STAT 520
MIDTERM
Disclaimer: You are to work alone on this midterm. You can ask questions of clarication
to me, but you can not discuss any part of this exam with anyone else. Giving or receiving
unauthorized assistance, or attempting to give or receive s
STAT 520
FALL 2011 FINAL
GROUND RULES:
This exam contains two parts:
Part 1. Multiple Choice (50 questions, 1 point each)
Part 2. Problems/Short Answer (10 questions, 5 points each)
The maximum number of points on this exam is 100.
Print your name at
STAT 520
HOMEWORK 1
1. The TSA library contains the data set co2, which lists monthly carbon dioxide (CO2 ) levels
in northern Canada from 1/1994 to 12/2004. To load the data in R, remember that you need
to rst type
> library(TSA)
> data(co2)
(a) Construc
STAT 520
FORECASTING AND TIME SERIES
2013 FALL
Homework 03
1.
1.(a) Here we obtain the expectation of Y
)
)
( n
( n
n
1
1
1
E(Y ) = E
Yt = E
E(Yt )
Yt =
n t=1
n
n t=1
t=1
1
1
=
= n = .
n t=1
n
n
Then Y is an unbiased estimator of .
1.(b) Here we obtain t
STAT 520
FORECASTING AND TIME SERIES
2013 FALL
Homework 01
370
365
350
355
360
CO2 levels
375
380
1.(a) Please see Figure 1 for the time series plot for carbon dioxide
levels. There are two distinctive patternsseasonality and increasing trend
over time. F
STAT 520
FORECASTING AND TIME SERIES
2013 FALL
Homework 02
1.
2.7.(a) Since cfw_Yt is a stationary process, it has constant mean over
time and autocovariance function k which is free of t. Letting Wt = Yt =
Yt Yt1 , we obtain the mean function of cfw_Wt
STAT 520
HOMEWORK 4
1. Do the following problems in Chapter 6 from Cryer and Chan: 6.17, 6.18, and 6.19.
2
2. Suppose that cfw_et is a zero mean white noise process with var(et ) = e , and consider the
AR(1) model with = 0.8, that is,
Yt = 0.8Yt1 + et .
STAT 520
HOMEWORK 3
1. Suppose that cfw_Yt is a stationary process with constant mean t = E(Yt ) = and autocorrelation function k . Dene
1 n
Yt
Y =
n t=1
to be the sample mean of Y1 , Y2 , ., Yn .
(a) Show that Y is an unbiased estimator of ; that is, sh
STAT 520
HOMEWORK 2
1. Do the following problems in Chapter 2 from Cryer and Chan: 2.7, 2.9(a), 2.10, 2.13,
2.14, and 2.19. Although not always stated, it is understood that cfw_et is a zero mean
2
white noise process with var(et ) = e .
2. Suppose that
STAT 520
FORECASTING AND TIME SERIES
2013 FALL
Homework 05
1.
ibm data:
The random walk model of rst dierences is chosen to be the suggest
model of ibm data. That is
(1 B)Yt = et
where et is a mean zero white noise process.
For the diagnose part, rst we d
STAT 520
HOMEWORK 5
Remark: Problem 1 is the most important problem on this assignment (it will prepare you
for your project). Problem 2 was taken largely from last years nal exam. Problem 3 consists
of a bunch of rambling on my part; I got tired of rambl
STAT 520
FORECASTING AND TIME SERIES
2013 FALL
Homework 04
1.
6.17. For a stationary AR(1) process Yt = Yt + et , the approximate
sampling (large-sample) distribution of rk is
(
[
])
2
2k
k 1 (1 + )(1 )
2k
rk AN ,
2k
.
n
1 2
Here we have = 0.7, n = 100 a