Exercises Flashcards
What are the steps to derive the unconditional variance?
Usually, e.g. when deriving from a random walk
Usually you want to rewrite the model to sum e.g. an AR or AR-MA model. Then you can derive it.
Derive the ARCH(inf) of a GARCH(1,1)
Solve
How to find the derivation of a function of sigma with respect to theta?
Find the derivative of sigma with respect to each variable in theta.
What is the Newton-Rapson algorithm?
x^(k+1) = x^(k) - f’(x^(k))/f’‘(x^(k))
What is the normal density?
How to test a parameter from a model, while knowing Omega hat?
Fill this value into a normal cdf (obv.)
How to draw a News Impact Curve?
y_t = 0 is omega,
y_t = +/-1 is omega + alpha,
y_t = +/- 2 is omega + alpha^2
etc.
Do you want higher or lower AIC/BIC?
Lower is better
Which of AIC/BIC should always be lower?
BIC since it “punishes” parameters more
What is z_0.05? And z_0.025?
-1.64, -1.96
When is the approximation for large h of sigma(h) better?
When alpha + beta is highest
What is the cond. expectation E[X | Y] and cond. variance Var[X | Y] of a bivariate model with
What is a requirement for a valid covariance matrix of a DVECH model (and other multivariate GARCH models)?
It needs to be symmetric (diagonally)
What is the uncond. variance of a VECH model
(I - A_1 - A_2 -..)W
What is corr rho?
rho_12 = sigma_12/(sigma_1 sigma_2)
What are important facts you need to know when deriving the kurtosis?
- The kurtosis of a normal distribution is three
- sigma^4 = sigma^2*2 = exp(2mu +2sigma)
A LogN + LogN distribution is?
LogN
Cov(a, b) = ?
In terms of the expectation
E[ab] - E[a]E[b]
How do you show that an indirect estimator is efficient?
If you have to check whether the auxiliary statistics of a estimation make sense, what do you need to look at?
- Are there enough auxiliary statistics
- Are the statistics relevant (e.g., no skewness for a symmetric distribution)
Which type of models make sense to check an SV model with using aux. statistics?
Models that check y^2_t and the autocov.
What are the steps of deriving the loglikelyhood?
- Find the mean and variance of the observation equation
- Fill these values into a normal pdf (1/sqrt(2pi sigma^2))exp((y - mu)^2/2sigma^2)
- Sum these into a log likelyhood, you may remove constants
- Start the sum at a t for which you have values
