The file arch.wf1 contains daily data for the logarithmic returns FTSE-100 (named r_ftse) and three more stocks of the UK stock market (named r_stock1, r_stock2 and r_stock3, respectively). For each of the stock series do the following:

(a) Estimate an AR(1) up to AR(15) model and test the individual and joint significance of the estimated coefficients.

(b) Compare AIC and SBC values of the above models and, along with the results for the significance of the coefficients, conclude which will be the most appropriate specification.

(c) Re-estimate this specification using OLS and test for the presence of ARCH(p)

effects. Choose several alternative values for p.

(d) For the preferred specification of the mean equation, estimate an ARCH(p) model and compare your results with the previous OLS results.

(e) Obtain the conditional variance and conditional standard deviations series and rename them with names that will show from which model they were obtained

(for example SD_ARCH6 for the conditional standard deviation of an ARCH(6)

process).

(f ) Estimate a GARCH(q,p) model, obtain the conditional variance and standard deviation series (rename them again appropriately) and plot them against the series you have already obtained. What do you observe?

(g) Estimate a TGARCH(q,p) model. Test the significance of the TGARCH coefficient.

Is there any evidence of asymmetric effects?

(h) Estimate an EGARCH(q,p) model. How does this affect your results?

(i) Summarize all models in one table and comment on your results.