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.