Find out whether each of the following processes {Xt} is weakly stationary or nonstationary. For theweakly stationary processes, find the mean and autocovariance functions. Consider in each question that{t}~ WN(0, 0²).Xo = 0, and X₁ = Xt−1 + €t for t≥ 1. Hint: note here that et must be independent of Xt-1.

Given the process Xt X0=0 and Xt=Xt-1+εt for t≥1 εt~WN0, σ2

Answered: Find out whether each of the following…

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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Which of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance one
Prove the following property of the compound Poisson process:1. E(xt) = λ t E(Y).
For b there are two cases and for c I have to plug the initial data into the ode
Assess whether the following AR (1) process satisfies the criteria for covariance stationarity, taking into consideration all three conditions that define a covariance stationary process. Assume that u~i.i.d(0, var_u), where var_u = 1. Provide the working steps and underlying assumptions used to prove if each property holds. y_t = 2 + 0.3y_(t-1)+u_t
f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.
Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions.
B) Let dP/dt =.5P - 50. Find the equilibrium solution for P. Furthermore, determine whether P is intially increasing faster if the initial population is 120 or 200.
Consider a random process X(t) defined by X(t) = U cos t + (V + 1) sin t, −∞ < t < ∞where U and V are independent random variables for which E(U) = E(V) = 0 E(U2) = E(V2) = 1(a) Find the autocovariance function KX(t, s) of X(t).(b) Is X(t) WSS?
Consider the geometric Brownian motion with σ = 1: dS = μSdt + SdX, and consider the function F(S) = A + BSα. Find any necessary conditions on A, B, and α such that the function F(S) follows a stochastic process with no drift.
A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next custom
Let (Nt)t>0 be a Poisson process with parameter λ=2, Find the following: (a) E(X3X4)
Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ and σ are constants and r is the risk-free rate. 1. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Xt = S_t^n , where n is a constant. 2. Compute E[X_t] and Var[X_t]. 3. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Y_t = S_tert

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