What is the global F test and why is it called the global test
What is the logic of this test
Becuase you are testing all of the coefficients as a group, and you are testing wether they are all equal to zero at the same time
For this you use the F test
MSR/MSE
Where the degrees of freedom for the mean squared error is equal to k and the degrees of freedom for the Mean squared error is equal to n-k-1
You basically are measuring the average regression function (the ammount of the variation that is predicted by the model) and then you are dividing it by the average error (the ammoiunt of difference from the predicted value to the actual value) if the average regression function is high and the average error is low it shows you that there is something that is important, and oyu would reject the null
What is the interpretation of a t value
The t value basically tells you how far your observed value is away from the value that the model initially predicted in terms of number of standard deviations. If the value of the observed value is a long way away from the hypothesised value then you can say that oyu can reject the null hypothesis.
What does AIC and BIC stand for and what value is better or worse
When you decide remove a value from a multiple regression model can you just use the coefficients that were already there when you modelled the output in the first place, or do you have to rerun the whole model and why
You have to rerun the whole model becuase if you were to take away a value in the regression model then it would have an impact on the rest of the values in a negative way.
What is the definition of unconditional heteroskedasticity
What is the difference between conditional and unconditional heteroskedasticity
Is when the variance of the error term changes depending on the x value. This means that the variance of the error term is different at different points
Basically in conditional heteroskedasticity the variance is directly linked in a proportional and predictable way to the x value whereas unconditional heteroskedasticity does not have a straightforward relationship with x but it does change over time, so you cannot define it as homoskedastic
What is the other term for a type one error
What type of heteroskedasticity does this usually happen for
False significance, you’re basically saying something is important when it actually isn’t
Usually this happens for conditional heteroskedasticity brocade your standard error is too small, that means that you’re dividing by a small number, which means that your coefficient is too big.
What is the basic definition of the breusch pagan test
It basically says that you regress the values of the squared error terms agains the value of x (the independent variables) the closer to 1 it is it means that the higher the r^2 correlation is to the independent variables and the error terms so you can say taht the values are conditionally heteroskedastic
If oyu have a high r^2 then you have the problem, and oyu reject the null. Therefore you have conditional heteroskedasticity
Question. What if oyu get a graph that’s non linear, like the x does follow a line but it’s not a linear line
What do white corrected standard errors do
You make all of the standard errors bigger becuase you have conditional heteroskedasticity wich means that oyu have a structurally too low standard error against all of your coefficients
Therefore your corrected t stats will be adjusted so you can change the interpretation of the T- value. This means that oyu might either accept or reject different values with the adjusted T stat
What does the positive autocorrelation assumption violation of regressions mean
What error do you get in this case
It means that values are consistently below the line in the early years and then consistently above in further out years. This is reflected in occasions such as compounding, where values continue to compound on themselves
You get a type one error which means that you are likely to underestimate the value of the residual consistently, which means that oyu have a false positive
What is the definition of an autogregressive time series analysis
What test would you use here
How would you work out if you have a seasonality what test do you use
It si when you regress a time series against itself, so you would be testing the value this year agains the value from last year.
You would use the
The Durban Watson test can only regress the period before.
You would use a lag error, so you might be regressing the value today and the value four quarters ago, if you have autocorrelation between these, then you have seasonality the BG breusch Godfrey test is used here which computes the autocorrlations across all the periods
Waht is the definition of Newy-West standard errors
This is when you adjust the standard errors higher and it takes into account the heteroskedasticity and serial correlation.
It does not get rid of these relationships it just ADJUSTS THE STANDARD ERRRORS which means that your analaysis about what is important is more accurate
What is the definition of multicolinearity
What type of error does this give you
When two or more variables are linked and therefore standard errors are too high,therefore t stats are too low, and b1=0 is
This gives you a type two error because you are saying that things are not important when they actually are
What does a variance inflation factor do
What does it show
When you test different combenations of independent variables against one another for escapee X1 and X2 regressed against just X3, then you can plug this into the VIF formula, and if the VIF formula is equal or greater than 10, then this is when you have a problem where the independent variables are related to one another.
You indicate that you have this issue if B1 b2 and b3 are equal or close to zero however your f test is significant and your r squared test is actually high too so the model is working well but each of the values is insignificant
It shows if oyu have multicolinearity
Which of these two series of data is covariance stationary and non covariance stationary
Waht is an AR model
Can you use a Durban Watson test?
The s and p index is non covariance stationary because it is not mean reverting, however the returns of the s and p index is covariance stationary becuase it is mean reverting, if it is covariance stationary you can use an AR model
An ar model is an autoregression model
It is where you are regressing the values in the future against hte value in the past
You cannot use a Durban Watson test when you are testing for autocorrelation in an autoregressive Durban Watson can only be used in a linear Trend
What is the formula for the standard error
Equal to 1/n^1/2
What does it mean when b1=1 and what does it mean about the mean reverting level and what type of model do you have
It means that you have a unit root, there is no mean reverting level, and therefore you have a random walk where the value is just predicted by the error term.
What is the dickey fuller test
Want to test if b1 is equal to 1
However if b1 is equal to one then you can’t directly test it.
You take a first difference instead to investigate the difference.
You basically investigate if b1 is equal to 1 by testing if b1-1 is equal to zero which implicitly is the same thing
You take the null hypothesis that b1-1 is equal to 0
If oyu reject the null hypothesis it means that oyu don’t have the problem.
