1. By
Srikavya
Ravi teja
Arun Nayak
Karthik
Amit Nayak

2.  Forecasting lays a ground for reducing the
risk in all decision making because many of
the decisions need to be made under
uncertainty.
 In business applications, forecasting serves as
a starting point of major decisions in
finance, marketing, productions, and
purchasing.

3.  Method or technique for estimating
many future aspects of a business or
other operation.
 It is used in the practice of
customer demand planning in every
day business forecasting for
manufacturing companies.

4. There are three types of forecasting
1.Qualitative or Judgmental methods
2.Extrapolative or Time series methods
3.Causal or Explanatory methods

5.  A time series is a sequence of data points,
measured typically at successive points in time
spaced at uniform time intervals.
 Time series forecasting is the use of a model to
predict future values based on previously observed
values.
 In this measurements are taken at successive
points or over successive periods.

6. Time-Series
Cyclical
Component
Random
Component
Trend
Component
Seasonal
Component

7.  Long-run increase or decrease over time
(overall upward or downward movement)
 Data taken over a long period of time
Upward trend
Sales
Time

8.  Trend can be upward or downward
 Trend can be linear or non-linear
Downward linear trend
Sales
Time
Upward nonlinear trend
Sales
Time
(continued)

9.  In this,Variation dependent on the
time of year
 Each year shows same pattern
 Often monthly or quarterly
Sales
Time (Quarterly)
Winter
Spring
Summer
Fall

10.  Up & down movement repeating over
long time frame
 Regularly occur but may vary in length
 Each year does not show same pattern
Sales
1 Cycle
Year

11.  Unpredictable, random, “residual”
fluctuations
 Due to random variations of
 Nature
 Accidents or unusual events
 “Noise” in the time series

12.  Moving Average Method - average of demands
occurring in several of the most recent
periods.
 Weighted Moving Average - allows for varying
weighting of old demands.
 Exponential Smoothing – exponentially
decreases the weighting of old demands.
 Linear method

13.  The Simple Moving Average smooth past data
by arithmetically averaging over a specified
period and projecting forward in time. This is
normally considered a smoothing algorithm
and has poor forecasting results in most
cases.
 A moving average is commonly used
with time series data to smooth out short-
term fluctuations and highlight longer-term
trends or cycles.

14. Question: What are the 3-
week and 6-week moving
average forecasts for
demand?
Assume you only have 3
weeks and 6 weeks of
actual demand data for the
respective forecasts
Question: What are the 3-
week and 6-week moving
average forecasts for
demand?
Assume you only have 3
weeks and 6 weeks of
actual demand data for the
respective forecasts
Week Demand
1 650
2 678
3 720
4 785
5 859
6 920
7 850
8 758
9 892
10 920
11 789
12 844
F =
A + A + A +...+A
n
t
t-1 t-2 t-3 t-n

15. Week Demand 3-Week 6-Week
1 650
2 678
3 720
4 785 682.67
5 859 727.67
6 920 788.00
7 850 854.67 768.67
8 758 876.33 802.00
9 892 842.67 815.33
10 920 833.33 844.00
11 789 856.67 866.50
12 844 867.00 854.83
F4=(650+678+720)/3
=682.67
F7=(650+678+720
+785+859+920)/6
=768.67
Calculating the moving averages gives us:

16. F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n
w = 1i
i=1
n
∑
While the moving average formula implies an equal weight being
placed on each value that is being averaged, the weighted moving
average permits an unequal weighting on prior time periods
While the moving average formula implies an equal weight being
placed on each value that is being averaged, the weighted moving
average permits an unequal weighting on prior time periods
wt = weight given to time period “t”
occurrence (weights must add to one)
wt = weight given to time period “t”
occurrence (weights must add to one)
The formula for the moving average is:The formula for the moving average is:

17. Weights:
t-1 .5
t-2 .3
t-3 .2
Week Demand
1 650
2 678
3 720
4
Question: Given the weekly demand and weights, what is
the forecast for the 4th
period or Week 4?
Question: Given the weekly demand and weights, what is
the forecast for the 4th
period or Week 4?
Note that the weights place more emphasis on the
most recent data, that is time period “t-1”
Note that the weights place more emphasis on the
most recent data, that is time period “t-1”

18. Week Demand Forecast
1 650
2 678
3 720
4 693.4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4

19. Drawback of previous models is carrying large amount
of Data.
As new data is added to this method, oldest observation
is dropped and the new forecast is calculated.
In many applications the most recent occurrences are
more indicative of the future than those in the more
distant past.
If this premise is valid then Exponential smoothing may
be the most logical method to use.
Most used and widely used in retail firms, wholesale
companies and service agencies.

20. Exponential smoothing is a technique
that can be applied to time series data,
either to produce smoothed data for
presentation, or to make forecasts.
Exponential smoothing methods give larger
weights to more recent observations, and
the weights decrease exponentially as the
observations become more distant.

21.  Premise: The most recent observations might have
the highest predictive value
 Therefore, we should give more weight to the more
recent time periods when forecasting
Ft = Ft-1 + α(At-1 - Ft-1)Ft = Ft-1 + α(At-1 - Ft-1)
constantsmoothingAlpha
periodepast t timin theoccuranceActualA
periodpast time1inalueForecast vF
periodt timecomingfor thelueForcast vaF
:Where
1-t
1-t
t
=
=
=
=
α

22. Question: What are
the exponential
smoothing forecasts
for periods 2-5 using
a =0.5?
Assume F1=D1
Question: What are
the exponential
smoothing forecasts
for periods 2-5 using
a =0.5?
Assume F1=D1
Week Demand
1 820
2 775
3 680
4 655
5

23. Week Demand 0.5
1 820 820.00
2 775 820.00
3 680 797.50
4 655 738.75
5 696.88
F1=820+(0.5)(820-820)=820 F3=820+(0.5)(775-820)=797.75

24.  Simple linear regression is the most commonly
used technique for determining how one variable
of interest is affected by changes in another
variable.
 Simple linear regression is used for three main
purposes:
1. To describe the linear dependence of one
variable on another
2. To predict values of one variable from values of
another, for which more data are available
3. To correct for the linear dependence of one
variable on another, in order to clarify other
features of its variability.
24

25. Yt = a + bx
0 1 2 3 4 5 x (Time)
YThe simple linear regression
model seeks to fit a line
through various data over
time
The simple linear regression
model seeks to fit a line
through various data over
time
a
Where
Yt is the regressed forecast value or dependent
variable in the model,
a is the intercept value of the the regression line, and
b is similar to the slope of the regression line.

26. a = y- bx
b =
xy- n(y)(x)
x - n(x2 2
∑
∑ )

27. Week Sales
1 150
2 157
3 162
4 166
5 177
Question: Given the data below, what is the simple linear
regression model that can be used to predict sales in future
weeks?
Question: Given the data below, what is the simple linear
regression model that can be used to predict sales in future
weeks?

28. Week Week*Week Sales Week*Sales
1 1 150 150
2 4 157 314
3 9 162 486
4 16 166 664
5 25 177 885
3 55 162.4 2499
Average Sum Average Sum
b =
xy- n(y)(x)
x - n(x
=
2499- 5(162.4)(3)
=
a = y- bx =162.4- (6.3)(3) =
2 2
∑
∑ −
=
) ( )55 5 9
63
10
6.3
143.5
Answer: First, using the linear regression formulas, we
can compute “a” and “b”
Answer: First, using the linear regression formulas, we
can compute “a” and “b”

29. Yt = 143.5 + 6.3x
180
Period
135
140
145
150
155
160
165
170
175
1 2 3 4 5
Sales
Sales
Forecast
The resulting regression model
is:
Now if we plot the regression generated forecasts against the
actual sales we obtain the following chart:

30. 30