lecture 4: trend and seasonal series
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Sep 8 ISMT/Stuart Zhu 1
Lecture 4: Trend and Seasonal Series
• Techniques for trend
• Techniques for seasonality
• Summary
• Readings: Page 79-92
Sep 8 ISMT/Stuart Zhu 2
Techniques for Trend
• Linear Trend Equation
• Ft = Forecast for period t• t = Specified number of time periods• a = Value of Ft at t = 0• b = Slope of the line
tt baF
Sep 8 ISMT/Stuart Zhu 5
Calculate a and b
n
tbya
ttn
ytytnb
n
ii
n
ii
n
ii
n
ii
n
ii
n
ii
n
iii
11
2
11
2
111 ,)(
where n = number of periods,
yi = value of the time series at time ti
(1)
(2)
Sep 8 ISMT/Stuart Zhu 7
Linear Trend Calculation
y = 143.5 + 6.3t
a = 812 - 6.3(15)
5 =
b = 5 (2499) - 15(812)
5(55) - 225 =
12495-12180
275 -225 = 6.3
143.5
Sep 8 ISMT/Stuart Zhu 8
Techniques for Seasonality
• Seasonal variations– Regularly repeating movements in series values
that can be tied to recurring events.
Sep 8 ISMT/Stuart Zhu 9
1 2 3 4
x
x xx
xx
x xx
xx x x x
xxxxxx x x
xx
x x xx
xx
xx
x
xx
xx
xx
xx
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xx
x
x
Year
Seasonal variationSeasonal variation
Linear
Trend
Linear
Trend
Sep 8 ISMT/Stuart Zhu 10
Two Models
• Additive model– Demand = Trend + Seasonality
• Multiplicative model– Demand = Trend * Seasonality
Sep 8 ISMT/Stuart Zhu 11
Using Seasonal Relatives
• Seasonal relative– Percentage of average or trend
• Computing Seasonal relatives – Centered moving average: a moving average
positioned at the center of the data
Sep 8 ISMT/Stuart Zhu 12
Example 7 at Page 84
• Compute estimated relatives for each day
• Suppose that the trend equation is given by
120 +5t
– Give Friday represents t=5, what is the forecast on Friday?
Forecast-s3
Sep 8 ISMT/Stuart Zhu 13
Summary
• Compute the trend equation– a, b,
• How to compute and use seasonal relatives
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