闪电代写 -代写CS作业_CS代写_Finance代写_Economic代写_Statistics代写_代码代做_IT代写_加急帮助

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

FI4003 Empirical Methods in Finance

Assignment #2

General Instructions

Please answer ALL questions in All Parts. Each part carries equal weight for the final mark.

You will be required to submit your assignment through SafeAssign via MyAberdeen. No paper copies are required to be submitted.

Part A

1. Define the following terms

• Stochastic process

• Weak stationarity

• Autocovariance

• Random walk

• Granger causality

[25 marks]

2. Consider the following stochastic process

yt = 0.4 + 0.3 yt- 1 + et- 1

where et- 1 is white noise with variance equal to 1. Find E[yt], E[yt |yt- 1], Var(yt), Corr(yt , yt+1), and Corr(yt , yt+2). Document all your calculations.

[25 marks]

3. Briefly discuss why vector autoregressions (VAR) have become popular for applications in Finance and Economics.

[25 marks]

4. Give an example from Finance, where an error correction model specifies the data generating process for a set of two (or more) variables. Explain, with reference to the error correction term, why such a model is expected to exist.

[25 marks]

Part B

Consider the simple regression model

(1) Δ! = + Δ! + !

where ! is the natural logarithm spot price of the Apple stock, ! is the natural logarithm of the forward price, and ! is a white noise error term.

1. Explain what is meant by Best Linear Unbiased Estimator (BLUE). Which assumptions about the error term ! must hold, in order for ordinary least squares (OLS) to be BLUE?

[25 marks]

2. Using formulas where appropriate, explain why OLS estimates of Eq.1 are of interest for financial risk management. Why is Eq.1 specified in first differences rather than the levels of the variables?

[30 marks]

3. Table 1 reports ordinary least squares estimates of Eq. 1. Describe the testing procedure for a t-test for statistical significance of the OLS coefficient estimates. Clearly describe the null and alternative hypotheses and the testing procedure. Fill in the missing t-statistics and p-values in Table 1 and interpret the test results.

[30 marks]

Table 1 Reports OLS estimates of Eq 1

Dependent Variable: SPOT_RETURN Method: Least Squares Sample (adjusted): 1999M7 2019M12 Included observations: 246 after adjustments
Variable	Coeﬃcient Std. Error t-Statistic Prob.
C		0.363302	0.444369
FUTURES_RETURN		0.123860	0.133790
R-squared	0.013422		Mean dependent var	0.004168
Adjusted R-squared	-0.002238		S.D. dependent var	0.043333
S.E. of regression	0.460232		Akaike info criterion	7.916378
Sum squared resid	51.6860		Schwarz criterion	7.887879
Log likelihood	-175.7145		Hannan-Quinn criter.	7.904903
F-statistic	0.857070		Durbin-Watson stat	2.969363

4. In light of your answers to question 2 and the results in Table 1, interpret the estimated coefficient .

[15 marks]

Part C

Assume that you have a sample of size N=1,000 generated from the AR(2) model

(2) ! = 0.2 + 0.9 ! " # + 0.01 ! "$ + ! where ! ~ (0, $ ) .

1. Given the sample data, explain how you can test if the AR(2) model of Eq. 2 has a unit root or not. Clearly describe the procedure, the variables used, and the test statistic and its hypotheses.

[25 marks]

2. What test result would you expect? Does your expectation change, if you only had a sample of size T=30.

[15 marks]

3. Assume that you have fitted an AR(1) model to the data generated by Eq. 1. The estimated model is

(3) 0! = 0. 19 + 0.92! " #

Discuss why you might prefer the estimated model of Eq. 3 over estimates of an AR(2) model if you wanted to use the estimated models for forecasting. How does your answer change, if you knew that your data has been generated by Eq. 2?

[20 marks]

4. Assume that the observed value of the time-series in period t is given by ! = 1.65 Using equations were appropriate, explain can how you obtain a 1-period ahead forecast !$# given the estimated model of Eq. 3? What is the forecasted value?