TM 745 Forecasting for Business & Technology Paula Jensen South Dakota School of Mines and Technology, Rapid City 7th Session 3/14/10: Chapter 6 Time-Series Decomposition

Frank Matejcik SD School of Mines & Technology 2 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

Frank Matejcik SD School of Mines & Technology 3 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

Frank Matejcik SD School of Mines & Technology 4 The Basic Time-Series Decomposition Model Identify?

Frank Matejcik SD School of Mines & Technology 5 Deseasonalizing the Data and Finding Seasonal Indexes The process verbally 1. Find the MA’s (moving averages) 2. From the MA’s compute the CMA’s 3. Find the SF (seasonal factors) by dividing the data by the CMA’s 4. Average the SF to find the SI’s SI: seasonal index Two products CMA’s & SI’s Use CMA’s & SI’s How?

Frank Matejcik SD School of Mines & Technology 6 Deseasonalizing the Data and Finding Seasonal Indexes 1. Find the MA’s (moving averages)

Frank Matejcik SD School of Mines & Technology 7 Deseasonalizing the Data and Finding Seasonal Indexes 1. Find the MA’s (moving averages) swimwear example

Frank Matejcik SD School of Mines & Technology 8 Deseasonalizing the Data and Finding Seasonal Indexes 1. Find the MA’s (moving averages) swimwear example Check arrows on previous slide

Frank Matejcik SD School of Mines & Technology 9 Deseasonalizing the Data and Finding Seasonal Indexes 2. From the MA’s compute the CMA’s check arrows again

Frank Matejcik SD School of Mines & Technology 10 Deseasonalizing the Data and Finding Seasonal Indexes 3. Find the SF (seasonal factors) by dividing the data by the CMA’s SF>1 means? SF<1 means?

Frank Matejcik SD School of Mines & Technology 11 Deseasonalizing the Data and Finding Seasonal Indexes 4 th ed

Frank Matejcik SD School of Mines & Technology 12 Deseasonalizing the Data and Finding Seasonal Indexes 4 th ed

Frank Matejcik SD School of Mines & Technology 13 Deseasonalizing the Data and Finding Seasonal Indexes

Frank Matejcik SD School of Mines & Technology 14 Deseasonalizing the Data and Finding Seasonal Indexes 4 th ed

Frank Matejcik SD School of Mines & Technology 15 Deseasonalizing the Data and Finding Seasonal Indexes 5 th ed.

Frank Matejcik SD School of Mines & Technology 16 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 gives PHSCAT = (TIME) a slightly downward trend

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Frank Matejcik SD School of Mines & Technology 18 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

Frank Matejcik SD School of Mines & Technology 19 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)

Frank Matejcik SD School of Mines & Technology 20 Overview of Business Cycles

Frank Matejcik SD School of Mines & Technology 21 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

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Frank Matejcik SD School of Mines & Technology 23 Cycle Factor for PHS Note period and troughs figure 6-6 CF = PHMCMA/PHCMAT June - 03: CF = / = 1.27

Frank Matejcik SD School of Mines & Technology 24 Cycle Factor for PHS

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Frank Matejcik SD School of Mines & Technology 26 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)

Frank Matejcik SD School of Mines & Technology 27 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

Frank Matejcik SD School of Mines & Technology 28 The Time-Series Decomposition Forecast: PHS FY = (CMAT)(SI)(CF)(I) PHSFTSD = (PHSCMAT)(SI)(CF)(1) Historical RMSE = 9.16 Holdout RMSE = see fig 6-8 Light on Math and Statistics Easy for end user to understand So, user has more confidence

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Frank Matejcik SD School of Mines & Technology 30 Forecasting Shoe Store Sales: Time-Series Decomposition

Frank Matejcik SD School of Mines & Technology 31 Forecasting Shoe Store Sales: Time-Series Decomposition

Frank Matejcik SD School of Mines & Technology 32 Forecasting Total Houses Sold: Time-Series Decomposition

Frank Matejcik SD School of Mines & Technology 33 Forecasting Total Houses Sold: Time-Series Decomposition

Frank Matejcik SD School of Mines & Technology 34 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 specified at least 24 hours in advance Only 1 hour’s capacity in a storage buffer Yikes!

Frank Matejcik SD School of Mines & Technology 35 Integrative Case: The Gap 4 th

Frank Matejcik SD School of Mines & Technology 36 Integrative Case: The Gap 4 th

Frank Matejcik SD School of Mines & Technology 37

Frank Matejcik SD School of Mines & Technology 38 Integrative Case: The Gap 4 th

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Frank Matejcik SD School of Mines & Technology 40 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

Frank Matejcik SD School of Mines & Technology 41 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)

Frank Matejcik SD School of Mines & Technology 42 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 Michigan’s Survey Research Center Measures consumer attitude

Frank Matejcik SD School of Mines & Technology 43 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 > GDP

Frank Matejcik SD School of Mines & Technology 44 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

Frank Matejcik SD School of Mines & Technology 45 Appendix Components of the Composite Indexes Lagging Commercial and industrial loans Consumer installment credit to personal income ratio Consumer price index for services