method of financial forecasting is that it is simple and inexpensive to use. To obtain a more precise projection of the firm’s future financing needs, however, the preparation of a cash budget is required. One important assumption behind the use of the method is that the firm is operating at full capacity. This means that the business has no production capacity to absorb a projected increase in sales, and thus requires an additional investment in assets.
16. Naive Forecasting Models
Introduction
Naive forecasting models are based exclusively on historical observation of sales or other variables such as earnings and cash flows being forecast. They do not attempt to explain the underlying causal relationships that produce the variables being forecast. Naive models may be classified into two groups. One group consists of simple projection models. These models require inputs of data from recent observations, but no statistical analysis is performed. The second group is comprised of models that, while naive, are complex enough to require a computer. Traditional methods such as classical decomposition, moving average, and exponential smoothing models are some examples. (See Sec. 17, Moving Averages, and Sec. 18, Exponential Smoothing.)
The advantages of naive forecasting models are that they are inexpensive to develop, store data, and operate. The disadvantages are that they do not consider possible causal relationships that underlie the forecasted variable.
How is it computed?
A simple example of a naive model type is to use the actual sales of the current period as the forecast for the next period. Let us use F as the forecast value and the symbol At as the actual value. Then:
F = At
If trends are considered, then:
F = At + (At − At-1)
This model adds the latest observed absolute period-to-period change to the most recent observed level of the variable.
If it is desirable to incorporate the rate of change rather than the absolute amount, then:
Example
Consider the following monthly sales data for 20×7:
| Month | Monthly sales of product |
| 1 | $5,504 |
| 2 | 5,810 |
| 3 | 6,100 |
Forecasts will be developed for the fourth month of 20×7, using the three models:
F = At = $6, 100
F = At + (At − At-1) = $6, 100 + ($6, 100 − $5,810) = $6, 100 + $290 = $6,390
How is it used and applied?
Naive models can be applied, with very little need of a computer, to develop forecasts for sales, earnings, and cash flows. These models, however, must be used in conjunction with more complex naive models such as classical decomposition and exponential smoothing and more sophisticated models such as regression analysis. The object is to pick the model (or models) that will best forecast performance.
17. Moving Averages
Introduction
A moving average is an average that is updated as new information is received. A manger employs the most recent observations to calculate an average, which is used as the forecast for the next period.
How is it computed?
For a moving average, simply take the most recent observations and calculate an average. Moving averages are updated continually as new data are available.
Example
Assume that the manager of Drake Hardware Store has the following sales data:
| Month | Sales (000) |
| April | 20 |
| May | 21 |
| June | 24 |
| July | 22 |
| August | 26 |
| September | 25 |
Using a 5-month average, predicted sales for October are computed as follows:
How is it used and applied?
Moving averages are used, for example, to project future sales. Once sales are projected, needed financing for production and inventory may be planned. Business owners can choose the number of periods to use on the basis of the relative importance attached to old versus current date.
For example, one can compare two possibilities, a 5-month and a 3-month period. In terms of the relative importance of new versus old data, the old data receive a weight of ⅘ and current data ⅕. In the second possibility, the old data receive a weight of ⅔, while current observation receives a ⅓ weight. This is a special case of the exponential smoothing method, in which a smoothing constant is in effect the weight given to the most recent data. See Sec. 18, Exponential Smoothing.
Sales forecast can be fairly accurate if the right number of observations to be averaged is picked. In order to pick the right number, the business manager may have to experiment with different moving-average periods. Measures of forecasting accuracy, such as the mean absolute deviation (MAD), can be used to pick the optimal number of periods. See Sec, 24, Measuring Accuracy of Forecasts.
18. Exponential Smoothing
Introduction
Exponential smoothing is a popular technique for short run business forecasting. It uses a weighted average of past data as the basis for a forecast. The procedure gives heaviest weight to recent information and smaller weights to observations in the more distant past. The reason for this is that the future is more dependent on the recent past than on the distant past.
How is it computed?
(The formula for exponential smoothing is
ŷt + 1 = αγt + (1 − γ)ŷt
or
ŷnew = αyold + (1 − γ)ŷold
| where | ŷnew | = exponentially smoothed average to be used as the forecast |
| yold | = most recent actual data | |
| ŷold | = most recent smoothed forecast | |
| αold | = smoothing constant |
The higher the α, the greater is the weight given to the more recent information.
Example
The following data on sales are given for an appliance business:
| Time period, t | Actual sales (1000), yt |
| 1 | $60.00 |
