FIN3018 - Financial Econometrics and Data Science

Semester 2020

Assignment 2 - Take home

4 November 2020 — Submission Deadline: 20 November 2020, 21:00h via Canvas

Part 1: Theory and Calculations

Problem 1 (22 Points)

Calculations Consider the GDP of France and the GDP of Germany for the same years

(all in $ Trillions):

Table 1: GDP of France and GDP of Germany

Year France Germany

2013 2.8085 3.7525

2014 2.8156 3.8793

2015 2.4188 3.4968

Problem 1.1 Calculation: Use the Ordinary Least Squares procedure to find out if there

is a relationship between the GDP of France x and the GDP of Germany y !

Hint: Estimate the linear regression yt = α+ βxt . (10 Points)

For 1.1, answer the following in Canvas:

• What value does αˆ take? (MC ABCD)

• What value does βˆ take? (MC ABCD)

Problem 1.2 Calculation: If the GDP of France is 2 750 Billions in 2016, what would be

the expected GDP of Germany in the same year? (2 Points)

For 1.2, answer the following in Canvas:

• What value does yˆt+1 take? (MC ABCD)

Problem 2.3 Calculation: Estimate the Standard Errors of αˆ and βˆ and discuss your

results! (10 Points)

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For 1.3, answer the following in Canvas:

• What value does SE(αˆ) take? (MC ABCD)

• What value does SE(βˆ) take? (MC ABCD)

• Without calculation, do the estimates appear statistically significant from zero?

(T/F)

• What would improve the quality of the estimation? (MC ABCD)

Problem 2 (12 Points)

The following model with three regressors, including the constant, is estimated over 15

observations:

y = β1 + β2x2 + β3x3 + u

and the following data have been calculated from the original xs:

(X ′X)−1 =

3 5 −15 1 8

−1 8 6.5

(X ′y) =

61.5

2

uˆ′uˆ = 8.92

Problem 2.1 Calculation: Calculate the coefficient estimates of the multivariate regres-

sion

y = β1 + β2x2 + β3x3 + u.

(6 Points)

For 2.1, answer the following in Canvas:

• What value does βˆ1 take? (MC ABCD)

• What value does βˆ2 take? (MC ABCD)

• What value does βˆ3 take? (MC ABCD)

Problem 2.2 Calculation: Estimate the standard errors for the function above. (6 Points)

Hint: To calculate the standard errors, an estimate of σ2 is required which we know to

calculate:

s2 =

uˆ′uˆ

T − k .

2

For 2.2, answer the following in Canvas:

• What value does SE(βˆ1) take? (MC ABCD)

• What value does SE(βˆ2) take? (MC ABCD)

• What value does SE(βˆ3) take? (MC ABCD)

Part 2: Applications in R

(42 Points)

Problem 3 (18 Points)

Use the data set commodity_prices_Britain.xlsx which contains series of monthly

commodity prices from 1790 to 1850. In what follows, calculate summary statistics for

each of the commodity price series.

The following questions will be answered in Canvas as a multiple choice selection (MC

ABCD).

2.1) What is the mean of the Copper prices taking into account all observations?

3.2) What is the excess kurtosis of the Oats prices?

3.3) Are the prices of Line seed oil symmetrical, left skewed or right skewed?

Plot the prices of Butter with the variable “Year” on the x-axis. Which of the following

statements are true?

The following will be answered in Canvas as T/F statement.

3.4) The prices of Butter are at a high between 1810 and 1820.

3.5) The prices of Butter are at an all-time low in early 1810.

3.6) The command type=“l” can be used to plot the Butter prices as a continuous

line.

Calculate simple monthly percentage changes for the prices of Copper (pc), using the

formula:

r ct = 100 ∗

pct − pct−1

pct−1

.

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Remove missing observations. Then look at summary statistics of simple Copper returns.

Which of the following statements are true?

The following will be answered in Canvas as T/F statement.

3.7) The standard deviation of the changes in copper prices is 2.642.

3.8) The median of the changes in copper prices is 0.829.

3.9) The mean of the changes in copper prices is 0.039.

Problem 4 (24 Points)

You are estimating a multiple linear regression model in R and obtain the following output:

Regarding the above output, which of the following statements about the regression

above are true?

The following will be answered in Canvas as T/F statement.

4.1) The Microsoft excess returns (ermsoft) are used as an independent variable.

4.2) The Microsoft excess returns (ermsoft) are used as an dependent variable.

4.3) Changes in inflation (dinflation) have significant explanatory power towards the

Microsoft excess returns.

4.4) The S&P 500 excess returns (ersandp) have significant explanatory power towards

the changes in inflation.

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4.5) The Microsoft excess returns (ermsoft) have significant explanatory power towards

the SP500 excess returns (ersandp).

4.6) If the SP500 excess returns increase by one unit, the Microsoft excess returns

increase by 1.255 units.

4.7) Changes in industrial production (dprod) have no significant explanatory power

towards the Microsoft excess returns.

4.8) The overall regression is significant.

Based on the above regression, you conduct the following hypothesis test:

Regarding the above hypothesis test output, which of the following statements about

the regression above are true?

The following will be answered in Canvas as T/F statement.

4.9) It is tested whether the coefficients of the variables dprod, dinflation, and

dmoney are jointly zero.

4.10) It is tested whether any of the coefficients of the variables dprod, dinflation, or

dmoney equal zero.

4.11) You do not have enough evidence to reject the null hypothesis.

4.12) The F -statistic does not exceed the critical F -value.

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