1. Forecasting
 Quantitative Approaches to Forecasting
 The Components of a Time Series
 Measures of Forecast Accuracy
 Using Smoothing Methods in Forecasting
 Using Trend Projection in Forecasting
 Qualitative Approaches to Forecasting

2. Quantitative Approaches to
Forecasting
 Quantitative methods are based on an analysis of
historical data concerning one or more time series.
 A time series is a set of observations measured at
successive points in time or over successive periods of
time.
 If the historical data used are restricted to past values
of the series that we are trying to forecast, the
procedure is called a time series method.
 If the historical data used involve other time series
that are believed to be related to the time series that
we are trying to forecast, the procedure is called a
causal method. E.g. Assess the effectiveness of
magazine, newspaper, and TV advertising on sales.

3. Time Series Methods
 Time series methods are:
 smoothing
 trend projection

4. Components of a Time Series
 The trend component accounts for the gradual
shifting of the time series over a long period of time.
 Any regular pattern of sequences of values above and
below the trend line is attributable to the cyclical
component of the series. The ups and downs in
business activities

5. Components of a Time Series
 The seasonal component of the series accounts for regular
patterns of variability within certain time periods, such as
over a year.
 The irregular component of the series is caused by short-
term, unanticipated and non-recurring factors that affect
the values of the time series. One cannot attempt to predict
its impact on the time series in advance.

6. Measures of Forecast Accuracy
 Mean Squared Error
The average of the squared forecast errors for
the historical data is calculated. The forecasting
method or parameter(s) which minimize this
mean squared error is then selected.
 Mean Absolute Deviation
The mean of the absolute values of all forecast
errors is 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.

7. 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 components of the
time series.
 Four common smoothing methods are:
 Moving averages
 Centered moving averages
 Weighted moving averages
 Exponential smoothing

8. Smoothing Methods
 Moving Average Method
The moving average method consists of
computing an average of the most recent n data
values for the series and using this average for
forecasting the value of the time series for the
next period.

9. Example: Rosco Drugs
Sales of Comfort brand headache medicine for
the past ten weeks at Rosco Drugs
are shown on the next slide. If
Rosco Drugs uses a 3-period
moving average to forecast sales,
what is the forecast for Week 11?

10. Example: Rosco Drugs
 Past Sales
Week Sales Week Sales
1 110 6 120
2 115 7 130
3 125 8 115
4 120 9 110
5 125 10 130

11. Example: Rosco Drugs
 Excel Spreadsheet Showing Input Data
A B C
1 Robert's Drugs
2
3 Week (t ) Salest Forect+1
4 1 110
5 2 115
6 3 125
7 4 120
8 5 125
9 6 120
10 7 130
11 8 115
12 9 110
13 10 130

12. Example: Rosco Drugs
 Steps to Moving Average Using Excel
Step 1: Select the Tools pull-down menu.
Step 2: Select the Data Analysis option.
Step 3: When the Data Analysis Tools dialog
appears, choose Moving Average.
Step 4: When the Moving Average dialog box
appears:
Enter B4:B13 in the Input Range box.
Enter 3 in the Interval box.
Enter C4 in the Output Range box.
Select OK.

13. Example: Rosco Drugs
 Spreadsheet Showing Results Using n = 3
A B C
1 Robert's Drugs
2
3 Week (t ) Salest Forect+1
4 1 110 #N/A
5 2 115 #N/A
6 3 125 116.7
7 4 120 120.0
8 5 125 123.3
9 6 120 121.7
10 7 130 125.0
11 8 115 121.7
12 9 110 118.3
13 10 130 118.3

14. Smoothing Methods
 Centered Moving Average Method
The centered moving average method consists of
computing an average of n periods' data and
associating it 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 indexes.

15. Smoothing Methods
 Weighted Moving Average Method
In the weighted moving average method for
computing the average of the most recent n
periods, the more recent observations are typically
given more weight than older observations. For
convenience, the weights usually sum to 1.

16. Smoothing Methods
 Exponential Smoothing
 Using exponential smoothing, the forecast for the
next period is equal to the forecast for the current
period plus a proportion ( ) of the forecast error in the
current period.
 Using exponential smoothing, the forecast is
calculated by:
[the actual value for the current period] +
(1- )[the forecasted value for the current
period],
where the smoothing constant, , is a number
between 0 and 1.

17. Trend Projection
 If a time series exhibits a linear trend, the method
of least squares may be used to determine a trend
line (projection) for future forecasts.
 Least squares, also used in regression
analysis, determines the unique trend line forecast
which minimizes the mean square error between
the trend line forecasts and the actual observed
values for the time series.
 The independent variable is the time period and
the dependent variable is the actual observed
value in the time series.

18. Trend Projection
 Using the method of least squares, the formula for the
trend projection is: Tt = b0 + b1t.
where: Tt = trend forecast for time period t
b1 = slope of the trend line
b0 = trend line projection for time 0
b1 = n tYt - t Yt b0 Y b1 t
n t 2 - ( t )2
where: Yt = observed value of the time series at time
period t
Y= average of the observed values for Yt
t = average time period for the n observations