If returns r_t follow an autoregressive process AR(1) with coefficient 0.5 , what is the autocorrelation at lag 2 (rho(2)) for this process?
Given, autoregressive coefficient = 0.5
We know that autocorrelation at lag h is
Autocorrelation at lag 2 is
If returns r_t follow an autoregressive process AR(1) with coefficient 0.5 , what is the autocorrelation...
3. We obtain autocorrelation function of residuals of the five autoregressive models: AR(1), AR(2), AR(3), AR(4) and AR(5). Choose a model that performs reasonably well, according to the plots of autocorrelation function. Explain the reason (no more than 20 words.) Autocorrelation function for AR(1) model Series ar1$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag Autocorrelation function for AR(2) model Serles ar2$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag...
5. [20+5+5] In the regression modely, x,B+ s, pe,+u, ,where I ρ k l and , , let ε, follow an autoregressive (AR) process u' ~ID(Qơ:) , t-l, 2, ,n . <l and u, - Derive the variance-covariance matrix Σ of (q ,6, , , ε" )". From the expression of Σ, identify and interpret Var(.) , t-1, 2, , n . Find the CorrG.ε. and explain its behavior as "s" increases, (s>0). (ii) (iii) 5. [20+5+5] In the regression...
True or false? You do not have to provide explanations. (a) Any moving average (MA) process is covariance stationary. (b) Any autoregressive (AR) process is invertible. (c) The autocorrelation function of an MA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off. (d) Suppose yt is a general linear process. The optimal 2-step-ahead prediction error follows MA(2) process. (e) Any autoregressive moving average (ARMA) process is invertible because any moving average (MA) process is invertible. (f) The...
1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie, MA(1): where e is a white noise process with N(0,1). Suppose that you estimate the model using STATA. You obtain ê-1, ê-0.5 and ớ2-1. You also know e,-2 and E1-1-3. (a) Obtain the unconditional mean and variance of Y (b) Obtain Cor(Y, Yi-1). (c) Obtain the autocorrelation of order 1 for Y 1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie,...
what is the correct answer? please provide the calculation . Consider the following MA(1) model with the errors Et having having zero mean, unit variance and being serially uncorrelated. Yt = 0.2 + E +0.5&t-1 The value of the autocorrelation coefficient at lag 1 is: 0.5 0.25 0 0.4
1. An AR(1) process is given by Xų = 0.727-1 + wt, where et represents a sequence of uncorrelated random variables of zero mean and constant variance 0.4 so that Rww 0.48(n). a. If in addition wt is normally distributed then what can we say about the output Xť ? b. Compute the autocorrelation function of the output process.
1. Consider the following autoregressive process 2+ = 4.0 + 0.8 2t-1 + Ut, where E (u+12+-1, Zt-2, ....) = 0 and Var (ut|2t-1, 2-2, ...) = 0.3. The unconditional E (Zt) and unconditional variance Var (zt) are: (a) E (2+) = 11.1111, Var (zł) = 0.8333 (b) E (2+) = 11.1111, Var (zt) = 1.5 (c) E (zt) = 20, Var (zt) = 0.8333 (d) E (2+) = 4, Var (zł) = 0.8333 (e) E (Zt) = 4,Var (z+)...
1. Autocorrelation test Given the model Consumption, = a + B.Year + B Disposible Income, +E, and the estimated model: Model 1: OLS, using observations 1959-1995 (T = 37) Dependent variable: c t-ratio p-value const time Disposable Income Coefficient Std. Error 2707.84 385.254 80.9122 13.6539 0.508123 0.0460444 Mean dependent var Sum squared resid R-squared F(2, 34) Log-likelihood Schwarz criterion rho 11328.65 304975.4 0.998650 12577.63 -219.3165 449.4657 0.551018 S.D. dependent var S.E. of regression Adjusted R-squared P-value(F) Akaike criterion Hannan-Quinn Durbin-Watson...
[8] 3. For an MA (1) process where {%ı} is a scq ucoce of i.i.d. raodom variables from WN((),()"). lild the asv mptotic distribution for where P Is the sample autocorrelation function of lag 2 (use the Bartlet's formula [8] 3. For an MA (1) process where {%ı} is a scq ucoce of i.i.d. raodom variables from WN((),()"). lild the asv mptotic distribution for where P Is the sample autocorrelation function of lag 2 (use the Bartlet's formula
2. (20 points) Use first principles to find the autocorrelation function for the stationary process defined by Y, – ste, - 3. (20 points) Identify the following as specific ARIMA models. That is, what are p, d, and 4 and what are the values of the parameters (the 4's and o's)? (a) Y = Y.-0.257,-2 +e, -0.le, -1. (b) Y - 27,,-Y2+, (c) , -0.5, -0,5% 2+e, -- 0.5e,.. +0.250,-2. [Solution]