2. (a) Consider the process X+ = -0.125X4–1 -0.5X4-2 + Zt, where {Z} is a white noise process with constant variance. Le

[answerhappygod]

2 A Consider The Process X 0 125x4 1 0 5x4 2 Zt Where Z Is A White Noise Process With Constant Variance Le 1 (104.43 KiB) Viewed 26 times

2. (a) Consider the process X+ = -0.125X4–1 -0.5X4-2 + Zt, where {Z} is a white noise process with constant variance. Let {X1, ... , Xx} be the observations. Compute E[XN+1|XN+1-i; i = 1, ... ,N] and E[XN+1/XN-i, i = 1, ... , N – 1] in terms of the observations. [5 marks] 2 The Hong Kong Polytechnic (b) For a time series {X;} of length 100, the sample autocorrelation function (ACF) and sample partial autocorrelation function (PACF) for {Xt} and its differenced sequence {VX;} are given below. Lag 1 2 3 4 5 6 7 8 Sample ACF of X 0.96 0.95 0.94 0.93 0.88 0.87 0.86 0.84 Sample PACF of X *** *** *** -0.07 -0.02 -0.13 0.08 -0.11 Sample ACF of VX -0.46 0.09 0.09 -0.04 -0.08 0.09 -0.06 -0.02 Sample PACF of VX -0.46 -0.08 0.23 -0.03 0.13 -0.11 -0.01 -0.09 i. Complete the above table by finding the corresponding sample PACF for {X,} up to order 3. [8 marks] ii. Propose two possible models for {Xt} and justify them. [4 marks) iii. If an ARIMA(0,1,0) model was fitted to {X/}, conduct a Ljung-Box test at а a = 0.05 to test whether the residuals are uncorrelated. [8 marks