For an arbitrary random variable Y and a ?-algebra F A, generated by observing some event A,

Question:

For an arbitrary random variable Y and a ?-algebra F_A, generated by observing some event A, the variance decomposition

holds. Show that the unconditional variance of the least-squares estimator|??? is

where X is the usual data matrix, containing a column of ones and the regressors X_t, for t = 1, . . . , T.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

A First Course in Quantitative Finance

ISBN: 978-1108419574

1st edition

Authors: Thomas Mazzoni

Question Posted: Feb 19, 2020 08:58 AM

See More Questions

Random variable Y = X - Z is a noisy observation of the continuous random variable X. The noise Z has zero expected value and unit variance and is independent of X. Find the conditional expectation...
For a Student t random variable Y with n degrees of freedom and any positive integer k, show that E(Y 2k ) exists if 2k < n. (Integrals of the form are finite if > 0, > 0, and > 1.) 00 1 dy (1+y")
Let X be a Gaussian random variable with zero mean and arbitrary variance, 2. Given the transformation Y= X3, find fY (y).
Gombas Company decided to analyze certain costs for October of the current year. There was no beginning inventory. Units started into production equaled 14000, units transferred out equal 12000, and...
Determine what alkyne and what reagent will give CI CI Cl a. b. CI Cl
Take a camera and conduct a photo audit of a specific servicescape. Photograph examples of excellent and very poor design features. Develop concrete suggestions on how this environment could be...
The wreck of the S.S. Central America waited 130 years at the bottom of the ocean for someone to come along and claim its trove of gold. Thomas G. Thompson, funded by a multitude of investors, was...
Condensed balance sheet and income statement data for Kersenbrock Corporation appear below. Additional information: 1. The market price of Kersenbrocks common stock was $4.00, $5.00, and $8.00 for...
Connect each yearly salary to the correct paycheck payment. A. $55,000 B. $60,000 C. $26,000 D. $129,000 E. $56,000 OS $500 weekly $5,000 monthly $2,333 semi-monthly $4,961 biweekly $4,583 monthly
Meg McIntyre opened a public relations firm called Pop Chart on August 1, 2024. The following amounts summarize her business on August 31, 2024: During September 2024, the business completed the...
Check that the expectation of (7.15) is the CAPM equation. (7.15) Rs = Ro + Bs(RMP Ro) + s %|
The original three-factor portfolio model of Fama and French (1993, 1996) is formulated in the form where SMB indicates the market capitalization spread (?small minus big?), and HML is the spread in...
Find two different spanning trees for each graph in Problems 1320. A B D E C
discuss the different benefits gained by UK in joining the EEC in 1973?
k) Assume that one of these portfolio's is the Market Portfolio and all portfolios, except Portfolio G, are fairly priced according to the CAPM. What is the highest utility score that can be achieved...
The hospital took out a $2,000,000 mortgage to facilitate the construction of a new sports performance center. The term of the mortgage is 30 years, the annual interest rate is 4.25%, and payment is...
Water flows in a 5 meter wide rectangular channel at a depth of 1.5 meter. The slope of the channel is So = 0.01 and has a manning coefficient n = 0.015. Based on this answer the following: 1. Is a...
To make the value of a stock offer equivalent to a cash offer of $400 million, how many shares should United Continental give to the owners of Express Air?
During the current year, merchandise is sold for $6,400,000. The cost of the goods sold is $5,376,000. a. What is the amount of the gross profit? b. Compute the gross profit percent. c. Will the...
Velshi Printers has contracts to complete weekly supplements required by fortysix customers. For the year 2018, manufacturing overhead cost estimates total $600,000 for an annual production capacity...
For the first five months of its existence (August through December 2018), the Estate of Amy Ennis had gross income (net of expenses) of $7,000 per month. For January through July 2019, the executor...
A complex trust has taxable income of $29,900 in 2018. The $29,900 includes $5,000 of rental income and $25,000 of taxable interest income, reduced by the $100 personal exemption. The trust makes no...
Suellen Symmes died on January 15, 2018. Her estate elected a November 30 year end. The executor projects that the estate will receive interest income of $50,000 by November 30, 2018, and will have...
Siya Dlamini is a partner at a law firm. He is 4 0 years old and unmarried. He has incurred a number of expenses during the 2 0 2 3 year of assessment. He would like to know if they are deductible in...
Ahmed was doing experiment with the laboratory technician and prepared standard solution in standard measuring flask by dissolving 6.5 g C3(PO4)2 in 550 ml water after that he added 3.5 g more...
Construct solid-liquid and solid-vapour phase boundaries for carbon tetrachloride CCl 2 given the following: Density of solid CCl2 = 1.809 g/cm Density of liquid CCl2 = 1.59 g/cm Enthalpy of fusion =...

For an arbitrary random variable Y and a ?-algebra F A, generated by observing some event A,

Question:

Var[ Y] = Var[E[ YF4]] + E[Var[ Y[FA] %3D Var[lß}] =o¿E[(X° X)-"),

Step by Step Answer:

Starting from the equation EXX1 XY where is the OLS estimator we can calculate the unconditional ...View the full answer

A First Course in Quantitative Finance

Students also viewed these Business questions