Chapter 19: Fitting models

Question 1

Merits of fitting a copula with Method of moments REP

Answer 1

o Range of parameter value may not be acceptable
o Easy to calculate
o Parameters are not most likely ones, just outcome of sample

Question 2

Merits of fitting a copula with Maximum likelihood estimate RON

Answer 2

o Ranges of parameters are acceptable
o Observation increase decreases bias
o Normality tendency of parameters (CLT)

Question 3

Assumptions of OLS NEVIL

Answer 3

o Normally distributed errors assumed
o Error terms are idd from input variables and each other
o Variance or error terms is constant and finite
o Inverse of data exists – variables are not linear transformations of each other
o Linear relationship exists between variables

Question 4

Quantitative tests of goodness of fit CLIFT

Answer 4

o Coefficient of determination (R-squared)
o Likelihood ratio test – did the included parameter significantly improve the LR?
o Information criterion – compare alternative models – ranking only, not performance
o F-test
o T-test – is a variable significantly different from zero

Question 5

Merits of Information Criterion test CANS

Answer 5

o Complex models penalised
o Additional Parameters benefit cancelled out
o Not limited to nested models (like LR test)
o Statistical significance not shown, only relative different between models

Question 6

Qualitative tests of goodness of fit QACH

Answer 6

• QQ plots
• ACFs for time series data
• CDF comparison: Actual vs. expected
• Histograms of data distributions and density functions fitted over it

Question 7

Merits of Bayesian networks FEESAP

Answer 7

Framework for decision-making created
• Explicit modelling of causal effect
• Expert judgement used when causal effect is lacking
• Scenario and causal analysis facilitated
• Audit is easy
• Probabilities can be conditionally calculated– conditional probabilities can be derived

Question 8

GLS approach to fit a model A DOCI

Answer 8

o Allowance can be made for non-constant variance and correlation in the error terms of a distribution
o Diagonal matrix created to scale variance
o Off-diagonal matrix created to allow for correlations between errors
o Combination can also be created
o Independent and constant errors terms allowed for

Question 9

The principles of SVD LALI SIT

Answer 9

o Least squares optimisation
o Assume continuation of linear relationship to predict next set of observations N variables M observations
o Linear combination of R orthogonal matrices expresses X
o Independent variables not required
o Smaller number of explanatory variables
o Intuitive meaning of explanatory variables lacks
o Terminate process when explanatory variables become sufficiently small