Fitting, Diagnosing, Selecting ARIMA Models
Fitting, Diagnosing, Selecting ARIMA Models
MAS 640 – Time Series Analysis and Forecasting
2/5/2018
Schedule
I Today –
I 2/7 – Forecasting
I 2/12 – Seasonal ARIMA
I 2/14 – Seasonal ARIMA
I 2/19 – Special/Advanced Topics
I 2/21 – Review
I 2/28 – Final
Homework 1
I Submissions:
I One submission per group, with everyone’s name.
I Don’t submit the same thing 3 times.
I Don’t submit one version with your group and a different
version on your own.
Homework 1
I RMD Comments
1. Don’t leave warnings and messages in your document
2. Don’t print out several pages of residuals, fitted values, etc. . .
never type myData into your document and leave it. . .
I LOOK AT YOUR OUTPUT
I If it’s hideous, fix it
I If it’s filled with unnecessary output, remove it
ACF With Trending / Nonstationary Series
I Previously, we determined if a time series was nonstationary via
the time series plot.
I It’s generally quite obvious.
I However, if unsure, fit the ACF
I Very slow decay if non-stationary/trending
I Keep this pattern in mind, if you forget to plot the time series
and jump straight to ACF/PACF, this should help you realize
you need to difference
Example with CREF Data
CREF Time Series
Time
C
R
E
F
0 100 200 300 400 500
1
7
0
1
9
0
2
1
0
0 5 10 15 20 25
0
.0
0
.4
0
.8
Sample Autocorrelations
Lag
A
C
F
Model Specification and Diagnostics
I What do we mean by model specification?
I How do we diagnose the appropriateness of a model?
1. How do we eyeball assumptions?
2. How do we get p-values to test assumptions?
Specification
I Specification involves studying the time series plot, the ACF,
PACF, and EACF and trying to determine an appropriate
model or models for the data
I Common to come away with a couple candidate models
I Reading ACF/PACF/EACF not always straight forward
I You’re trying to find a reasonable starting point, and you want
to be able to justify that model should you ultimately use it
Residual Diagnostics
I Residual diagnostics to check appropriateness of the model
I Normality
I Histogram, Normal QQ plot, Shapiro-Wilks test
I Independence
I Time series plot, ACF of residuals, Ljung-Box p-values
Overfitting
I After going through the steps to specify a model, you fit that
model and diagnose the fit
I If it looks bad, you start iterating through the process of
overfitting
I Add an MA term, check results
I Add an AR term, check results
Overfitting
I When overfitting, you are looking at these things –
1. Are the added terms significant?
2. Do the assumptions appear to better hold (better residual
diagnostics)
3. Did the AIC/BIC improve?
Model Comparison
I There is often multiple models that will fit the data well and
look appropriate according to the residual diagnostics
I Can select between them using AIC/BIC
I Want a simple model that fits well
I If an ARMA(1,1) and an ARMA(3, 5) both fit reasonably well,
I’m going with the ARMA(1,1)