Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 2.4, Problem 4E
To determine
Fill in the blank with an appropriate word or phrase for the given statement.
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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 2 Solutions
Essential Statistics
Ch. 2.1 - 1. The following table lists the types of aircraft...Ch. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYUCh. 2.1 - Prob. 4CYUCh. 2.1 - Prob. 5ECh. 2.1 - In Exercises 5–8, fill in each blank with the...Ch. 2.1 - Prob. 7ECh. 2.1 -
In Exercises 5–8, fill in each blank with the...Ch. 2.1 - Prob. 9ECh. 2.1 - In Exercises 9–12, determine whether the statement...
Ch. 2.1 - Prob. 11ECh. 2.1 -
In Exercises 9–12, determine whether the...Ch. 2.1 - Prob. 13ECh. 2.1 - 14. The most common blood typing system divides...Ch. 2.1 - 15. Following is a pie chart that presents the...Ch. 2.1 - 16. Student expenses: The following pie chart...Ch. 2.1 - 17. Food sources: The following side-by-side bar...Ch. 2.1 -
18. Super Bowl: The following side-by-side bar...Ch. 2.1 - Prob. 19ECh. 2.1 - 20. Popular video games: The following frequency...Ch. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - 26. How secure is your job? In a survey, employed...Ch. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - 30. Bought a new car lately? The following table...Ch. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.2 - Using the data in Table 2.7, construct a frequency...Ch. 2.2 - Prob. 2CYUCh. 2.2 - Prob. 3CYUCh. 2.2 - Prob. 4CYUCh. 2.2 - Prob. 5ECh. 2.2 -
In Exercises 5-8, fill in each blank with the...Ch. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - In Exercises 9-12, determine whether the statement...Ch. 2.2 - Prob. 13ECh. 2.2 - In Exercises 13–16, classify the histogram as...Ch. 2.2 - Prob. 15ECh. 2.2 - In Exercises 13–16, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - In Exercises 17 and 18, classify the histogram as...Ch. 2.2 - Prob. 19ECh. 2.2 - 20. Trained rats: Forty rats were trained to run a...Ch. 2.2 - 21. Interpret histogram: The following histogram...Ch. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Skewed which way? For which of the following data...Ch. 2.2 - Prob. 25ECh. 2.2 - 26. Batting average: The following frequency...Ch. 2.2 - Prob. 27ECh. 2.2 - 28. Murder, she wrote: The following frequency...Ch. 2.2 - BMW prices: The following table presents the...Ch. 2.2 - Geysers: The geyser Old Faithful in Yellowstone...Ch. 2.2 - Prob. 31ECh. 2.2 - Internet radio: The following table presents the...Ch. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - 37. Silver ore: The following histogram presents...Ch. 2.2 - Classes of differing widths: Consider the...Ch. 2.3 - Weights of college students: The following table...Ch. 2.3 - Prob. 2CYUCh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - In Exercises 3–6, fill in each blank with the...Ch. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - 14. List the data in the following stem-and-leaf...Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - BMW prices: The following table presents the...Ch. 2.3 - How’s the weather? The following table presents...Ch. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Tennis and golf: Following are the ages of the...Ch. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - 24. Safety first: Following are the numbers of...Ch. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - 30. Going for gold: The following time-series plot...Ch. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - 34. Arctic ice sheet: The following table presents...Ch. 2.3 - Prob. 35ECh. 2.4 - The population of country A is twice as large as...Ch. 2.4 - Prob. 2CYUCh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - College degrees: Both of the following time-series...Ch. 2.4 - Food expenditures: Both of the following...Ch. 2.4 - Prob. 15ECh. 2 - Prob. 1CQCh. 2 - Prob. 2CQCh. 2 - Prob. 3CQCh. 2 - Prob. 4CQCh. 2 - Prob. 5CQCh. 2 - 6. True or false: A histogram can have more than...Ch. 2 - Prob. 7CQCh. 2 - Prob. 8CQCh. 2 - Prob. 9CQCh. 2 - Prob. 10CQCh. 2 - Prob. 11CQCh. 2 - Prob. 12CQCh. 2 - Prob. 13CQCh. 2 - Prob. 14CQCh. 2 - Prob. 15CQCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 1WAICh. 2 - Prob. 2WAICh. 2 - Prob. 3WAICh. 2 - Prob. 4WAICh. 2 - Prob. 1CSCh. 2 - Prob. 2CSCh. 2 - In the chapter introduction, we presented gas...Ch. 2 - Prob. 4CSCh. 2 - Prob. 5CSCh. 2 - Prob. 6CSCh. 2 - Prob. 7CSCh. 2 - Prob. 8CSCh. 2 - Prob. 9CS
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