Lecture notes on
forecasting
Robert
Nau
Fuqua School of Business
Duke University
This web
site contains notes for an advanced elective course on statistical forecasting
that has been taught at the Fuqua School of Business, Duke University, for many
years. Most of the examples of computer output were generated with Statgraphics, a general-purpose statistical
analysis program that offers interactive graphics and has especially good
features for fitting and comparing models for time series data, including a
forecasting procedure that I designed. The site is currently undergoing some
long-overdue upgrades. Future material dealing with multivariate data analysis
and regression models will include examples of output generated by RegressIt, a free Excel add-in that I have developed more recently, whose procedures
for descriptive data analysis and ordinary linear regression offer high-quality
output and support for good modeling practices. However, these notes are
platform-independent. Any statistical software package ought to provide the
analytical capabilities needed for the various topics covered here.
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)
Averaging and exponential smoothing models
Spreadsheet implementation of seasonal adjustment and
exponential smoothing
4. Linear regression models
Notes on linear
regression analysis (pdf)
Introduction to linear regression analysis
Regression example, part 1:
descriptive analysis
Regression example, part 2: fitting a simple model
Regression example, part 3: transformations of variables
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
Spreadsheet with
regression formulas
Stepwise and all-possible-regressions
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
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
7. Forecasting resources
Forecasting Principles web site
(J. Scott Armstrong and Kesten Green)
Forecasting Principles and Practice
on-line textbook (Rob Hyndman and George Athanasopoulos)
International
Institute of Forecasters links (sites, references, software)
StatPages web site (John Pezzullo)
StatSci web site (Gordon Smyth)
Talk Stats forum
StackExchange Cross-Validated forum
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This site receives around 2000 visitors per day on average. Last
updated on September 20, 2014.