1.1 Consider a time series process given by (1-B)x, =(1-6,B)z,, where the sequence {z, ) is a whitenoise with mean zero and variance o. Determine the first four weights of process x, if an ARMA(1,1) model fitted to the data gave =0.8 and 9 = 0.34(4)Consider an AR(2) model: x=(x)+(x2-x)+2,, where z, - wn(0,0²).1.2QUESTION 1Show that = A(-A) and =1-Ausing LSE method.

Step No: 1 1.1 In time series analysis, the autoregressive moving average (ARMA) model…

Answered: QUESTION 1 1.1 Consider a time series…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following panel model to examine the effect of retirement on consumption expenditure, consit, of individual i over years t=1,…,3: (B1) log⁡(consit) = β0 + β1retiredit + β2ageit + β3marriedit + β4healthit + δ1Yr2t + δ2Yr3t + ai + uit Where: retiredit is a dummy variable equal to 1 if individual i is retired on year t and 0 otherwise ageit is the individual's age in years marriedit is an indicator variable for whether the individual is married (1) or not (0) in year t healthit is an indicator variable equal to 1 if the individual is in 'good health' and 0 otherwise Yr2 is a dummy variable equal to 1 in year t=2 and 0 otherwise Yr3 is a dummy variable equal to 1 in year t=3 and 0 otherwise Using the information above, answer the following 3 questions. [i] Give two (2) examples of the kind of variables captured by the term ai in Model (B1). [ii] What is the crucial assumption we must make so that the random effects (RE) estimator is consistent? Under this assumption, why is…
Question 1 1. Suppose you are given that a continuous random variable has a moment generating function of 1 M (t) = 1-3.2t Find the mean and variance of the random variable. mean = var =
Question 3. Let X₁,, Xn be a random sample from a distribution with the pdf given by f₁₁x(x) = exp(-ª) if x ≥ A, otherwise f(x) = 0, where > 0. Find the MLE's of 0 and X. Start by writing the likelihood function and note the constraint involving A. Question 4. #4.2.9 of the textbook.
In time-series decomposition, seasonal factors are calculated by Multiple Choice O O O O O SFt (Y) (CMA). SFt= Y/CMAt (CMA+) x (SFt) =Yt. SFt = Yt - CMAt. None of the options are correct.
In this question you will consider ergodicity and time series averages. Consider the following MA (2) time series model: Ytt 01€t-1 - 0₂€t-2 - Var (Y) = 7+²7 ²2 (1-1) T (2-1) +2 + (-0₁ +010₂) (1 + 0² +02) (1 + 0² +02) (1) (d) You are told that o² = 1, 0₁ = 0.2 and 0₂ = -0.1 is the variance for the time series mean estimator less efficient or more efficient than the T = 20 sample size ensemble average i.i.d. case? Justify your answer with a relevant calculation and explanation using the formula in Equation (1) provided above in part (c) of this question.
Consider drawing samples of size n = 12 from U(0,12) Consider estimators for the population variance. One such estimator is the familiar s. When you draw such a sample, what is E(s') ? Another is the sample range r, where r= ymax - Ymin %3D When you draw such a sample, what is E(r) ? Hint: E(y max) = 144/13 using Theorem 3.10.1 Isr unbiased? Isr consistent?
Ben thinks that people living in a rural environment have a healthierlifestyle than other people. He believes the average lifespan in the USA is 77years. A random sample of 12 obituaries from newspapers from rural towns inIdaho give x = 81.61 and s = 2.76. Does this sample provide evidence thatpeople living in rural Idaho communities live longer than 77 years?(a) State the null and alternative hypotheses: (Type "mu" for the symbol u , e.g.mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not= 1 for the mean is not equal to 1)H:H:(b) Find the test statistic, t =(c) Answer the question: Does this sample provide evidence that people living inrural Idaho communities live longer than 77 years? (Use a 10% level ofsignificance
Consider an MA(7) model with01= 1,02=-0.5,03= 0.25,04=-0.125,05= 0.0625,06=-0.03125, and07= 0.015625. Find a much simpler model that has nearly the samey-weights.

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