Throughout, let {et} be a white noise process with constant variance o²1. Consider the Yule-Walker equations for an AR(2) process, and estimation ofthe coefficients of Xt-1 and Xt-2. Assume that the necessary autocorrelationcoefficient(s) are known.a. Write down the two equations in the unknown coefficients and solvefor those parameters.b. Suppose a time series {X+} is observed, and its partial autocorrelationfunction (say for lags 1 to 20) estimated. Will either result in (a) beused in this function? If so, explain.

Answered: Throughout, let {et} be a white noise…

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 randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1
2. Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature x (° F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y= 5 - 0.01x and the standard deviation o=0.075. a. What is the expected reaction time when temperature is 250° F? b. Suppose that five observations are made independently on reaction time, each one for a temperature of 250° F. What is the probability that all five times are between 2.4 and 2.6 hours?
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…
Let X11 X12, Xini and X21, X22, X2n2 be two independent random samples of size n₁ and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively. (a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first population (X₁). Using analogy, state the mle's of the parameters of the second population. (b) Find the pooled estimator of the common variance when it is assumed that of = = ². Suggest an unbiased estimator of o². |
16. Suppose the true average growth μ of one type of plant during a 1-year period is identical to that of a second type, but the variance of growth for the first type is σ², whereas for the second type the variance is 40². Let X₁,..., X be m independent growth observations on the first type [so E(X;) = µ, V(X;) = σ²], and let Y₁,..., Y be n independent growth observations on the second type [E(Y) =μ, V(Y) = 4σ²]. a. Show that the estimator û = 8X + (1 - 8) is unbi- ased for μ (for 0 < 8 <1, the estimator is a weighted average of the two individual sample means). b. For fixed m and n, compute V(u), and then find the value of 8 that minimizes V(i). [Hint: Differentiate V(u) with respect to 8.]
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.
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. If this scenario was simulated, the random interarrival time variate in minutes calculated from the U(0, 1) random number generator value 0.4258 is closest to

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