FORECASTING
Chapter 5
Forecast
It is a statement about the
future value of a variable of
interest.
Features Common to
All Forecasts
1.
Techniques assume some underlying
causal system that what existed in the
past will persist into the future
2.
Forecasts are not perfect
3.
Forecasts for groups of items are more
accurate than those for individual items
4.
Forecast accuracy decreases as the
forecasting horizon increases
Elements of a
Good Forecast
•
timely
•
accurate
•
reliable
•
expressed in meaningful units
•
in writing
•
technique should be simple to
understand and use
•
cost effective
Approaches to Forecasting
Qualitative Forecasting
• permit the inclusion of soft information such as:
- Human factors
- Personal opinions
- Hunches
• These factors are difficult, or impossible, to quantify
Quantitative Forecasting
• involve either the projection of historical data or the development of associative methods that attempt
to use causal variables to make a forecast
• Relies on hard data
Forecasting Techniques
I. Judgmental Forecasts
II. Time-series Forecasts
III. Associative Model
I
JUDGEMENTAL
FORECAST
Forecasts that use subjective inputs such as opinions from consumer surveys,
sales staff, managers, executives, and experts.
I. Judgmental Forecasts
Executive opinions
Sales-force opinions
Consumer surveys
Delphi method
II
TIME-SERIES
FORECASTING
Forecasts that project patterns identified in recent time-series observations.
II. Time-Series Forecasting - NAÏVE FORECAST
I. Naïve Forecast - The forecast for a time period is
equal to the previous time period’s value
Forecast for any period = previous period’s actual
value
Ft = At-1
F= forecast
A= Actual t= time period
Naïve Forecast Example
WEEK
SALES (ACTUAL)
SALES (FORECAST)
ERROR
t
A
F
A-F
1
20
-
-
2
25
20
5
3
15
25
-10
4
30
15
15
5
27
30
-3
II. Time-Series Forecasting
Averaging - They can handle step changes or gradual
changes in the level of a series.
Techniques:
1. Moving average
2. Weighted moving average
3. Exponential smoothing
II. Time-Series Forecasting
MOVING AVERAGE
n
At i

It averages the number
Ft  MA n  i 1
of recent actual values,
n
updated as new values where
Ft  Forecast for time period t
become available.
MA n  n period moving average
At 1  Actual value in period t  1
n  Number of periods in the moving average
II. Time-Series Forecasting
MOVING AVERAGE
Compute a three-period moving average forecast given demand for
shopping carts for the last five periods.
Period
Actual Demand
1
42
2
40
3
43
4
40
5
41
II. Time-Series Forecasting
MOVING AVERAGE
F6= (43 + 40 + 41)/3
= 41.33
If actual demand in period 6 turns out to be 38, what is the
moving average forecast for period 7?
II. Time-Series Forecasting
MOVING AVERAGE
Period
Actual Demand
1
42
2
40
3
43
4
40
5
41
6
38
F7= (40 + 41 + 38)/3
= 39.67
II. Time-Series Forecasting
WEIGHTED MOVING AVERAGE
More recent values in a series are given more weight in
computing a forecast.
Ft  wt ( At )  wt 1 ( At 1 )  ...  wt  n ( At  n )
where
wt  weight for period t , wt 1  weight for period t  1, etc.
At  the actual value for period t , At 1  the actual value for period t  1, etc.
II. Time-Series Forecasting
WEIGHTED MOVING AVERAGE
a. Compute a weighted average forecast using a weight of
.40 for the most recent period, .30 for the next most recent,
.20 for the next, and .10 for the next.
b. If the actual demand for period 6 is 38, forecast demand
for period 7 using the same weights as in part a.
Period
F6 = .10(40) + .20(43) + .30(40) + .40(41) = 41.0
F7 = .10(43) + .20(40) + .30(41) + .40(38) = 39.8
Actual
Demand
Actual
Demand
1
42
42
2
40x.10
40
3
43x.20
43x.10
4
40x.30
40x.20
5
41x.40
41x.30
6
38x.40
II. Time-Series Forecasting
EXPONENTIAL SMOOTHING
Based on previous forecast plus a percentage of the forecast
error.
Ft  Ft 1   ( At 1  Ft 1 )
where
Ft  Forecast for period t
Ft 1  Forecast for the previous period
 = Smoothing constant
At 1  Actual demand or sales from the previous period
II. Time-Series Forecasting
EXPONENTIAL SMOOTHING
Compute exponential smoothing using smoothing constant
of .10
Period
Actual Demand
1
42
2
40
3
42
4
40
5
41
III
ASSOCIATIVE
MODEL
Forecasting technique that uses explanatory variables to predict future
demand.
Linear Trend Equation
Ft =a+bt
Where:
Ft = Forecast for period t
a = Value of Ft at t = 0, which is the y intercept b = Slope of the line
t = Specified number of time periods from t = 0
Linear Trend
Equation
The coefficients of the
line, a and b, are based
on the following two
equations:
SAMPLE:
The cellphone sales for a company for the last 5 years are as follows.
Use linear trend to forecast sales for year 6 and 7.
Year
Sales (in million)
2018
74
2019
79
2020
80
2021
90
2022
105
2023
?
2024
?
SAMPLE:
The cellphone sales for a company for the last 5 years are as follows.
Use linear trend to forecast sales for year 6 and 7.
𝑛𝛴𝑡𝑦 −𝛴𝑡𝛴𝑦
𝑡 2
b= 𝑛𝛴𝑡 2 −
Year
Sales (in
million)
(y)
number of
time periods
(t)
ty
(1) 2018
74
1
74
1
(2) 2019
79
2
158
4
(3) 2020
80
3
240
9
(4) 2021
90
4
360
16
(5) 2022
105
5
525
25
2023
?
𝐹𝑡 = 𝑎 + 𝑏𝑡
= 63.7 + 7.3 6
Y6 = 107.5
2024
?
N= 5
428
55
𝐹𝑡 = 𝑎 + 𝑏𝑡
= 63.7 + 7.3 7
Y7 = 114.8
15
1,357
t²
5 1,357 − 15 428
5 55 − 15 2
365
50
=
=
= 7.3
𝑎=
𝑦−𝑏
𝑛
428− 7.3 15
5
=
= 63.7
𝑡
Simple Linear Regression
yc =a+bx
Where:
yc = Predicted (dependent) variable
x = Predictor (independent) variable
b = Slope of the line
a = Value of yc when x = 0
Simple Linear Regression
The coefficients a and b of the line are based on the following two
equations:
SAMPLE:
Mr. Sy wants to see how the number of absences of a student affects the
student’s final grade.
No. of Absences (x)
(x)
Final Grade
(y)
9
65
11
70
3
90
0
92
7
75
4
84
SAMPLE:
Mr. Sy wants to see how the number of absences of a student affects the
student’s final grade.
b=
No. of
Absences
(x)
Final
Grade
(y)
xy
9
65
585
81
11
70
770
121
3
90
270
9
0
92
0
0
7
75
525
49
4
84
336
16
34
476
2,486
276
𝑥2
𝑛(𝛴𝑥𝑦) − 𝛴𝑥 (𝛴𝑦)
𝑛 𝛴𝑥 2 − 𝑥 2
𝑎=
𝑦−𝑏
𝑛
𝑥
476− −2.536 34
=
6 2,486 − 34 476
6 276 − 34 2
=
6
= 93.704
= - 2.536
REGGRESION EQUATION
Yc= 𝑎 + 𝑏𝑥
= 93.704 + −2.536 x
e.g. Student’s final grade with 5 absences
Yc= 𝑎 + 𝑏𝑥
= 93.704 + −2.536 (5)
= 81.02