Question 1

Consider the MA(2) model:

y_t = δ + θ₁ε_t-1 + θ₂ε_t-2 +ε_t

where |θ₁|<1, |θ₂|<1 and ε_t~WN(0,σ²). Calculate

(a) E(y_T+i | Ω_T) for i =1, 2, 3 ,4 where Ω_T is all information up to and including time T.
(b) var (y_T+i | Ω_T) for i =1, 2, 3 ,4.
(c) Derive an expression for a two-standard error confidence band around the forecast of y_T+i for i=1,2,3,4. ie E(y_T+i | Ω_T)+ 2√var(y_T+i) |Ω_T . Your answer to (a) gives the forecast and your answer to (b) gives you the standard error of your forecast.

Question 2

Testing for significance in AC and PAC

Open an Eviews workfile for 1044 daily price observations on three bank stocks from BANKS_DAILY.xls, CBA, AMP and MBL. Compute the simple RETURNS to each of the series.

Reset the sample to 2-101.

Recall that we can construct an approximate 95% confidence interval for the ACF and PACF using ±1.96/√T . An individual AC or PAC coefficient is irrelevant within the confidence interval.

To test a block of autocorrelations we can use the Ljung-Box Q statistic:

Q = T(T+2) ∑_i=1^k ρ_i²/T-i

which is distributed χ² with k degrees of freedom.

(a) Open the series for the simple return to CBA, AMP or MBL and using the ‘View' menu, generate the correlogram and test the first three AC and PAC values for significance, individually and in a block of three, using the Eviews output to help you. State the null hypotheses and conclusions in all cases.

(b) Open the series for the returns to one other bank returns series and do the same as for (a).

(c) Comment on the autocorrelation structure of both of these series. Are they long or short memory processes? Are either of the returns series likely to be forecastable?

(d) Based on the ACF and PACF what time of model would you recommend for both series? Estimate this model and comment on it.

Attachment:- BANKS_DAILY.rar