TM 745 Forecasting for Business

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TM 745 Forecasting for Business TechnologyDr.
Frank Joseph Matejcik
6th Session 6/21/07 Chapter 6 Time-Series
Decomposition Completed Chapter 7 ARIMA
(Box-Jenkins)-Type Forecasting Models

• South Dakota School of Mines and Technology,
  Rapid City

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Agenda New Assignment

• A few more comments from
• Chapter 7 problems to be assigned later (on
  dont suffer)
• First Test was taken by only one student
• Chapter 7 ARIMA (Box-Jenkins)-Type Forecasting
  Models

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Tentative Schedule
Chapters Assigned 17-May 1 e-mail,
contact problems 1,4, 8 24-May 2
problems 4, 8, 9 31-May 3,4 problems
ch3(1,5,8,11) ch4(6,10) 07-June 5 problems
5,8 14-June 6 start Test (Covering chapters 1-4)
Study Guide is on the class website. problems 4,
7 21-June 6 finish, 7 problems to be
assigned 28-June 8 05-July Final 9
Attendance Policy Help me work with you.
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Web Resources

• Class Web site on the HPCnet system
• http//sdmines.sdsmt.edu/sdsmt/directory/courses/2
  007su/tm745001
• Streaming video http//its.sdsmt.edu/Distance/
• Answers at http//www.hpcnet.org/what63
• 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.

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Integrative Case The Gap 4th
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Integrative Case The Gap 4th
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Integrative Case The Gap 4th
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Using ForecastX to Make Time-Series
Decomposition Forecasts

• Should we try it?

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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

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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)

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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

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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

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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

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Appendix Components of the Composite Indexes
Lagging

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

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ARIMA (Box-Jenkins)-Type Forecasting Models

• Introduction
• The Philosophy of Box-Jenkins
• Moving-Average Models
• Autoregressive Models
• Mixed Autoregressive Moving-Average Models
• Stationarity

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ARIMA (Box-Jenkins)-Type Forecasting Models

• The Box-Jenkins Identification Process
• Comments from the field INTELSAT
• ARIMA A Set of Numerical Examples
• Forecasting Seasonal Time Series
• Total Houses Sold
• Integrative Case The Gap
• Using ForecastXTM to Make ARIMA (Box-Jenkins)
  forecasts

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Introduction

• Examples of times series data
• Hourly temperatures at your office
• Daily closing price of IBM stock
• Weekly automobile production of Fords
• Data from an individual firm sales, profits,
  inventory, back orders
• An electrocardiogram
• NO causal stuff, just series data

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Introduction

• ARIMA Autoregressive Integrated Moving Average
• Box-Jenkins
• Best used for longer range
• Used in short, medium long range
• Advantages
• Wide variety of models
• Much info from a time series

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The Philosophy of Box-Jenkins

• Regression view point
• Box-Jenkins view point

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The Philosophy of Box-Jenkins

• What is white noise?
• No relationship between previous values
• Previous values no help in forecast
• Examples are bit lame in text
• Dow Jones last digits, Lotto
• A good random number generator (for Simulation)
  is a better
• In Stats books the assumptionis iid Normal(0,s 2)

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The Philosophy of Box-Jenkins

• Standard Regression Analysis
• 1. Specify the causal variables.
• 2. Use a regression model.
• 3. Estimate a b coefficients.
• 4. Examine the summary statistics try other
  model specs.
• 5. Choose the most best model spec. (often based
  on RMSE).

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The Philosophy of Box-Jenkins

• For Box-Jenkins methodology
• 1. Start with the observed time series.
• 2. Pass the series through a black box.
• 3. Examine the series that results from passage
  through the black box.
• 4. If the black box is correct, only white noise
  should remain.
• 5. If the remaining series is not white noise,
  try another black box.

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The Philosophy of Box-Jenkins

• Wait a bit on the distinction of methods
• A common regression check is a probability paper
  plot of the residuals
• In Katyas triangle we look forwhite noise in
  the residuals
• Some regression checks resemblethe Box-Jenkins
  approach

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The Philosophy of Box-Jenkins

• Three main types on Models
• MA moving average
• AR autoregressive
• ARMA autoregressive moving average
• ARIMA what is the I?

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Moving-Average Models

• Weighted moving average, may be a better term
  than moving average
• MA(k) k number of steps used

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Moving-Average Models

• Example in text table 7.2 of MA(1)

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MA ModelsAutocorelation

• Autocorrelation was in chapter 2.

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Correlograms An Alternative Method of Data
Exploration
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AR ModelsPartial Autocorelation

• Degree of association between Yt Yt-kwhen all
  other lags are held constant
  solve below for Y s

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Moving-Average Ideal MA(1)
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Moving-Average Ideal MA(2)
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Moving-Average Generated ACF
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Moving-Average Generated PACF
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Autoregressive Models

• How do we check for this model?
• Where did we see it before?

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Autoregressive Models

• Lets check the PACF and ACF plots
• AR(k) k is the number of steps used

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ACF PACF Ideal AR(1)
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ACF PACF Ideal AR(2)
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Mixed Autoregressive and Moving-Average Models

• We call these are ARMA models
• Check out the ACF PACF plots

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Mixed Autoregressive and Moving-Average Models
Ideal
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Mixed Autoregressive and Moving-Average Models
Ideal
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Stationarity

• There is a fix for some forms of
  non-stationarity. Where have seen it before?

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Stationarity

• When that doesnt work. Try it again!

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Stationarity

• When we use the differencing we cal the models
  ARIMA(p,d,q) .

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Stationarity Example
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Stationarity Example
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Stationarity

• When we use the differencing we cal the models
  ARIMA(p,d,q) .

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Box-Jenkins Identification Process

• What do we use for diagnostics?

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The Box-Jenkins ID Process

• 1.If the autocorrelation function abruptly stops
  at some point-say, after q spikes-then the
  appropriate model is an MA(q) type.
• 2.If the partial autocorrelation function
  abruptly stops at some point-say, after p
  spikes-then the appropriate model is a AR(p).
• 3.If neither function falls off abruptly, but
  both decline toward zero in some fashion, the
  appropriate model is an ARMA(p, q).

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The Box-Jenkins ID Process

• Ljung-Box statistic
• Informal measures are also used

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ARIMA A Set of Numerical Examples Example 1

• Use Elmo

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ARIMA A Set of Numerical Examples Example 2

• Use Elmo

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ARIMA A Set of Numerical Examples Example 3

• Use Elmo

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ARIMA A Set of Numerical Examples Example 4

• Use Elmo

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Forecasting Seasonal Time Series

• Its complicated call it
• treat the season length like it is a times
  series.
• Notation in next example
• Use a second (p,d,q) set for seasonals

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Case INTELSAT

• Communication Satellites 15 years out
• Freeway in example in I-75 Atlanta
• ARIMA (1,0,1)(0,1,1)672 Best of All

Case Intelligent Transportation
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Total Houses Sold

• Done rather quickly in the text, Why?
• Use ELMO?

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Integrative Case The Gap

• Same Data
• ARIMA (2,0,2)(0,2,1) seems to fit, other models
  do work.

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Using ForecastXTM to Make ARIMA (Box-Jenkins)
forecasts

• Can we try it?