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Classical DecompositionPowerPoint Presentation

Classical Decomposition

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Presentation Transcript

Overview:

- Time series models & classical decomposition
- Brainstorming exercise
- Classical decomposition explained
- Classical decomposition illustration
- Exercise
- Summary
- Bibliography & readings list
- Appendix A: exercise templates

Time Series Models & Classical Decomposition

- Time series models are sequences of data that follow non-random orders
- Examples of time series data:
- Sales
- Costs

- Time series models are composed of trend, seasonal, cyclical, and random influences

Time Series Models & Classical Decomposition

- Decomposition time series models:
- Multiplicative: Y = T x C x S x e
- Additive: Y = T + C + S + e
- T = Trend component
- C = Cyclical component
- S = Seasonal component
- e = Error or random component

Time Series Models & Classical Decomposition

- Classical decomposition is used to isolate trend, seasonal, and other variability components from a time series model
- Benefits:
- Shows fluctuations in trend
- Provides insight to underlying factors affecting the time series

Brainstorming Exercise

- Identify how this tool can be used in your organization…

Classical Decomposition Explained

Basic Steps:

- Determine seasonal indexes using the ratio to moving average method
- Deseasonalize the data
- Develop the trend-cyclical regression equation using deseasonalized data
- Multiply the forecasted trend values by their seasonal indexes to create a more accurate forecast

Classical Decomposition Explained: Step 1

- Determine seasonal indexes
- Start with multiplicative model…
Y = TCSe

- Equate…
Se = (Y/TC)

Classical Decomposition Explained: Step 1

- To find seasonal indexes, first estimate trend-cyclical components
Se = (Y/TC)

- Use centered moving average
- Called ratio to moving average method

- For quarterly data, use four-quarter moving average
- Averages seasonal influences

Example

Classical Decomposition Explained: Step 1 Use centered moving average to position data in middle of the period

- Four-quarter moving average will position average at…
- end of second period and
- beginning of third period

Example

Classical Decomposition Explained: Step 1

- Find seasonal-error components by dividing original data by trend-cyclical components
Se = (Y/TC)

- Se = Seasonal-error components
- Y = Original data value
- TC = Trend-cyclical components
(centered moving average value)

Example

Classical Decomposition Explained: Step 1

- Unadjusted seasonal indexes (USI) are found by averagingseasonal-error components by period
- Develop adjusting factor (AF) so USIs are adjusted so their sum equals the number of quarters (4)
- Reduces error

Example

Example

Classical Decomposition Explained: Step 1

- Adjusted seasonal indexes (ASI) are derived by multiplying the unadjusted seasonal index by the adjusting factor
ASI = USI x AF

- ASI = Adjusted seasonal index
- USI = Unadjusted seasonal index
- AF = Adjusting factor

Example

Classical Decomposition Explained: Step 2

- Deseasonalized data is produced by dividing the original data values by their seasonal indexes
(Y/S) = TCe

- Y/S = Deseasonalized data
- TCe = Trend-cyclical-error component

Example

Classical Decomposition Explained: Step 3

- Develop the trend-cyclical regression equation using deseasonalized data
Tt = a + bt

- Tt = Trend value at period t
- a = Intercept value
- b = Slope of trend line

Example

Classical Decomposition Explained: Step 4

- Use trend-cyclical regression equation to develop trend data
- Create forecasted data by multiplying the trend data values by their seasonal indexes
- More accurate forecast

Example

Example

Classical Decomposition Explained: Step Summary

Summarized Steps:

- Determine seasonal indexes
- Deseasonalize the data
- Develop the trend-cyclical regression equation
- Create forecast using trend data and seasonal indexes

Classical Decomposition:Illustration

- Gem Company’s operations department has been asked to deseasonalize and forecast sales for the next four quarters of the coming year
- The Company has compiled its past sales data in Table 1
- An illustration using classical decomposition will follow

Classical Decomposition Illustration: Step 1

- (a) Compute the four-quarter simple moving average
Ex: simple MA at end of Qtr 2 and beginning of Qtr 3

(55+47+65+70)/4 = 59.25

Explain

Classical DecompositionIllustration: Step 1

- (b) Compute the two-quarter centered moving average
Ex: centered MA at middle of Qtr 3

(59.25+61.25)/2

= 60.500

Explain

Classical Decomposition Illustration: Step 1

- (c) Compute the seasonal-error component (percent MA)
Ex: percent MA at Qtr 3

(65/60.500)

= 1.074

Explain

Classical DecompositionIllustration: Step 1

- (d) Compute the unadjusted seasonal index using the seasonal-error components from Table 2
Ex (Qtr 1): [(Yr 2, Qtr 1) + (Yr 3, Qtr 1) + (Yr 4, Qtr 1)]/3

= [0.989+0.914+0.926]/3 = 0.943

Explain

Classical DecompositionIllustration: Step 1

- (e) Compute the adjusting factor by dividing the number of quarters (4) by the sum of all calculated unadjusted seasonal indexes
= 4.000/(0.943+0.851+1.080+1.130) = (4.000/4.004)

Explain

Classical DecompositionIllustration: Step 1

- (f) Compute the adjusted seasonal index by multiplying the unadjusted seasonal index by the adjusting factor
Ex (Qtr 1): 0.943 x (4.000/4.004) = 0.942

Explain

Classical DecompositionIllustration: Step 2

- Compute the deseasonalized sales by dividing original sales by the adjusted seasonal index
Ex (Yr 1, Qtr 1):

(55 / 0.942)

= 58.386

Explain

Classical DecompositionIllustration: Step 3

- Compute the trend-cyclical regression equation using simple linear regression
Tt = a + bt

t-bar = 8.5

T-bar = 69.6

b = 1.465

a = 57.180

Tt = 57.180 + 1.465t

Explain

Classical DecompositionIllustration: Step 4

- (a) Develop trend sales
Tt = 57.180 + 1.465t

Ex (Yr 1, Qtr 1):

T1 = 57.180 + 1.465(1) = 58.645

Explain

Classical DecompositionIllustration: Step 4

- (b) Forecast sales for each of the four quarters of the coming year
Ex (Yr 5, Qtr 1):

0.942 x 82.085

= 77.324

Explain

Classical DecompositionIllustration: Graphical Look

Classical Decomposition:Exercise

- Assume you have been asked by your boss to deseasonalize and forecast for the next four quarters of the coming year (Yr 5) this data pertaining to your company’s sales
- Use the steps and examples shown in the explanation and illustration as a reference
Basic Steps

Explanation

Illustration

Templates

Summary

- Time series models are sequences of data that follow non-arbitrary orders
- Classical decomposition isolates the components of a time series model
- Benefits:
- Insight to fluctuations in trend
- Decomposes the underlying factors affecting the time series

Bibliography &Readings List

DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management. Homewood: Business One Irwin, 1991.

Shim, Jae K. Strategic Business Forecasting. New York: St Lucie, 2000.

StatSoft Inc. (2003). Time Series Analysis. Retrieved April 21, 2003, from http://www.statsoft.com/textbook/sttimser.html

Appendix A:Exercise Templates

Appendix A:Exercise Templates

Appendix A:Exercise Templates

Appendix A:Exercise Templates

Appendix A:Exercise Templates

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