Statistical
forecasting:
notes on regression and time series analysis
Robert
Nau
Fuqua School of Business
Duke University
This web
site contains notes and materials for an advanced elective course on
statistical forecasting that is taught at the Fuqua School of Business, Duke
University. It covers linear regression and time series forecasting models as
well as general principles of thoughtful data analysis. The time series
material is illustrated with output produced by Statgraphics, a statistical software
package that is highly interactive and has good features for testing and
comparing models, including a parallel-model forecasting procedure that I
designed many years ago. The material on multivariate data analysis and linear
regression is illustrated with output produced by RegressIt, a free Excel add-in
which I also designed. However, these notes are platform-independent. Any
statistical software package ought to provide the analytical capabilities
needed for the various topics covered here.
If you use
Excel in your work or in your teaching to any extent, you should check out the
latest release of RegressIt, a free Excel add-in for linear and logistic
regression. See it at regressit.com. The linear regression version runs on both PC's and Macs and
has a richer and easier-to-use interface and much better designed output than
other add-ins for statistical analysis. It may make a good complement if not a
substitute for whatever regression software you are currently using,
Excel-based or otherwise. RegressIt is an excellent tool for
interactive presentations, online teaching of regression, and development of
videos of examples of regression modeling. It includes extensive built-in documentation
and pop-up teaching notes as well as some novel features to support systematic
grading and auditing of student work on a large scale. There is a separate logistic regression version with highly interactive tables and charts that runs
on PC's. RegressIt also now includes a two-way interface with R that allows you to run linear and logistic regression
models in R without writing any code whatsoever.
If you have
been using Excel's own Data Analysis add-in for regression (Analysis Toolpak),
this is the time to stop. It has not
changed since it was first introduced in 1993, and it was a poor design even
then. It's a toy (a clumsy one at that), not a tool for serious work. Visit
this page for a discussion: What's wrong with Excel's Analysis Toolpak for regression
1. Get to know your data
Principles and risks
of forecasting (pdf)
Famous forecasting quotes
How to move data around
Get to know your data
Inflation adjustment (deflation)
Seasonal adjustment
Stationarity and differencing
The logarithm transformation
2. Introduction to
forecasting: the simplest models
Statistics
review and the simplest forecasting model: the sample mean (pdf)
Notes on the random
walk model (pdf)
Mean (constant) model
Linear trend model
Random walk model
Geometric random walk model
Three types of forecasts: estimation period, validation
period, and the future
3. Averaging and smoothing
models
Notes on
forecasting with moving averages (pdf)
Moving average and exponential smoothing models
Slides
on inflation and seasonal adjustment and Winters seasonal exponential smoothing
Spreadsheet implementation of seasonal adjustment and exponential
smoothing
Equations
for the smoothing models (SAS web site)
4. Linear regression models
Notes on linear regression
analysis (pdf)
Introduction to linear regression analysis
Mathematics
of simple regression
Regression examples
- Beer sales
vs. price, part 1: descriptive analysis
- Beer sales
vs. price, part 2: fitting a simple model
- Beer sales
vs. price, part 3: transformations of variables
- Beer sales
vs. price, part 4: additional predictors
- NC natural gas consumption vs.
temperature
- More regression datasets at regressit.com
What to look for in
regression output
What's a good value for R-squared?
What's the bottom line? How to compare models
Testing the assumptions of linear regression
Additional notes on regression analysis
Stepwise and all-possible-regressions
Excel file with simple
regression formulas
Excel file with regression
formulas in matrix form
Notes on logistic regression (new!)
RegressIt: free Excel add-in for
linear and logistic regression and multivariate data analysis
5. ARIMA models for time
series forecasting
Notes on nonseasonal
ARIMA models (pdf)
Slides on seasonal and
nonseasonal ARIMA models (pdf)
Introduction to ARIMA: nonseasonal models
Identifying the order of differencing
Identifying the orders of AR or MA terms
Estimation of ARIMA models
Seasonal differencing
Seasonal random walk: ARIMA(0,0,0)x(0,1,0)
Seasonal random trend: ARIMA(0,1,0)x(0,1,0)
General seasonal ARIMA models: ARIMA(0,1,1)x(0,1,1) etc.
Summary of rules for identifying ARIMA models
ARIMA models with regressors
The
mathematical structure of ARIMA models (pdf)
6. Choosing the right
forecasting model
Steps in choosing a forecasting model
Forecasting flow chart
Data transformations and forecasting models: what to use
and when
Automatic forecasting software
Political and ethical issues in forecasting
How to avoid trouble: principles of good data analysis
7. Statistics resources on the web
Forecasting
Principles and Practice (R-based on-line textbook by Rob Hyndman and George
Athanasopoulos)
OpenIntro
Statistics (David Diez, Christopher Barr, Mine Cetinkaya-Rundel)
Stat 510:
Applied Time Series (R-based on-line course at Penn State)
Online StatBook (David Lane)
International
Institute of Forecasters links (sites, references, software)
Forecasting Principles web site
(J. Scott Armstrong and Kesten Green)
HyperStat Online web site (David
Lane)
Institute
for Digital Research and Education at UCLA
Statsblogs (links to many blogger sites)
StatPages web site (John Pezzullo)
StatSci web site (Gordon Smyth)
Talk Stats forum
StackExchange Cross-Validated forum
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