Question 1 (a)
Based on the first 10 Lag of the ACF Plot and the result from the Ljung-Box test (p-value=0), rt is predictable since it shows significant autocorrelation.
(b)
AR(1) model is not appropriate as there are still autocorrelations patterns seen while AR(2) model is appropriate as it fully captured the autocorrelation pattern.
(c)
The model is appropriate since it has fully captured the autocorrelation pattern but the Santa Clause effect is not significant as it has a p-value of 0.410.
(d)
The model is appropriate since it has fully captured the autocorrelation pattern but the Tax Loss Selling effect is not significant as it has a p-value of 0.992.
(e)
The model is appropriate since it has fully captured the autocorrelation pattern but the volume effect is not significant as it has a p-value of 0.580.
(f)
Although all the other models except for AR(1) fully captured the autocorrelation patter of rt, AR(2) has shown the lowest AIC and BIC, as shown below, indicating that AR(2) is the best fitting model. AR(2) has 702.83 AIC and 716.88 BIC.
(g)
The VaR is $5,419.35. If Peter invests $100,000 in the ANZ stock, he would expect that there is 5% chance of losing $5,419.35 or more if he holds the stock for one week.
(h)
The VaR is $3,282.80. If Peter invests $100,000 in the ANZ stock, he would expect that there is 1% chance of losing $3,282.80 or more if he holds the stock for one day.
I would inform Peter of these probabilities when holding the stock. We can see that holding the stock for one day has less value at risk which Peter may go for but it will really depend on how much risk Peter is willing to take. fit1 = AR(1)
fit2 = AR(2)
fit3 = Santa Claus Rally model
fit4 = Tax Loss Selling model
fit5 = Volume effect model
