This preview shows pages 1–3. Sign up to view the full content.
STSCI 4550 / ILRST 4550 / ORIE 5550
Applied Time Series Analysis, Spring 2012
Professor David S. Matteson
Exam #1
Suggested Solutions
Out of 100 possible points
1. The ﬁgure above contains plots of six diﬀerent time series.
(i) Which of the series (a)(f) appear nonstationary?
[5]
a,c,f
(ii) For each of the series which appear nonstationary, brieﬂy state why.
[5]
a  random walk
c  appears cyclic
f  increasing variance
(iii) For each of the series which appear nonstationary, is there a simple transformation that would
lead to a stationary series? If so, state it.
[5]
a  ﬁrst order diﬀerencing 1B
c  apply backshift operator (seasonal)
f  rescale relative to the time index
y
t
=
x
t
/t
α
,
where
α
is something like 0.5, 1, or 2.
2. The ﬁgure above contains plots of four diﬀerent time series. Match each of the series (a)(d)
with one of the following processes:
[10]
(i) White noise
d
(ii) AR(1)
c
(iii) MA(1)
a
(iv) Random walk
b
3. The ﬁgure above contains plots of the sample autocorrelation functions (ACF) for four diﬀerent
time series. Match each of the ACF(s) (a)(d) with one of the following processes:
[10]
(i) White noise
a
(ii) AR(1)
c
(iii) MA(1)
d
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document(iv) Random walk
b
4. Let
a
t
be a stationary Gaussian process. Write the following models for
z
t
in
B
(backshift)
notation. Also, state whether or not the model is stationary.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '12
 MATTESON

Click to edit the document details