QFC Quantitative Finance Statistical & Mathematical Analysis 2

Question 1

Which test is used to assess whether a time series is stationary by testing for a unit root?

Accepted Answer

Augmented Dickey-Fuller test

Answer

The Augmented Dickey-Fuller (ADF) test checks for the presence of a unit root, with rejection of the null indicating stationarity.

Question 2

In a multivariate normal distribution, if the covariance between two variables is zero, what can be concluded?

Accepted Answer

The variables are independent

Answer

For multivariate normal distributions, zero covariance implies statistical independence, unlike in general distributions.

Question 3

What does the Ljung-Box Q-statistic test for in financial time series?

Accepted Answer

Presence of autocorrelation in residuals

Answer

The Ljung-Box test checks whether any of a group of autocorrelations of a time series are different from zero.

Question 4

A portfolio has returns that follow a distribution with excess kurtosis of 3. How does this compare to a normal distribution?

Accepted Answer

It has heavier tails than normal

Answer

Excess kurtosis of 3 means total kurtosis of 6 (since normal has kurtosis 4 in some conventions, or excess kurtosis of 3 means leptokurtic with fatter tails than normal).

Question 5

In OLS regression, what assumption is violated when the error variance changes systematically with an independent variable?

Accepted Answer

Heteroskedasticity

Answer

Heteroskedasticity occurs when the variance of the error term is not constant across observations, violating the OLS assumption of homoskedasticity.

(QFC) Quantitative Finance Certification Practice Test

(QFC) Quantitative Finance Certification Practice Test

QFC Quantitative Finance Statistical & Mathematical Analysis 2