Solution for Time Series HW1
February 7, 2016
1.1 a) For any c R we have
E[(Y c)2 ] = E[(Y + c)2 ]
= E[(Y )2 ] + 2E[(Y )( c)] + E[( c)2 ]
= E[(Y )2 ] + 2( c)E[(Y )] + ( c)2
= E[(Y )2 ] + 0 + ( c)2
E[(Y )2 ]
Therefore c = is the minimizer.
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2.14 For time series
Xt = A cos(!t) + B sin(!t)
we have (h) = (h) = cos(!h)
(a) Find P1 X2 and its MSE. Suppose P1 X2 =
(0)
11
11 X1 ,
then we have
= (1)
Therefore
11
= (1) = cos !, P1 X2 = cos !X1
And
1 = E(X2
(b) P2 X3 =
21 X2
+
22 X1
P1 X2 )2 = (1
and

SOLUTIONS
IE409: Time Series Analysis
Fall 2011
Homework 3
18 November 2011
(1) (B&D 3.5) Let cfw_Yt be the ARMA plus noise time series defined by
Yt = Xt + Wt ,
2
where cfw_Wt WN(0, w
), cfw_Xt is the ARMA(p, q) process satisfying
(B)Xt = (B)Zt , cfw_

Solution for Time Series HW5
March 18, 2016
3.1 (20 points, 4 points for each)
3.2 (15 points) (a)
(c)
(d)
3.3 (15 points)
3.4 (15 points)
3.5 (15 points) a. Denote X (h) and Y (h) as the ACVF of X and Y .
Cov(Yt , Yt+h ) =Cov(Xt + Wt , Xt+h + Wt+h )
=Cov

The Islamic University of Gaza
Faculty of Commerce
Department of Economics and Applied Statistics
Time Series Analysis and Forecasting
STAT 4321 - Spring 2011
Chapter 2 - Solutions
1
2

We ‘gt‘nd ’rhe knea/K"P?edfc+ar“ ;aXn fb , 0f-
th by efﬂude 'a and b Suck tar/That,
Hth — ﬁrmso and Eﬁmﬂ'xmpéxh ] =o‘ We
have 7' . - . - I
lEE xm. 469;] = IE'CXQ'wa‘Xh'E’]
. w ‘ . ‘47 EEXMH']5Q'EX&*LC
. .= ﬂU—a), w I; . -
3 . ‘19)
= :E [th V"- J:—. a

Solution for Time Series HW2
February 7, 2016
1.3 For a strictly stationary time series, we know that (X1 , ., Xn ) and (X1+h , ., Xn+h )
has the same distribution. Therefore we have that
X (t) = E(Xt ) = E(X1 ) = X (1) = const
and, given that E(Xt2 ) < ,

Linear Regression Models
Statistics W4315 Fall 2015
Assignment 6
Reading:
By Friday, November 13, read Chapters 68 and Sections 10.1 & 10.5 of Applied Linear Regression
Models by Kutner, Nachtsheim and Neter (KNN).
For Friday, November 20, read Chapter 9