Question

The following table contains the demand from the last 10 months:

Month	Actual Demand
1	31
2	34
3	33
4	35
5	37
6	36
7	38
8	40
9	40
10	41

(a) Calculate the single exponential smoothing forecast for these data using an$\alpha$of .30 and an initial forecast (F1) of 31.

(b) Calculate the exponential smoothing with trend forecast for these data using an $\alpha$of .30, and$\delta$of .30, an initial trend forecast ( T1 ) of 1, and an initial exponentially smoothened forecast ( F1 ) of 30.

(c) Calculate the mean absolute deviation (MAD) for each forecast. Which is best?

Short answer

Exponential smoothing with the trend is a forecasting method of time-series for univariate data which is further extended to support the data with the trend or seasonal constituent. It is the most powerful forecasting technique of forecasting.

Step-by-step solution

(a) Calculate the single exponential smoothing forecast for these data

Insingle exponential smoothing, if the information has no trend and seasonal pattern, is thought of as single exponential smoothing, during this system of forecasting the statistic is employed. This forecasting method is especially used as a weighted moving average with reducing weights.

Formulas used for calculating the forecast, trend by the formulas shown below:

After calculating the forecast and trend as shown in the below table, the next step is to add and find the forecasting including the trend The calculation is shown in the table shown below:

(b) Calculate the exponential smoothing with trend forecast for these data using an a   of .30, and d of .30, an initial trend forecast ( T1 ) of 1, and an initial exponentially smoothened forecast ( F1 ) of 30

The formula shown below is used to calculate exponential smoothing with trend forecast, the calculation is shown in the table shown below:

(c) Calculate the mean absolute deviation (MAD) for each forecast

The mean absolute deviation is defined as the average distance between each data point and therefore the mean. It gives us a plan for the variability in an exceeding data set. Mean’ refers to the average of the observations and deviation implies departure or variation from a present standard. When putting together, we can define deviation because of the distance of every observation from the mean of the information.

Based upon the MAD of each forecast, the exponential smoothing with the trend is better forecasting model.

Without trend:

With trend:

$MAD>MA{D}_t$