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SEMESTER 2 2022/23

MANG 6008

Quantitative Research in Finance

Group Coursework

Group Coursework Brief:

You should be aware that all members of your group share responsibility for any academic integrity breaches or other issues that may arise from your group’s coursework submission. The awarded mark to a group implies that each member of that GROUP receives the same mark as others in the same group. Use STATA for estimations and tests. Assume, where relevant the significance level of 5%. PLEASE NOTE THAT ONLY ONE MEMBER OF THE GROUP SHOULD SUBMIT THE ASSIGNMENT TO BLACKBOARD TURNITIN.

Answer ALL Questions in Full

Question ONE

Question ONE requires using the data from the module page on Blackboard. The data file Q1.XLS contains the short-term interest rates for selected OECD countries, the US policy interest rate (i.e., effective federal funds rate) (USinterest), the US VIX volatility index (VIX), and the US economic policy uncertainty index (EPU). These data are obtained from the OECD database and the Federal Reserve Bank St Louis’ database.

Suppose that you want to study the (spillover) effect of US monetary policy on the short-term interest rates in the OECD countries. To this end, consider the following regression model:

Ri,t  = a + F1Rt(US)  + ui,t                     ,                                                                                                                                   

(1)

where Ri,t  is the short-term interest rate for an OECD country i (each group will be allocated a country), Rt(US) is the US policy interest rate, and ui,t  is the random disturbance term.

IMPORTANT NOTE: You MUST answer each part of the question separately and clearly.

Required for Question ONE

a) What assumptions would you make on the random disturbance term and/or the explanatory variable so that the estimated coefficients are BLUE? Do you expect these assumptions to hold for the model outlined in Equation (1)? Discuss.

b) Estimate Equation 1 using OLS. Summarise the goodness of fit of the model and test the hypothesis that the short-term interest rate in the selected country responds positively to the US policy interest rate. Outline the null and alternative hypotheses for this test. Perform the test and comment on the result.

c) Perform a test for heteroscedasticity in the residuals from Equation (1). Comment on the result. What inferences would you  make  in the  presence of heteroscedasticity? What methods would you employ to remedy the presence of heteroscedasticity?

d) Perform a test for serial correlation in the residuals from Equation (1). Comment on the result. What inferences would you make in the presence of serial correlation? What methods would you employ to remedy the presence of serial correlation?

e) In addition to the monetary policy, it is believed that uncertainty is another important factor in explaining the short-term  interest  rate. Suppose that there are two types of uncertainty  under your consideration, economic policy uncertainty (EPU) (measured by the US economic policy uncertainty index) and financial uncertainty (VIX) (measured by the VIX volatility index). Consider the following regression model:

Ri,t  = a + F1Rt(US)  + F2Ut(US)  + ui,t ,                                                                                                                          (2A,B)

where Ut(US)  is the uncertainty index measured by either VIX or EPU. Perform OLS estimations of Equation (2A,B) twice. Use VIX to measure Ut(US)  in Equation 2A and use EPU in in Equation 2B. Compare your results across the three specifications (Equations 1, 2A and 2B). Which regression specification should be employed? Which uncertainty measure (VIX or EPU) should be included in the regression model?

[50 marks] [Maximum 1000 words]

Question TWO

Question TWO requires to use the same data file as for Question ONE. Required for Question TWO a) Depict the short-term interest rate, Ri,t , on a time series graph. Comment on the result.

b) Perform a unit root test on the interest rate. Is the variable I(0) or I(1)? Carefully outline the test equation, as well as the null and alternative hypotheses for this test. Discuss if an intercept and/or linear trend need to be included in the test equation.

If the interest rate is I(1), for the remainder of this question transform it into FIRST DIFFERENCES. If the interest rate is found I(0) no transformation is necessary; continue using the variable in LEVELS.

c) Estimate the autocorrelation and partial autocorrelation functions for the interest rate (in LEVELS or DIFFERENCES, depending on part b). Comment on the estimation output.

d) Estimate AR(p) models with p=1,2,3, and ARMA(p,q) models with p=1,2,3 and q=1,2,3. Summarise in tables the coefficient estimates, the estimated standard errors, the information criteria AIC and BIC, as well as the Ljung-Box Q test for the first 12 autocorrelations in the residual series. Comment on the results.

e) Based on the estimation output in d), select the optimal time-series model. Justify your choice.

[25 marks]

[Maximum 500 words]

Question THREE

Question THREE requires to use the same data file as for Question ONE. Required for Question THREE

If the interest rate is I(1), for the remainder of this question transform it into FIRST DIFFERENCES. If the interest rate is found I(0) no transformation is necessary; continue using the variable in LEVELS.

a) Depict Ri,t on a time series graph and discuss if there is evidence of volatility clustering in the data. Comment on the result. Calculate the squared Ri,t and depict graphically the correlation and partial correlation functions of the squared Ri,t. Comment on the result.

b) With respect to the series Ri,t, test for the presence of conditional heteroscedasticity in the residuals of the conditional mean model, formulated as in Equation (1). Perform the LM-ARCH test for lag orders 1 and 6. Comment on the results. Is there evidence of conditional heteroscedasticity in the residuals? Please use the same conditional mean model in c) and d) below.

c) Proceed to estimate ARCH(p) models with p=1,…,6. Summarise the estimated models in a table. Discuss the results. Which of the estimated models provides the best fit? The conditional mean model is as in b).

d) Now estimate the conditional variance using GARCH(1,1) and TGARCH(1,1) models. Discuss the results. Which of the two models provides the best fit? The conditional mean model is as in b).

e) Now estimate a GARCH(1,1)-M model, in which the conditional mean model is formulated as . Comment on the results.

[25 marks]

[Maximum 500 words]

Nature of Assessment: This is a SUMMATIVE ASSESSMENT. See ‘Weighting’ section above for the percentage that this assignment counts towards your final module mark.

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