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TM 745 Forecasting for Business & Technology Dr. Frank Joseph Matejcik 8th Session 3/29/10: Chapter 7 ARIMA (Box-Jenkins)-Type Forecasting Models South Dakota School of Mines and Technology, Rapid City Agenda & New Assignment Chapter 7 problems 3,4,5(series A)7B

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tm 745 forecasting for business technology dr frank joseph matejcik

TM 745 Forecasting for Business & TechnologyDr. Frank Joseph Matejcik

8th Session 3/29/10:

Chapter 7 ARIMA (Box-Jenkins)-Type Forecasting Models

South Dakota School of Mines and Technology, Rapid City

agenda new assignment
Agenda & New Assignment
  • Chapter 7 problems 3,4,5(series A)7B
  • Chapter 7 ARIMA (Box-Jenkins)-Type Forecasting Models
  • Don’t have your exams graded, yet.
tentative schedule
Tentative Schedule

Chapters Assigned

25-Jan 1 problems 1,4,8

e-mail, contact

1-Feb 2 problems 4,8,9

8-Feb 3 problems 1,5,8,11

15-Feb President’s Day

22-Feb 4 problems 6, 10

1-Mar 5 problems 5, 8

8-Mar Break

15-Mar Exam 1 Ch 1-4 Revised

22-Mar 6 problems 4, 7

29-Mar 7 3,4,5(series A) 7B

Chapters Assigned

5-Apr Easter

The Rest undecided

web resources
Web Resources
  • Class Web site on the HPCnet system
  • http://sdmines.sdsmt.edu/sdsmt/directory/courses/2010sp/tm745M001
  • Answers will be online. Linked from ^
  • I have gotten D2L and Elluminate! sites, and have gotten started on Elluminate! documentation.
  • The same class session that is on the DVD is on the stream in lower quality. http://www.flashget.com/ will allow you to capture the stream more readily and review the lecture, anywhere you can get your computer to run.
arima box jenkins type forecasting models
ARIMA (Box-Jenkins)-Type Forecasting Models
  • Introduction
  • The Philosophy of Box-Jenkins
  • Moving-Average Models
  • Autoregressive Models
  • Mixed Autoregressive & Moving-Average Models
  • Stationarity
arima box jenkins type forecasting models6
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
introduction
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
introduction8
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
the philosophy of box jenkins
The Philosophy of Box-Jenkins
  • Regression view point
  • Box-Jenkins view point
the philosophy of box jenkins10
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)
the philosophy of box jenkins11
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).
the philosophy of box jenkins12
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.
the philosophy of box jenkins13
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 Katya’s triangle we look for“white noise” in the residuals
  • Some regression checks resemblethe Box-Jenkins approach
the philosophy of box jenkins14
The Philosophy of Box-Jenkins
  • Three main types on Models
  • MA: moving average
  • AR: autoregressive
  • ARMA: autoregressive moving average
  • ARIMA what is the I?
moving average models
Moving-Average Models
  • Weighted moving average, may be a better term than moving average
  • MA(k) k: number of steps used
moving average models16
Moving-Average Models
  • Example in text table 7.2 of MA(1)
ma models autocorelation
MA ModelsAutocorelation
  • Autocorrelation was in chapter 2.
slide19

AR ModelsPartial Autocorelation

  • Degree of association between Yt & Yt-kwhen all other lags are held constant solve below for Y ’s
autoregressive models
Autoregressive Models
  • How do we check for this model?
  • Where did we see it before?
autoregressive models25
Autoregressive Models
  • Let’s check the PACF and ACF plots
  • AR(k) : k is the number of steps used
mixed autoregressive and moving average models
Mixed Autoregressive and Moving-Average Models
  • We call these are ARMA models
  • Check out the ACF & PACF plots
stationarity
Stationarity
  • There is a fix for some forms of non-stationarity. Where have seen it before?
stationarity32
Stationarity
  • When that doesn’t work. Try it again!
stationarity33
Stationarity
  • When we use the differencing we cal the models ARIMA(p,d,q) .
stationarity36
Stationarity
  • When we use the differencing we call the models ARIMA(p,d,q) .
box jenkins identification process
Box-Jenkins Identification Process
  • What do we use for diagnostics?
the box jenkins id process
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).
the box jenkins id process41
The Box-Jenkins ID Process
  • Ljung-Box statistic
  • Informal measures are also used
arima a set of numerical examples example 3 4
ARIMA: A Set of Numerical Examples Example 3 & 4
  • Use Elmo was in the old slides, but we have no more.
  • Let’s skip in discussion
forecasting seasonal time series
Forecasting Seasonal Time Series
  • It’s 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
case intelsat
Case: INTELSAT

Case: Intelligent Transportation

  • Communication Satellites 15 years out
  • Freeway in example in I-75 Atlanta
  • ARIMA (1,0,1)(0,1,1)672 Best of All
total houses sold
Total Houses Sold
  • Done rather quickly in the text, Why?
  • Use ELMO?
integrative case the gap
Integrative Case: The Gap
  • Same Data
  • ARIMA (2,0,2)(0,2,1) seems to fit, other models do work.