OPENINTRO:STATISTICS
4th Edition
ISBN: 9781943450077
Author: OPENINTRO
Publisher: amazon.com
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Chapter 1.3, Problem 26E
To determine
State whether it will be a good measure of household size, if the students at an elementary school are selected at random and ask them about their family size.
State whether the average is biased. If so, provide whether it is an overestimate or underestimate of the true value.
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6 (Model Selection, Estimation and Prediction of GARCH) Consider the daily returns rt
of General Electric Company stock (ticker: "GE") from "2021-01-01" to "2024-03-31",
comprising a total of 813 daily returns. Using the "fGarch" package of R, outputs of
fitting three GARCH models to the returns are given at the end of this question.
Model 1 ARCH (1) with standard normal innovations;
Model 2
Model 3
GARCH (1, 1) with Student-t innovations;
GARCH (2, 2) with Student-t innovations;
Based on the outputs, answer the following questions.
(a) What can be inferred from the Standardized Residual Tests conducted on Model 1?
(b) Which model do you recommend for prediction between Model 2 and Model 3?
Why?
(c) Write down the fitted model for the model that you recommended in Part (b).
(d) Using the model recommended in Part (b), predict the conditional volatility in the
next trading day, specifically trading day 814.
4 (MLE of ARCH) Suppose rt follows ARCH(2) with E(rt) = 0,
rt = ut, ut =
στει, σε
where {+} is a sequence of independent and identically distributed (iid) standard normal
random variables.
With observations r₁,...,, write down the log-likelihood function for the model esti-
mation.
5 (Moments of GARCH) For the GARCH(2,2) model rt =
0.2+0.25u1+0.05u-2 +0.30% / -1 +0.20% -2, find cov(rt).
0.0035 ut, ut =
στει,στ
=
Chapter 1 Solutions
OPENINTRO:STATISTICS
Ch. 1.1 - Prob. 1GPCh. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.2 - Prob. 2GPCh. 1.2 - Prob. 3GPCh. 1.2 - Prob. 4GPCh. 1.2 - Prob. 6GPCh. 1.2 - Prob. 7GPCh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4E
Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.3 - Prob. 9GPCh. 1.3 - Prob. 11GPCh. 1.3 - Prob. 12GPCh. 1.3 - Prob. 13GPCh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.4 - Prob. 16GPCh. 1.4 - Prob. 17GPCh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1 - Prob. 35ECh. 1 - Prob. 36ECh. 1 - Prob. 37ECh. 1 - Prob. 38ECh. 1 - Prob. 39CECh. 1 - Prob. 40CECh. 1 - Prob. 41CECh. 1 - Prob. 42CECh. 1 - Prob. 43CECh. 1 - Prob. 44CE
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