Week 6

Question 1

How and when to use PIT for time series

Answer 1

Question 2

Generalisation of probability integral transforms to any RVs

Answer 2

Question 3

Convert PIT to Gaussian

Answer 3

Question 4

Explain how and when to use Kolmogorov Smirnov Test

Answer 4

Each I_{[-inf, x]}(X_i) is the indicator function for the P of getting a value less than or equal to current val

when summing the indicator RVs you get a step function which approximates the CDF

D_n is testing for the largest gap between the stat formed from dimming and the exact distribution

Question 5

Evaluating density forecasts 2 tests

Answer 5

Test uniformity (KS)

Test independence

Question 6

Test independence

Answer 6

Question 7

If independence test fails

Answer 7

Lag may be wrong

Therefore go for more complicated model

Question 8

If KS test fails

Answer 8

Therefore not uniform

There we may not be heavy tailed enough

Question 9

General form of EGARCH

Answer 9

Question 10

Stationarity of EGARCH

Answer 10

Question 11

Represent GARCH models by log

Answer 11