1. For the ARIMA model below, give values for IE (Yt) and Var (Yt).
Yt = Yt−1 − 0.08Yt−2 + et − 0.02et−1?
1. For the ARIMA model below, give values for IE (Yt) and Var (Yt). Yt =...
QUESTION 2 (a) For each of the ARIMA models below, give the values for E(VY) and Var(VY) 0.Tet-1 (ii) Yt = 10 + 1.25%-1-0.25Yt-2 et-0.14-i (b) Show that the function Z, a t-1 not stationary, but the first difference of Z, is stationary QUESTION 5 (a) From a series Y, of length 100, the sample autocorrelations at lags 1-3 are 0.8, 0.5 and 0.4, respectively. Furthermore, the respective sample mean and sample variance of the series are 2 and s-5....
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et) = σe2 and Cov(et, es) = 0 for t ≠ s. Define a new time series {Yt} by Yt = et + 0.6 et -- 1 – 0.4 et – 2 + 0.2 et – 3. 1. Find E(Yt ) and Var(Yt ). 2. Find Cov(Yt , Yt – k) for k = 1, 2, ...
Consider the model, Yt = BO + p1 Yt-1 + Ut, select the assumption(s) that are needed to prove unbiased parameter estimates. (A. E[Ut Us |X, Yt-1, Yt-2, ... ] = 0 B. |p1|< 1 C. E[ Ut? |X, Yt-1, Yt-2, ... ] = su? D. E[ Ut |X, Yt-1, Yt-2, ... ] = 0
Consider the model, Yt = 0.8 + 0.1 Yt-1 +0.5 X1,t + 1.7 X2,t + Ut. Complete the following table for the predicted values (2 decimals): 2018 2019 2020 2021 Year Yt 7.1 7.63 1.25 1.35 X1,5 KX2,0 1.30 1.9 1.40 2.4 2.5 3.20
consider the ARIMA model
8. Consider the ARIMA model X,-4 + Xt-1 + W-0.75W,-1, W, ~ WN(0, σ*) a. Identify p, d, and q. Write the corresponding ARMA (p,q) model. b. Find E VX and VarVX
8. Consider the ARIMA model X,-4 + Xt-1 + W-0.75W,-1, W, ~ WN(0, σ*) a. Identify p, d, and q. Write the corresponding ARMA (p,q) model. b. Find E VX and VarVX
Box-Jenkins : For each of the non-seasonal models presented below, indicate whether or not it complies with the Box-Jenkins approach, ie is it stationary and invertible? Justify your answers. a) Yt = et − 0,67 Yt−1 b) Yt = et + 0,43 Yt−1 − 0,37 Yt−2 c) Yt = et + 0,25 et−1 d) Yt = et + 0,9 Yt−1 + 0,3 Yt−2 e) Yt = et + 0,9 Yt−1 + 0,3 et−1
Box-Jenkins : For each of the non-seasonal models presented below, indicate whether or not it complies with the Box-Jenkins approach, ie is it stationary and invertible? Justify your answers. a) Yt = et − 0,67 Yt−1 b) Yt = et + 0,43 Yt−1 − 0,37 Yt−2 c) Yt = et + 0,25 et−1 d) Yt = et + 0,9 Yt−1 + 0,3 Yt−2 e) Yt = et + 0,9 Yt−1 + 0,3 et−1
Below is an atomic instruction: func (var) { var = var + 6; if(var >= 0) { sign = 1; } else { sign = 0; } return sign; } Using func, implement Mutual Exclusion in a multiprocessing system. Also, give the initial value of var and give the entire set of possible initial values for var. Aim to minimize bus traffic.