Describe two extensions to the original garch model what

Question

PART A -

Question 1 - An analyst considers to test the order of integration of some time series data. She decides to use the DF test. She estimates a regression of the form

Δy_t = μ + ψy_t-1 + u_t

and obtains the estimate ψ^{^} = -0.03 with standard error = 0.32.

a) What are the null and alternative hypotheses for this test?

b) Given the data, and a critical value of -2.88, perform the test?

c) What is the conclusion from this test and what should be the next step?

d) Why is it not valid to compare the estimated test statistic with the corresponding critical value from a t-distribution?

Question 2 - 'macro.wf1' data file contains monthly interest rate series (1986 - 2013) corresponding to three and six months, and one, three five and ten years. Each series has a name in the file starting with the letters 'ustb'. Answer the following questions.

a) Which interest rate series are non-stationary in levels? Use the ADF test to check that.

b) Do you need to include a deterministic trend in the ADF test?

c) Do you agree that the results obtained from the ADF test are consistent with an output from the Phillips-Perron test?

PART B -

Question 1 - (a) Why, in the recent finance literature, have researchers preferred GARCH(1, 1) models to standard ARCH(p)?

(b) Describe two extensions to the original GARCH model. What additional characteristics of financial data might they be able to capture?

(c) Consider the following GARCH(1, 1) model

y_t = μ + u_t, u_t ∼ N(0, σ_t²) (1)

σ_t² = α₀ + α₁u²_t-1 + βσ²_t-1 (2)

where y_t is a daily stock return series. What range of values are likely for the coefficients defined in equations (1) and (2)?

(d) Suppose that a researcher wanted to test the null hypothesis that αα₁ + ββ = 1 in equation (2). Explain how this might be achieved within the maximum likelihood framework.

Question 2 - In EViews open 'log returns 9 series.wf1' file that contains 1471 daily observations of log-returns for the foreign exchange, equity and bond markets in Japan, Europe and the US. Use 3 foreign exchange series to answer the following questions.

(a) Estimate GARCH, EGARCH and GJR models for each of the series and interpret coefficients in these models. Do you agree that the coefficients on the asymmetry terms are consistent to what would have been expected? Why?

(b) Compare volatility estimates obtained from part (a) with absolute returns in each of the markets. Is it true that absolute returns have similar patterns to volatility estimates across time?

(c) Plot News Impact Curves (NICs) for the European foreign exchange returns using coefficients implied from GARCH and EGARCH model estimates in part (a). Explain why these NICs are different.

Attachment:- Assignment Files.rar