Stat 349 Introduction to Time Series
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamer-tu-log
Z. Zhang (UW-Madison)
Stat 349 Week 1-2
January 20-29, 2015
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Outline
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STAT 349
DISCUSSION 3
Lu Yang
Review
Linear trend in time
Yt = t + Xt , t = 0 + 1 , where E(Xt ) = 0 for all t.
n
1 =
(Yt Y )(t t)
t=1
n
(t t)2
t=1
0 = Y 1 t
Seasonal trend
1 , for t=1,13,25, . . .
2 , for t=2,14,26, . . .
Yt = t + Xt , t =
12 , for t
STAT 349
DISCUSSION 1
Lu Yang
Review
The Variance of X is dened as
var(X) = E[X E(X)]2 = E(X 2 ) [E(X)]2 .
The Covariance of two random variable, X1 and X2 , is dened as
cov(X1 , X2 ) = E[cfw_X1 E(X1 )cfw_X2 E(X2 )] = E(X1 X2 ) E(X1 )E(X2 ).
Properties
STAT 349
DISCUSSION 2
Lu Yang
Review
Weak stationarity
A random processcfw_Y t is weakly (or second order) stationary if 1st and
2nd moments do not vary with respect to time.
k = cov(Yt , Ytk ), 0 = V ar(Yt )
k
,
0
k = corr(Yt , Ytk ),k =
0 = 1
k = k
Chapter 12 Time Series Models of
Heteroscedasticity
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamer-tu-log
Z. Zhang (UW-Madison)
Stat 349 Week 15
April 25-27, 2016
279 / 311
Financial risk: Is it important?
be
State Space Models and Kalman Filter
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamer-tu-log
Z. Zhang (UW-Madison)
Stat 349 Week 16
May 2, 2016
301 / 311
State Space Models
What are state-space models?
A state
Chapter 10 Seasonal Models
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamer-tu-log
Z. Zhang (UW-Madison)
Stat 349 Week 13
April 11-13, 2016
213 / 311
Introduction
Seasonal dependency (seasonality) is another ge
Chapter 11 Time Series Regression Models
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamer-tu-log
Z. Zhang (UW-Madison)
Stat 349 Week 13-14
April 18-20, 2016
254 / 311
Time Series Regression Models
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