Question

Question:

a)Discuss three stylized features of Financial data

b) Explain how the features in (a) can be modeled using linear time series models

c)

i) Ecplain the moments of a random variable ii) How can you estimate these in emphirical applications

d)

i) Explain the Jaque-Bera Test (JB) , stating clearly , the null alternative hypothesis.

ii) In the case of financial data , do you agree JB test to accept or reject the null hypothesis?Explain

Answer 1

a)

1- A) The autocorrelation function of returns decays slowly as a function of the time lag. Autocorrelations of absolute-valued returns raised to a positive power are maximized when this power equals unity

B) Low-starting and slowly decaying autocorrelation function of the squared or absolute-valued observations. Different measures of volatility display a positive autocorrelation over several days, which quantifies the fact that high volatility events tend to cluster in time.

C) High kurtosis: Kurtosis in returns. Returns are not normally distributed. They are either Platykurtic (kurtosis <3) or leptokurtic distribution (Kurtosis>3)

b- First order linear models for modelling linear time series data are used:

These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH and the Autoregressive Stochastic Volatility model.

3- The “moments” of a random variable (or of its distribution) are expected values of powers or related functions of the random variable.

First Moment = Mean, Second Moment = Skewness (Zero, Positive or Negative), Third Moment = Kurtosis ( Platykurtic, Leptokurtic, Mesokurtic).

d) Jarque-Bera Test is a test for normality. the test matches the skewness and kurtosis of data to see if it matches a normal distribution. A normal distribution has a skewness of zero (i.e. it’s perfectly symmetrical around the mean) and a kurtosis of three.

Null Hypothesis ; Data is Normally Distribured.