TM 745 Forecasting for Business

1
TM 745 Forecasting for Business TechnologyDr.
Frank Joseph Matejcik
7th Session 3/31/08 Chapter 6 Time-Series
Decomposition 6th Lecture

• South Dakota School of Mines and Technology,
  Rapid City

2
Agenda New Assignment

• Chapter 6 problems 4, 7 (on 7d dont suffer)
• Chapter 6 Time-Series Decomposition Forecasting

3
Tentative Schedule
Chapters Assigned 28-Jan 1 problems
1,4,8 e-mail, contact 4-Feb 2 problems 4,
8, 9 11-Feb 3 problems 1,5,8,11 18-Feb
Presidents Day 25-Feb 4 problems 6,10 3-Mar
5 problems 5,8 10-Mar Exam 1 Ch 1-4
Revised 17-Mar Break 24-Mar Easter 31-Mar
6 problems 4, 7
Chapters Assigned 7-Apr 7 3,4,5(series
A) 7B 21-Apr 8 Problem 6 28-Apr
9 05-May Final
4
Web Resources

• Class Web site on the HPCnet system
• http//sdmines.sdsmt.edu/sdsmt/directory/courses/2
  008sp/tm745M021
• Streaming video http//its.sdsmt.edu/Distance/
• Answers will be online. Linked from
• The same class session that is on the DVD is on
  the stream in lower quality. http//www.flashget.c
  om/ will allow you to capture the stream more
  readily and review the lecture, anywhere you can
  get your computer to run.

5
Time-Series Decomposition

• Trend, seasonal, cyclical, random
• Oldest, but popular
• 1. They make good forecasts
• 2. Easy to understand explain
• 3. How managers look at data (in the other
  books, courses)
• Ratio to moving average
• Classical time-series decomposition

6
The Basic Time-Series Decomposition Model

• Y T x S x C x I
• T long term trend in the data
• S seasonal adjustment factor
• C cyclic adjustment factor
• I irregular or random variations in the series

7
The Basic Time-Series Decomposition Model
Identify?
8
Deseasonalizing the Data and Finding Seasonal
Indexes

• The process verbally
• 1. Find the MAs (moving averages)
• 2. From the MAs compute the CMAs
• 3. Find the SF (seasonal factors) by dividing the
  data by the CMAs
• 4. Average the SF to find the SIsSI seasonal
  index
• Two products CMAs SIs
• Use CMAs SIs How?

9
Deseasonalizing the Data and Finding Seasonal
Indexes

• 1. Find the MAs (moving averages)

10
Deseasonalizing the Data and Finding Seasonal
Indexes

• 1. Find the MAs (moving averages) swimwear
  example

11
Deseasonalizing the Data and Finding Seasonal
Indexes

• 1. Find the MAs (moving averages) swimwear
  exampleCheck arrows on previous slide

12
Deseasonalizing the Data and Finding Seasonal
Indexes

• 2. From the MAs compute the CMAs
  check arrows again

13
Deseasonalizing the Data and Finding Seasonal
Indexes

• 3. Find the SF (seasonal factors) by dividing the
  data by the CMAsSFgt1 means? SFlt1 means?

14
Deseasonalizing the Data and Finding Seasonal
Indexes 4th ed
15
Deseasonalizing the Data and Finding Seasonal
Indexes 4th ed
16
Deseasonalizing the Data and Finding Seasonal
Indexes
17
Deseasonalizing the Data and Finding Seasonal
Indexes 4th ed
18
Deseasonalizing the Data and Finding Seasonal
Indexes 5th ed.
19
Finding the Long-Term Trend

• Usually linear, but can be other.
• Gap data was fit to exponential
• CMA f (TIME) a b (TIME)
• Linear fit to PHSCMA givesPHSCAT 134.8 -
  0.04(TIME)a slightly downward trend

20
(No Transcript)
21
Measuring the Cyclical Component

• CF CMA/CMAT
• CF cycle factor
• CMA centered moving average
• CMAT centered moving average trend
• Most difficult to analyze
• Can hint at future by noting characteristics of
  the cycle

22
Overview of Business Cycles

• Expansion phase
• Contraction phase (recession)
• Business Cycles
• amplitude is not constant
• period is not constant
• Official definitions of beginning end of
  recession (3 month rule)

23
Overview of Business Cycles
24
Business Cycle Indicators

• Can be used a independent variables (predictors)
  in regression analysis
• Major indexes or components useful
• Major indexes see table 6.4 page 300
• I. of leading economic indicators
• I. of coincident economic indicators
• I. of lagging economic indicators
• Figure 6-5 follows

25
(No Transcript)
26
Cycle Factor for PHS

• Note period and troughs figure 6-6
• CF PHMCMA/PHCMATJune - 03 CF
  153.10/120.42 1.27

27
Cycle Factor for PHS
28
(No Transcript)
29
The Time-Series Decomposition Forecast

• Y T x S x C x I
• T Long-term trend
• based on the deseasonalized data
• centered moving average trend (CMAT)
• S Seasonal indexes (SI)
• Normalized avgs of seasonal factors
• Ratio of each period's actual value (Y) to the
  deseasonalized value (CMA)

30
The Time-Series Decomposition Forecast

• Y T x S x C x I
• C Cycle component.
• Cycle factor (CF CMA/ CMAT)
• gradual wavelike series about the trend line
• I Irregular component. (random)
• Assumed equal to 1, usually
• If a shock occurred, not 1
• When doing simulation, random

31
The Time-Series Decomposition Forecast PHS

• FY (CMAT)(SI)(CF)(I)
• PHSFTSD (PHSCMAT)(SI)(CF)(1)
• Historical RMSE 9.16
• Holdout RMSE 12.29 see fig 6-8
• Light on Math and Statistics
• Easy for end user to understand
• So, user has more confidence

32
(No Transcript)
33
Forecasting Shoe Store Sales Time-Series
Decomposition
34
Forecasting Shoe Store Sales Time-Series
Decomposition
35
Forecasting Total Houses Sold Time-Series
Decomposition
36
Forecasting Total Houses Sold Time-Series
Decomposition
37
Forecasting at Vermont Gas Systems Winter Daily
Forecast

• 26,000 customers in NW Vermont
• Closest big city for customers?
• Gas suppliers in western Canada
• Storage along Trans-Canada pipeline
• Quantities must be specifiedat least 24 hours in
  advance
• Only 1 hours capacity in a storage buffer
  Yikes!

38
Integrative Case The Gap 4th
39
Integrative Case The Gap 4th
40
(No Transcript)
41
Integrative Case The Gap 4th
42
(No Transcript)
43
Using ForecastX to Make Time-Series
Decomposition Forecasts

• Should we try it?

44
Appendix Components of the Composite Indexes
Leading

• Average weekly hours, manufacturing
• Average weekly initial claims for unemployment
  insurance
• Manufacturers' new orders, consumer goods
  materials
• Vendor performance, slower deliveries diffusion
  index

45
Appendix Components of the Composite Indexes
Leading

• Manufacturers' new orders, nondefense capital
  goods
• Building permits, new private housing units
• Stock prices, 500 common stocks
• Money supply M2 (inflation adjusted)
• demand deposits, checkable deposits,savings
  deposits, balances in money market funds (money
  like stuff)

46
Appendix Components of the Composite Indexes
Leading

• Interest-rate spread, 10-year Treasury bonds less
  federal funds
• Difference between long short rates
• Called the yield curve
• negative recession,
• Index of consumer expectations
• U. of Michigans Survey Research Center
• Measures consumer attitude

47
Appendix Components of the Composite Indexes
Coincident

• Employees on nonagricultural payrolls
• U.S. Bureau of Labor Statistics
• Payroll employment
• Personal income less transfer payments
• Industrial production
• Numerous sources
• Valued added concept
• Manufacturing and trade sales
• Aggregate sales gt GDP

48
Appendix Components of the Composite Indexes
Coincident

• Average duration of unemployment
• Inventories to sales ratio, manufacturing and
  trade
• Labor cost per unit of output, manufacturing
• Average prime rate

49
Appendix Components of the Composite Indexes
Lagging

• Commercial and industrial loans
• Consumer installment credit to personal income
  ratio
• Consumer price index for services