Quantitative Methods Flashcards
What are the two formulas for R Squared?
R sq = Correlation Squared
R sq = RSS / SST
What is the formula to calculate the t-stat for the correlation coefficient?
t = (r√n-2) / (1-r2)
What does R Squared represent?
R squared represents the amount of variation in the dependent variables accounted for by an independent variable.
Does regression analysis assume that:
a) The independent variable is uncorrelated with the residuals.
b) The dependent variable is uncorrelated with the residuals.
It only assumes that the Independent Variable is uncorrelated with the residuals.
For a single-factor regression model, how many degrees of freedom does the critical T for calculation of a confidence interval for:
a) A parameter estimate.
b) A “Y-Value” estimate.
2 degrees of freedom for both.
What are the formulas for Mean Squared Regression and Mean Squared Error?
MSR = RSS/ df
MSE = SSE/ df
What is the formula for Standard Error of the Estimate?
SEE = √MSE
What is the formula for F-Stat?
F-Stat = MSR/MSE
What is the formula for calculating a confidence interval?
Confidence Interval = Coefficient Estimate +/- (Critical T)(Standard Error)
What is the formula for calculating t-stat for a parameter?
T-Stat = (Coefficient Estimate - Value to Compare) / Standard Error
What is spurious correlation?
Spurious correlation is when there there appears to be a statistical correlation between variables, but no actual relationship exists.
How many degrees of freedom does the regression have?
k degrees of freedom.
How many degrees of freedom does the error have?
n - k - 1 degrees of freedom.
How should the upper and lower Durbin-Watson values be used to determine whether to accept or reject the null hypothesis.
0 - Lower = Reject H0; Positive serial correlation exists
Lower - Higher = Inconclusive
> Higher = Do not reject H0
Would failing to include a variable that affects the dependent variable lead to misspecification?
Yes.
Would using actual inflation as a proxy for expected inflation lead to misspecification?
Yes.
Would using a lagged variable lead to misspecification?
Yes.
How will be the coefficients be when a model is misspecified?
Biased and inconsistent.
What is the solution to serial correlation?
Use Hansen method to adjust the standard errors.
What should all qualitative variables be tested for?
Heteroskedasticity, Serial Correlation and Multi-Collinearity.
What is a potential solution when a time series has a unit root?
Model the first differences, as these usually do not exhibit a unit root.
What is a trend model?
A model in which the independent variable is time (t).
When is a loglinear model used?
When a time series grows at a constant rate.
What does covariance stationary mean?
That the time series will be mean-reverting.
How is annual seasonal lag of quarterly returns?
a) By adding a t-4 parameter
b) By adding a t-12 paramater
c) By adding both
By adding a t-4 parameter.
How do you know if a time series is a random walk?
It has a unit root.
What is the null hypothesis of the Dickey-Fuller/ Engle-Granger test?
That the time series has a unit root/ is nonstationary.
Does the Dickey-Fuller test use conventional or adjusted:
a) t-statistics
b) Criticial t-values
The Dickey-Fuller test uses a conventional t-statistic but compares it to adjusted critical t-values.
What does a 4th autocorrelation need to differ significantly from for a model to exhibit seasonality?
Zero.
What is Autoregressive Conditional Heteroskedasticity (ARCH).
When an error is correlated with a lagged error.
What will the R2 and coefficient t-stats be if multicollinearity is present?
High R2 and insignificant t-stats.
How does historical simulation estimate VaR?
It uses actual returns and takes the 5th percentile.
What is the formula for VaR?
VaR = Mean Return - (Critical T * Standard Deviation)
How do you adjust annual standard deviation (volatility) in VaR to calculate daily standard deviation?
Daily SD = Annual SD / √No. Of Days
Note the square root of days, not the no. of days.
What is maximum drawdown?
The worst drop in performance from peak to trough, or the worst historical performance in a period.
How many degrees of freedom are there when determing the critical t-stat?
N - K - 1 degrees of freedom.
What is the general limit for a t-stat to be significant?
Greater than 2.
What is serial correlation?
When there is correlation between regression errors.
What is heteroskedasticity?
When the variance of errors is not constant, and is related to the independent variables.
What is reverse stress testing?
Creating a hypothetical event that would affect a company’s top exposure at the same time.
What is the test for heteroskedasticity and what part of the regression does it test?
The Breusch-Pagan Chi Squared test is carried out on the R-Squared
What part of the regression does the Hansen method adjust?
The standard errors.
What are the two steps to test for ARCH?
- Square the residuals.
2. Regress the squared residuals against squared residuals from previous periods.
What is the formula for the standard error of the autocorrelation?
1 / √n
If a regression covers periods that should have their own regressions, what type of misspecification is this?
Functional form misspecification.
What do unbiased and consistent mean?
Unbiased means the sample is representative of the population.
Consistent means that as the sample size increases, the estimate gets closer to the population.
