1. Forecasting Methods
Dr. T. T. Kachwala

2. Importance of Forecasting
In management situations, forecasting is important because the lead time for decision making ranges from several years (for case of capital investment) to few days (for transportation schedules) to few hours (for production schedules).
The important component of forecasting is the distinction between uncontrollable external events (originating with National economy, governments, customers and competitors) and controllable internal events (such as marketing or manufacturing decision within the firms). The success of a company depends on both the type of events, but forecasting applies directly to the former (uncontrollable external events), while decision making applies directly to the latter (controllable internal events). Planning is the link that integrates them.

3. Importance / Definition of Forecasting
Suppose we forecast the sales volume for a particular product for the next quarter of the year. Production schedules, raw material purchasing plan, inventory policies & sales quota will be affected by the quarterly forecast we provide. Consequently, poor forecast will result in increased cost for the firm.
Definition: The word forecast means projection of past into the future for e.g. Demand forecasting: based on past demand, we forecast future demand values.

4. Types of Forecasting Techniques
Two general types of forecasting techniques are used for demand forecasting.
Quantitative Method
Qualitative Method
Quantitative forecasting methods can be used when:
past information about variable being forecast is available
information can be quantified
assuming that pattern of past will continue into the future

5. Time Series Methods
If historical data are restricted to past values of the variable that we are trying to forecast, the forecasting procedure is called time series method.
The objective of time series method is to discover a pattern in the historical data and then extrapolate this pattern into the future
The forecast is based solely on past values of the variable that we are trying to forecast and past forecast errors.

6. Random Fluctuation in Time Series
In time series analysis, measurements may be taken at regular intervals. They generally exhibit random fluctuation as indicated below (Average Sales is Constant)

7. Random Fluctuations / Trend in the Time Series
Random fluctuations of the time series is the residual factor that includes deviation of actual time series values from those expected due to random variability in the time series. The irregular component is caused by the short term, unanticipated, uncontrollable and non recurring factors that affect the time series. Because this component accounts for random variability in the time series it is unpredictable.
Sometimes the time series may show gradual shifts or movements to relatively higher or lower values over a long period of time. The gradual shifting of time series is referred as the trend in the time series.

8. Trend in the Time Series
This shifting or trend is usually the result of long term factors such as changes in population, changes in technology & customer preferences.

9. Seasonal Component in Time Series
Whereas a trend component of a time series are identified by analysing multiyear movements in historical data, many time series show a regular pattern over 1-year period. These situations in business & economics involve period to period comparisons

10. Forecasting Methods of Time Series
1. Smoothing Methods
a) Moving Average
b) Weighted Moving Average
c) Exponential Smoothing
2. Trend Projection
3. Trend Projection Adjusted for Seasonal Influence
4. Causal Forecast (Two Variable & Three Variable Regression Models)

11. Smoothing Methods
The objective of smoothing method is to “smooth” out “the random fluctuations” caused by the irregular component of the time series. The popular smoothing methods are: moving average, weighted moving average & exponential smoothing. These smoothing methods are appropriate for a stable time series i.e. one that exhibits no significant trend or seasonal effects. Many manufacturing environments require forecast for thousands of items weekly or monthly. Thus in choosing a forecasting technique simplicity & ease of use are important criteria. Smoothing methods are easy to use & generally provide high accuracy for short range forecast such as forecast for the next time period.

12. Simple Average Method f t+1 = forecast for period ‘t + 1’
d t = actual demand for period ‘t’
d t-1 = actual demand for period ‘t - 1’
Simple Moving average method is not very popular because it uses distant past data. The more popular method is the Moving Average Method

13. Moving Average Method
This method uses the average of the most recent data values in the time series as a forecast for the next period.
The term moving indicates that, as the new observations become available for the time series, it replaces the oldest observation and the new average is computed. As a result the average will move as the new observations will become available.
The first decision we have to take while using moving average is to decide the number of periods

14. 3 Period Moving Average
Assuming three periods

15. 4 Period Moving Average
Assuming four periods

16. Selecting the number of Periods in Moving Average Method
An important consideration in selecting a forecasting method is the accuracy of forecast. We define forecast error as ≡ et = │dt - ft│
We want the forecast errors to be small. The MSE (Mean Squared Error) is an often used measure of the accuracy of a forecasting method.
For a particular time series, different lengths of moving averages, will affect the accuracy of the forecast. One possible approach in moving average to choosing the number of periods to be included, is to use trial & error to identify the number of periods that minimizes MSE.
We must forecast the next value in the time series using the number of data values that minimizes the MSE for the historical times series.

17. Weighted Moving Average Method
In moving average method, each observation in the calculation receives the same weight. One variation known as Weighted Moving Average, involves selecting different weights for different data values and then computing a weighted average of the most recent data.
To use the weighted moving average method, we must select the number of periods and then choose weights for each of the periods.
In general, if we believe that the recent past is a better predictor of the future than the distant past, larger weights should be given to the more recent periods.

18. Weighted Moving Average Method
f t+1 = forecast for period ‘t + 1’
are the weights associated with
respectively such that:
If we believe what is more recent is more relevant then:
The only mandatory requirement in selecting the weights is that their sum must be equal to 1. The two decisions we have to take while using weighted moving average is to decide the number of periods & the value of weights

19. 3 Period Weighted Moving Average
(Assuming 3 periods)
One set of suggested values of  are:
For a particular time series, different values of weight, will affect the accuracy of the forecast. One possible approach is to use trial & error to identify the values of weight that minimizes MSE.

20. Exponential Smoothing Method
Exponential smoothing is a special case of the weighted moving averages method in which we select only one weight – the weight for the most recent observation. The weights of the other data values are automatically computed using geometric progression and get smaller & smaller as observations move further into the past. The advantage of exponential smoothing over weighted moving average is that we have to select only one value of  in exponential smoothing whereas in weighted average we select more than one value for example 0, 1 and so on
f t + 1 = forecast for period ‘t + 1’
 = smoothing constant such that (0    1)
dt = actual demand for period ‘t’
ft = forecast for period ‘t’

21. Exponential Smoothing Method
Initialization of calculation - Assume that f1 = d1 or f2 = d1
f3 onwards can be calculated using the formula as indicated below:
Substitute t = 2, f3 =  d2 + (1 - ) f2
Substitute t = 3, f4 =  d3 + (1 - ) f3
Although any value of  between 0 & 1 are acceptable, some values will yield a better forecast than the others.

22. Selecting the value of  in Exponential Smoothing
The criterion we use to determine the desirable value for the smoothing constant  is the same as the criterion for determining the number of periods of data to include in the moving average calculation. i.e. we choose the value of  that minimizes MSE through trial & error.
Spreadsheet packages like Excel spreadsheets are an effective aid in choosing a good value for  for exponential smoothing & selecting weights for weighted moving average method & selecting number of periods for moving average method.
With the time series data & forecasting formulas in the spreadsheets, one can experiment with different values of , or moving average weights or number of periods & choose the values providing the smallest MSE.

23. Causal Methods of Forecasting
Forecast can also be developed using causal methods, which is based on the assumption that the variable we are trying to forecast exhibits a cause-effect relation with one or more other variable.
Regression analysis is used as a causal forecasting method. For example, Sales volume for any product is influenced by advertising expenditures, so regression analysis may be used to develop an equation showing how these two variables are related. Then, once the advertisement budget has been set for next period, we could substitute this value into the equation to develop a prediction or forecast of the sales volume for that period.
Note that if a time series method had been used to develop the forecast then advertisement expenditure would not even have been considered. i.e. time series method would base the forecast solely on past sales.