Chapter4
Moving average and smoothing method
Smoothing method
What Is Forecasting?
 Process of predicting a future event .
 Underlying basis of all business decisions .
Realities of Forecasting
 Forecasts are seldom perfect
 Most forecasting methods assume that there is some there is some
underlying stability in the system and future will be like the past
(causal factors will be the same). Accuracy decreases with length
of forecast
Forecasting Methods
Qualitative Methods are subjective in nature since they rely are
subjective on human judgment and opinion.
 Used when situation is vague & little data exist
–– New products
–– New technology
 Involve intuition, experience Quantitative Methods use
mathematical or simulation models based on historical demand
or relationships between variables.
 Used when situation is ‘stable’ & historical data exist
–– Existing products Existing products
–– Current technology Current technology
 Involve mathematical techniques
Smoothing Methods
 In cases in which the time series is fairly stable and has no
significant trend, seasonal, or cyclical effects, one can use
smoothing methods to average out the irregular component of
the time series.
Common smoothing methods are:
1. Moving Averages
2. Weighted Moving Averages
3. Centered Moving Average
4. Exponential Smoothing
Moving Averages Method
The moving averages method consists of computing an average of the
most recent of the most recent data values for the series and using this
average for forecasting the value of the time series for the next period.
Moving averages are useful if one can assume item to be forecast. will
stay fairly steady over time. Series of arithmetic means Series of
arithmetic means
-- used only for smoothing, provides overall impression of
data over time Moving Averages.
Example
Let us forecast sales for 2007 using a 3-period moving average.
2002
4
2003
6
2004
5
2005
3
2006
7
2007
?
Solve
Centered Moving Averages
The centered moving average method consists of computing an average
n periods' data and associating with the midpoint of the periods. For
example, the average with the midpoint of the periods.
For example, the average for periods 5, 6, and 7 is associated with
period 6. This methodology is useful in the process of computing season
methodology indexes.
5
10
6
13
7
11
10+13+11: 3= 11.33
Weighted Moving Averages
 Used when trend is present
– Older data usually less important
 The more recent observations are typically given more weight
than older
 Weights based on intuition Weights based on intuition
– Often lay between 0 & 1, & sum to 1.0
Exponential Smoothing Methods
 Single Exponential Smoothing
– Similar to single MA
 Double (Holt’s) Exponential Smoothing
– Similar to double MA
– Estimates trend
 Triple (Winter’s) Exponential Smoothing
– Estimates trend and seasonality
Exponential Smoothing Model
Single Exponential Smoothing
 weighted moving average
 Weights decline most exponentially, most recent observation
weighted.
 The weighting factor is α
– Subjectively chosen
– Range from 0 to 1
– Smaller α gives more smoothing, larger gives more
smoothing gives less
smoothing
 The weight is:
– Close to 0 for smoothing out unwanted cyclical and
irregular
– Close to 1 for forecasting
Sales vs. Smoothed Sales
 Seasonal fluctuations have been smoothed
 The smoothed value in this case is generally a little since the low,
trend is upward sloping and the weighting factor is only 0.2
Double Exponential Smoothing
 Double exponential smoothing is sometimes called exponential
smoothing with trend .
 If trend exists, single exponential smoothing may need adjustment.
 There is a need to add a second smoothing constant to account for
trend .
Measures of Forecast Accuracy
Mean Squared Error (MSE)
The average of the squared forecast errors for the historical data is
calculated. The forecasting method or parameter(s) data is calculated.
which minimize this mean squared error is then selected.
Mean Absolute Deviation (MAD)
The mean of the absolute values of all forecast errors is calculated,
and the forecasting calculated, and the forecasting method or
parameter(s) which minimize this measure is selected. The mean
absolute deviation measure is less sensitive to individual large
forecast errors than the mean squared error measure. errors than the
mean squared error measure.
You may choose either of the above criteria for evaluating accuracy
of a method (or parameter).
For example
Comparing Smoothing Techniques
 Since the three period moving average technique (MA3)
provides to lowest MSE value, this is the best smoothing
technique to use for forecasting these Sales data in our
technique to use in our example.