when the mistakes made in both the directions lead to approximately same loss. Here if the rain forecast goes wrong and people caught up in rain, the level of dissatisfaction on the forecast would be much higher comparing to the situation where people carry umbrella based on forecast and it does not rain. People would give a very low rating in the former situation and they may not even respond in the later one. Hence loss would be much higher in the first case and hence the loss function would be asymmetric.

b. The loss function would be symmetric here. If the forecast goes wrong and the dam is built with less height compared to the water flow, the dam will be able to store less water and if the dam is built with more height and the water flow is less compared to height, still the dam would store less water compared to the height. The loss is similar in both forecast errors.

c. The loss function would be asymmetric if the forecast goes wrong in the case of post retirement expenses. If the person forecast less, the person would have less money to spend in future and if forecasts higher than required, he may have shortage in present. But the cost and sufferings of the forecasting errors would not be similar in both situations because the value of money changes over time and hence the loss also would not be similar.

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