Consider the AR(1) model xt = 0:5x_t-1 + w_t. Derive the partial acf hh when h...

Consider the AR(1) model xt = 0:5x_t-1 + w_t. Derive the partial acf hh when h = 1 and 2. Show your work or provide justification. You need to start from the definition.

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orchestra answered 1 year ago

Consider the first-order autoregressive model Xt = ρXt-1 + "єt,= 1,..,T with X0 = 0 and...

Consider the first-order autoregressive model Xt = ρXt-1 + "єt,= 1,..,T with X0 = 0 and {єt} ~ i.i.d.(0, σ 2). Explain what is the Dickey-Fuller test in the context of this model. In particular, your answer should include the null and alternative hypotheses, the definitions of both the coe¢cient test and the t test version of the Dickey-Fuller test and how the critical values are obtained. Consistency is a desirable property of statistical test. Explain the definition of a...

1. Find the ACF and PACF and plot the ACF ρk for k = 0, 1,...

1. Find the ACF and PACF and plot the ACF ρk for k = 0, 1, 2, 3, 4, 5 for the following model where the wt is a Gaussian white noise process. Zt = −0.5Zt−1 + wt

Show that the AR(2) process Xt=X(t-1)+cX(t-2)+Zt is stationary provided by-1<c<0. Find the autocorrelation function when c=-3/16....

Show that the AR(2) process Xt=X(t-1)+cX(t-2)+Zt is stationary provided by-1<c<0. Find the autocorrelation function when c=-3/16. Show that the AR(3) process Xt=X(t-1)+cX(t-2)-cX(t-2)+Zt is non-stationary for all values of c.

1. Consider the process {Xt} in which Xt = Zt + 0.5Zt-1 - 2Zt-2. Investigate the...

1. Consider the process {Xt} in which Xt = Zt + 0.5Zt-1 - 2Zt-2. Investigate the stationarity of the process under the following conditions. Calculate the ACF for the stationary models. (a) Zt ~ WN(0,(sigma)2) ; (sigma)2 < infinity (b) {Zt } is a sequence of i.i.d random variables with the following distribution: fzt(z) = 2/z3 ; z > 1

Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2...

Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2 ). (i)What are the mean function and the variance function of this time series? Is this time series stationary? Justify your answer (ii). Consider the first differences of the time series above, that is, consider Yt = Xt − Xt−1. What are the mean function and autocovariance function of this time series? Is this time series stationary? Justify your answer

(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !,...

(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !, where a is a constant. (a) At t = 0, we measure the energy of the system, what possible values will we obtain? (b) At later time t, we measure the energy again, how is it related to its value we obtain at t = 0 ? (c) If at t = 0, the system is equally likely to be in its two possible...

Consider the hypothesis test below. H 0: p 1 - p 2 0 H a: p 1 - p 2 >...

Consider the hypothesis test below. H 0: p 1 - p 2 0 H a: p 1 - p 2 > 0 The following results are for independent samples taken from the two populations. Sample 1 Sample 2 n1 = 100 n2 = 300 p1 = 0.24 p2 = 0.13 Use pooled estimator of p. What is the value of the test statistic (to 2 decimals)? What is the p-value (to 4 decimals)? With = .05, what is your hypothesis testing conclusion?

Let G = Z4XZ3XZ2 and consider the two cyclic subgroups H = h(0; 1; 1)i and...

Let G = Z4XZ3XZ2 and consider the two cyclic subgroups H = h(0; 1; 1)i and K = h(2; 1; 1)i of G. (a) Find all cosets (along with the elements they contain) to H and K, respectively. (b) Write down Cayley tables for the factor groups G=H and G=K, and classify them according to the Fundamental Theorem of Finite Abelian Groups.

Q1. Let {Xt |t ∈ [0, 1]} be a stochastic process such that EX2 t <...

Q1. Let {Xt |t ∈ [0, 1]} be a stochastic process such that EX2 t < ∞ for all t ∈ [0, 1] which is strictly stationary. Show that it is stationary . Q2. Let {Xt |t ∈ I} be strictly stationary. Prove or disprove that process is with stationary increments. Q3. Let {Xt |t ∈ I} be with stationary increments. Prove or disprove that the process is stationary. Q4. Prove or disprove that the stochastic process {Xn|n ≥ 0},...

Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases,...

Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases, verify if the ‘zero conditional mean’ and ‘homoscedasticity in errors’ assumptions are satisfied: a. If ? = 9? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 b. If ? = 5.6 + ? where ?(?⁄?) = 0, ???(?⁄?) = 3? 2 c. If ? = 3?? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 2) D. In which of the cases above are we...

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