Chapter 15 - Fitting models

Question 1

Fitting a model to data

Answer 1

Least squares regression

i) Ordinary least squares
ii) Generalised least squares

Methods based on a likelihood function

i) Likelihood ratio test - test whether adding variables improves explanatory power
ii) Information criteria - used to compare alternative models, only enables ranking (not statistical significance)

Principal component analysis (PCA)
Facilitates stochastic projections, explanatory powers are limited

Singulat value decomposition (SVD)
Operates on original data - no requirement to identify independent variables

Question 2

Information criteria

Answer 2

Akaike information criteria AIC
Bayesian information criteria BIC
BIC more sevre on extra parameters
Lower value better fit of model
Only sued for ranking models, not quantifying statistical significance

Question 3

Qualitative graphical diagnostic tests

Answer 3

QQ plots
Histograms vs Density functions
Empirical CDFs vs Fitted CDFs
Autocorrelation functions of time series data

Question 4

Fitting a distribution to data

Answer 4

Method of moments:
Sample moments equated to population moments to solve equation
Copulasses estimates of rank correlations to solve for parameters

Maximum likelihood:
Maximise log likelihood through differentiation by parameters and setting equal to 0
Copulas: Max loh likelihood or sum log copula density functions
Can pick best copula from values of MaxLike functions

Question 5

Common observations of financial time series

Answer 5

Returns are not iid
Absolute or squared returns show strong serial correlation
Conditional expected returns close to zero
Heteroskedastic - volatility varies over time
Leptokurtic - high peaks, fats tails
Extreme returns appear in clusters