Forecasting_and_Time_Series_Methods

Forecasting_and_Time_Series_Methods - Forecasting & Time...

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3/4/2009 1 Forecasting & Time Series Methods Kwok Leung Tsui Industrial & Systems Engineering Georgia Institute of Technology
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3/4/2009 2 References ± Textbooks and Reference ± Business Forecasting, Hanke, Wichern, and Reitsch, 8th Edition, Prentice Hall, 2005 (BF) ± Marketing Engineering, Lilien and Rangaswamy, 2nd Edition, Prentice Hall, 2003 (ME) ± Forecasting Methods and Applications, Makridakis, Wheelwright, and Hyndman, NY, John Wiley & Sons, 1998
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3/4/2009 3 Other Resources ± Some useful URL links: ± Course: TBD ± Reference: http://www- marketing.wharton.upenn.edu/forecast/welcome.html ± IIF (International Institute of Forecasters): http://www.forecasters.org/ ± Dataset ± Textbook examples: downloadable from http://wps.prenhall.com/bp_hanke_busforecast_8 ± Competitions: M-series competitions: http://www.ms.ic.ac.uk/iif/data/mcomp/mcomp.htm ± Other internet resources: economic data, stock prices, census data … http://www-marketing.wharton.upenn.edu/forecast/data.html ± Software: ± General: Excel, Minitab, Splus, Matlab, SPSS, SAS, … ± Specific: ForecastPro, … … … … ± YOUR OWN!
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3/4/2009 4 Outline • Two Basic Forecasting Approaches – Adaptive Smoothing Methods – Time Series and ARIMA Models • Forecasting Applications • Forecasting Strategies
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3/4/2009 5 Adaptive Smoothing Methods
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3/4/2009 6 Linear Regression For Time Series Time is the ONLY explanatory variable ε t is i.i.d. of mean 0 and variance σ 2 • Least-squared estimation can be derived = = = T t k k t t t t x L L 1 2 2 2 1 0 ) ( ) ( where ) ( arg ˆ min ββ β L t k k t t t t x εβ + + + + + = K 2 2 1 0
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3/4/2009 7 Linear Regression For Time Series • If constant, simple average • If linear trend, = t x T 1 ˆ 0 β = = = = = = = + = = = + = = T t t i i T t i i n t t T t t x t SX t ST SX ST ST t x t L SX ST T t x L 1 1 1 2 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 , where 0 ) ( 2 0 ) ( 2 ββ t t t t x x T T ST ST ST SX ST SX T ST ST T SX ST SX ˆ ˆ 2 ˆ ˆ ˆ ˆ 2 2 2 1 2 0 1 1 0 2 2 1 1 1 0 1 = = = = ε σ
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3/4/2009 8 Linear Regression For Time Series • How about higher order? – Example:Tab 4-1 – Too aggressive in trend due to historical data • Forecast is made • Better to utilize most recent information. k k h T h T h T h T x ) ( ˆ ) ( ˆ ) ( ˆ ˆ ˆ 2 2 1 0 + + + + + + + = + β ββ K
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3/4/2009 9 Linear Regression For Time Series Sales of Saws for ACME (Tab 4-1) 0 100 200 300 400 500 600 700 800 900 Raw Data 4 per . Mov. Avg. (Ser ies2) Linear (Ser ies2) Poly. (Series2)
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3/4/2009 10 Static vs. Dynamic • Linear regression model assumes a time- invariant relationship - static – Natural variation – Coefficients – Example: Tab 4-1 • Dynamic/Adaptive Models – Moving Average – Exponential Smoothing
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3/4/2009 11 Single Exponential Smoothing • Simple average • Moving average • Single Exponential smoothing (EWMA) + = + = T t t T T T T x T x x T x 1 1 1 ˆ ) 1 ( ˆ + = + = T w T t t T x w x 1 1 1 ˆ 1 1 1 2 2 1 1 ˆ ) 1 ( ) 1 ( ) 1 ( ) 1 ( ˆ ) 1 ( ˆ x x x x x x x x T T T T T T T T λλ λ + + + + = + = + L
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3/4/2009 12 Weighting Coefficients Moving Average 0 0.05 0.1 0.15
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This note was uploaded on 11/13/2010 for the course ISE 680 taught by Professor Santanu during the Spring '10 term at Purdue University Calumet.

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Forecasting_and_Time_Series_Methods - Forecasting & Time...

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