Time Series Analysis using SAS
prepared by
John Fahey
(former Load Forecaster at NSPI)
and
Voytek Grus
(former Sales and Revenue Forecaster at BC Gas Inc.)
for
SAS user group, Halifax
February 6, 2009
Overview
• A little bit about Times Series Analysis in general.
• Statistical tools available in SAS to conduct
Analysis.
• Empirical example using SAS
What is Time Series Analysis?
• Time Series - a sequence of data points, measured
typically at successive times.
• Times Series Analysis is a collection of statistical
techniques used to understand time series by trying
to find an internal mechanism that explains their
behavior.
– Series decomposition; trend, cyclicality, seasonality,
irregularity (random effect)
– A central idea to Time series analysis is that it is a
statistical (stochastic) process but it has not always
been this way…
• Time series analysis ≠ Forecasting
• Applications
A little bit of history…
– Time a mysteries concept – TS considered a deterministic
concept
– XIX century – explain TS in terms of trigonometric fcns
(fourier series).
– 1927 – Udny Yule introduced statistical approach
(sun-spot studies)
– 1950’s and 60’s regression with error modeling
(econometrics)
– 1960’s state space models (Kalman filter or Bayesian
Forecasting)
– Mid 1970’s Box Jenkins introduced ARIMA models
Other: multivarate time series, non-linear models, bispectra
Approaches to time series analysis.
• Analysis in time domain.
– Trend extrapolation: use linear, polynomials, & sine waves functions
for trend extrapolation. (regression and auto regression)
– Moving Averages: fit in polynomial of order p to the last (2m+1) points.
– Exponential smoothing
• Winters, Holt-Winters, Harrison (additive vs multiplicative models)
– ARIMA models (differencing, stationarity, correlograms)
• Dynamic regression (arimax)
– Statespace / structural models: decompose series into trends, cycle,
season, and white noise.
– Mulitvariate time series – feedback loop effect
– Non-linear models: poly-spectra, bi-linear, random coefficients etc.
• Analysis in frequency domain –
– spectrum analysis (periodograms, harmonics)
– Wavelet analysis
Introduction: TS 3 stage process with 6 Analytical
Steps
Data Screening
Trends,
seasonal effect,
outliers
Forecasting
Adjustments
Transformations,
Trend removal, etc
Identifications
Examine serial
correlation
structure
Model Checking
Estimation
Goodness of fit,
residuals
Estimate
parameters
Identification: Correlogram of SACF
(non-stationary series)
Identification: Correlogram of SACF
(stationary series)
TS Analysis using SAS
• SAS procedures
– Analysis in time domain:
•
•
•
•
Trend extrapolation: proc autoreg, proc reg, proc forecast
Box Jenkins: proc arima.
Trend decomposition: proc X11, proc satespace, proc ucm.
Multivariate analysis: proc varmax.
– Analysis in frequency domain: proc spectra.
• SAS/ETS Time Series Forecasting System
– Window-based pull-down menus environment (Solutions/Analysis/Time
Series Forecasting System)
• Enterprise Guide 3.0
– Point and click
• SAS Matrix programming language.
How to get started?
- SAS help
- Chapter 34 of “Getting started with time series
forecasting” gives a good overview of TS
forecasting system using drop down windows.
- Provides outline of the forecasting process
-
Specify data inputs
Provide a valid time ID
Select and Fit a forecasting model for each series
Produce the forecasts
Save your work
- Concept of time and date measurement in SAS.
Some Literature
• Time Series Third Edition Sir Maurice Kendall
and J Keith Ord (1990)
• Classical and Modern Regression with
Applications Raymond H. Myers (1986)
• Applied Linear Regression by Sanford Weisberg (
1985)
• SAS Help Examples
Questions?