Question

Question:

a)Distinguish between the following:

i) Non- Parametric Methods

ii) Semi-Parametric Methods

iii) Parametric Methods

b) Discuss the following statistical properties of asset returns:

i) Heavy tails

ii) Ergodicity

iii)Autocorrelation -absence of linear autocorrelation

C)Explain the following Diagnostic tests of the error term

i) White Test of heteroscedasticity

ii)Normality Test

Answer 1

(a)

(i) Non-Parametric Methods, also called Distribution Methods are a type of statistic that do not require that the population being analyzed meet certain assumptions or parameters.

(ii) Semi-Parametric Methods are statistical model that have parametric and non-parametric components. These methods lie in the grey area between parametric and nonparametric methods. These methods achieve greater precision than Non-Parametric Methods but with weaker assumptions than Parametric Methods.

(iii) Parametric Methods are branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of parameters.

(b)

(i) Heavy tails, also called fat tails, of asset returns are those which exhibit excess kurtosis.

(ii) Ergodicity in asset returns is a characteristic possessed by a stochastic process by which its statistical proporties can be deduced from a single random sample of the process.

(iii) Autocorrelation, also called serial correlation, is the correlation between the elements of a series and others from the same series seperated from them by a given interval. One of the basic assumptions in Linear Regression Model the absence of Linear Autocorrelation: The random error components are identically and independently distributed and the correlation between the successive disturbances is zero.

(c)

(i) White test of heteroscedasticity is a statistical test that establishes whether the variance of the errors in a Regression model is constant, that is for homoskedasticity.

(ii) Normality Test is a statistical process used to determine whether a sample fits a Standard Normal Distribution.