Question: Consider an AR(1) process X = X-1+Z with 50 observations {XX50} Given an expression of the log-likelihood function () of X. (X-X-1))-(1-) 50 0

Consider an AR(1) process X = X-1+Z with 50 observations {XX50} Given

Consider an AR(1) process X = X-1+Z with 50 observations {XX50} Given an expression of the log-likelihood function () of X. (X-X-1))-(1-) 50 0 (0) = -In (50) +in, O (6) = In (50) +In x(1-6) +2(X-X-11+(1-) 50 ((*) = -(50) +[Xx;(1-6)+22(X-4X4-1) - / - O 50 (*) = -In(50) +In x(1-6) + 2(x,-X,-1)-50 (1-8) (0) = -In(50) +In +inx +[X1-23 +24-04-2)-501-89 (0) = In(50) 50) + X(1-0)- 2, 05-05-0-241-91 -In(1-)

Step by Step Solution

★★★★★

3.38 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solution Given that An AR1 process x x with 50 o... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The log likelihood function for the linear regression model with normally distributed disturbances is shown in Example 4.6. Show that at the maximum likelihood estimators of b for and e'e/n for 2 ,...

Consider a two-part process with an expansion from 3 to 6 ft3 at a constant pressure of 20 lbf/in 2 followed by an expansion from 6 to 12 ft3 with a linearly rising pressure from 20 lbf/in 2 ending...

Consider an AR (2) process which is described by the recursion Y [n] = a1Y [n 1] + a2Y [n 2] + X [n] Where is an IID random process with zero- mean and variance Ï2X. (a) Show that the...

Consider a constant random process, X (t) = A, where A is a random variable. Use Definition A discrete random process, X[n], is generated by repeated tosses of a coin. Let the occurrence of a head be...

Recall that if x is the number of successes in n trials of a binomial setting with probability of success p on each trial, the likelihood function, p( x p), can be expressed as p(x|) = x (1 )n-x...

A continuous random variable X has a uniform distribution if it has a probability density function of the form (a) Show that (b) Find the mean g and variance (2 of the uniform distribution. (c) If a...

(Limited Information Maximum Likelihood Estimation) Consider a bivariate distribution for x and y that is a function of two parameters, and . The joint density is f (x, y | , ). We consider maximum...

Consider a heat treatment process in which steel rods with a 10 cm diameter at an initial temperature of 600C are inserted into an oil bath at 25C. Assuming a convection coefficient of 400 W/m 2 K...

The force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when...

The range of the random variable X is [0, 1, 2, 3, x], where x is unknown. If each value is equally likely and the mean of X is 6, determine x.

A local power commission sent a survey to homeowners to determine household power efficiency. Following is a list of major electrical appliances and their total kilowatt-hour (kWh) usage for one...

The ratio of the force on the right side of a belt drive to the pulling force on the slack side of the belt drive is 3: 1. The pulling force on the tight side is 100 N. The driver pulley rotates at...

Becker CPA Review 1 - 2 Which of the following is not a required conduct for a preparer of an income tax return, under AICPA Tax Standards? a . Abide by the tax Code and legally minimize the...

Del Arbr Ltd (hereafter referred to as "DA") is a property development company listed on the JSE. The company was founded by Mr Labuschagne and Mr Kaiser in 1974 and has since grown to be one of the...

Use google to find out how CA RE taxes are prorated (references sources!). Suppose any tax payments are made on the due date, and the annual tax bill is $12,000. Compute who owes who (seller vs...

A salesperson wants to visit 25 cities while minimizing the total number of miles she has to drive. Because she has studied computer science, she decides to design an algorithm to determine the...

HCI's growth to date has been financed by its profits. When the company had sufficient capital, it would open a new store. Other than scouting locations, relatively little formal analysis has been...

The company FPA has the following income, expense, and loss items for the current year. Sales $850,000 Tax-exempt interest $40,000 Long-term capital gain $85,000 Short-term capital loss $35,000...

A buffer system is comprised of 0.15 M H2CO3 and 0.20 M HCO3. What is the pH of the buffer? Hint: The pKa of carbonic acid is 6.37. 7.68 7.10 6.49 7.22

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

Consider the AR(2) model y1 = 25 + 0.6y1 _ 1 + 0.25Yr-2 + E1 Assume that the variance of the white noise process is rr 2 = I. a. Sketch the theoretical ACF and PACF for this model. b. Generate 50...

Considerthe AR(l) model y, = 25 + 0.75y,_1 +,.Assume that the variance of the white noise process is a 2 = 10. a. Sketch the theoretical ACF and PACF for this model. b. Generate 50 realizations of...

Q16 Find the mean, the variance, the first three autocorrelation functions (ACF) and the first 3 partial autocorrelation functions (PACF) for the following AR (2) process X= 0.4Xt-1 - 0.2Xt-2+ Et,...

Consider a WSS random process X (t) with 1- 71, -1ST$1 Rx(T) = O, otherwise Find the pad of X (t), Sx(w), and E[X2(t)]

The Matrix for a Markov chain is (A) Show that R = [.4 0 .6] and S = [0 1 0] are both stationary matrices for P. Explain why this does not contradict Theorem 1 A. (B) Find another stationary matrix...