Moving average, forecasting method

Moving average. These methods try to eliminate randomness in a time series and smooth the curve of the data. This method of forecasting tends to lag a trend, and the more periods included in the average, the greater the lag will be. This method is best suited for products that have a stable demand. 

A general approach was developed by G.E.P. Box and G.M. Jenkins (S) which combines these various methods into an analysis which permits choice of the most appropriate model, checks the forecast precision, and allows for interpretation. The Box-Jenkins analysis is an autoregressive integrated moving average model (ARIMA). This approach, as implemented in the MINITAB computer program is one used for the analyses reported here. 

Note that efforts described above would not take care of the major problem, that is x, to some degree, is determined by x, i, which is somewhat determined by x, 2> and so on. Forecasting methods, such as moving averages, are better in these situations. 

Brown s ejqtonential smoothing method is used for forecasting time series data that have a linear trend. This method is similar to double moving average techniques. Only one smoothing constant is used in this method. 

MM Agent forecasts using the moving average method of order n, which estimates the demand in any period as the average of the latest n demands. It can be expressed as ... 

To develop the tool, we have considered only simple forecasting methods, such as moving averages and exponential smoothing, so that each level of the chain uses the best one that suits the demand it should deal with. With them, it is possible to achieve great results in reducing Bullwhip Effect. Even so, we have also shown that the inclusion of more advanced forecasting methods (ARIMA models) allows an even better system performance. 

No statistical forecast methods or only very basic models (e.g., moving average) are used to plan business volume. 

A second time-series forecasting method is the weighted moving average. Instead of simply taking the average of a set number of periods, this method weights the more recent periods heavier than the older periods. 

Continuing to use the example above, where demand for the last 4 weeks was 100,120, 130, and 120 for weeks 1 to 4, respectively, we will forecast demand in week 5. To do this we must have the forecast for period 4 to get the forecast for period 4, we need the forecast for period 3. This continues until period 1, when we recognize that we need to initiate the method by creating a forecast for period 1 using a different method. One common technique to obtain the first week s forecast is to say the forecast for period 1 was equal to actual demand for period 1 (i.e., we set the forecast for week 1 equal to 100 since actual demand for week 1 was 100). The formula for the exponential moving average is ... 

To determine the best weights for the weighted moving average method, a linear programming (LP) model can be used. The objective of fhe LP model is to find fhe opfimal weighfs fhaf minimize the forecast error. Let denote the forecast error in period t. Then, e, is given by... 

For the sake of illustration, the forecasts for the first quarter of 2011, using the Naive method and the 4-quarter moving average method are also given in the following ... 

Taco Bell (Hueter and Swart, 1998) Lunch time sales were forecasted using the moving average method and were used for estimating labor needs at Taco Bell restaurants. 

A refinement is to take a moving average. In Table 4.3, the last three periods are averaged. This method provides a response to trends, and also dampens fluctuations. Although there are still significant variations shown in Table 4.3, the forecasts for periods 7 and 8 are more accurate than those shown in Table 4.2. 

Exponential smoothing is similar to the moving average methods but it eliminates some of the calculations. The model uses a smoothing factor (less than 1) for forecasting the next period activity. The mathematical formula is... 

Consider monthly demand for the ABC Coiporation as shown in Table 7-3. Forecast the monthly demand for Year 6 using moving average, simple exponential smoothing, Holt s model, and Winter s model. In each case, evaluate the bias, TS, MAD, MAPE, and MSE. Which forecasting method do you prefer Why ... 

---