Statistics
4th Edition
ISBN: 9780393929720
Author: David Freedman, Robert Pisani, Roger Purves
Publisher: Norton, W. W. & Company, Inc.
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Chapter 23.6, Problem 14SRE
To determine
Compute the chance that a person has a perfect score on both midterms, if possible.
Explain the reason.
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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 23 Solutions
Statistics
Ch. 23.1 - Prob. 1EACh. 23.1 - Prob. 2EACh. 23.1 - Prob. 3EACh. 23.1 - Prob. 4EACh. 23.1 - Prob. 5EACh. 23.1 - Prob. 6EACh. 23.1 - Prob. 7EACh. 23.1 - Prob. 8EACh. 23.1 - Prob. 9EACh. 23.1 - Prob. 10EA
Ch. 23.2 - Prob. 1EBCh. 23.2 - Prob. 2EBCh. 23.2 - Prob. 3EBCh. 23.2 - Prob. 4EBCh. 23.2 - Prob. 5EBCh. 23.2 - Prob. 6EBCh. 23.2 - Prob. 7EBCh. 23.2 - Prob. 8EBCh. 23.2 - Prob. 9EBCh. 23.3 - Prob. 1ECCh. 23.3 - Prob. 2ECCh. 23.3 - Prob. 3ECCh. 23.3 - Prob. 4ECCh. 23.3 - Prob. 5ECCh. 23.3 - Prob. 6ECCh. 23.4 - Prob. 1EDCh. 23.4 - Prob. 2EDCh. 23.4 - Prob. 3EDCh. 23.4 - Prob. 4EDCh. 23.4 - Prob. 5EDCh. 23.4 - Prob. 6EDCh. 23.4 - Prob. 7EDCh. 23.5 - Prob. 1RECh. 23.5 - Prob. 2RECh. 23.5 - Prob. 3RECh. 23.5 - Prob. 4RECh. 23.5 - Prob. 5RECh. 23.5 - Prob. 6RECh. 23.5 - Prob. 7RECh. 23.5 - Prob. 8RECh. 23.5 - Prob. 9RECh. 23.5 - Prob. 10RECh. 23.5 - Prob. 11RECh. 23.5 - Prob. 12RECh. 23.6 - Prob. 1SRECh. 23.6 - Prob. 2SRECh. 23.6 - Prob. 3SRECh. 23.6 - Prob. 4SRECh. 23.6 - Prob. 5SRECh. 23.6 - Prob. 6SRECh. 23.6 - Prob. 7SRECh. 23.6 - Prob. 8SRECh. 23.6 - Prob. 9SRECh. 23.6 - Prob. 10SRECh. 23.6 - Prob. 11SRECh. 23.6 - Prob. 12SRECh. 23.6 - Prob. 13SRECh. 23.6 - Prob. 14SRECh. 23.6 - Prob. 15SRECh. 23.6 - Prob. 16SRECh. 23.6 - Prob. 17SRECh. 23.6 - Prob. 18SRECh. 23.6 - Prob. 19SRECh. 23.6 - Prob. 20SRECh. 23.6 - Prob. 21SRECh. 23.6 - Prob. 22SRECh. 23.6 - Prob. 23SRECh. 23.6 - Prob. 24SRECh. 23.6 - Prob. 25SRECh. 23.6 - Prob. 26SRECh. 23.6 - Prob. 27SRECh. 23.6 - Prob. 28SRECh. 23.6 - Prob. 29SRECh. 23.6 - Prob. 30SRE
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