Statistical Properties Of Stock Returns

Statistical Properties of Stock Returns


In exercise we use periodic AFGX stock index observations starting at 2006/12/29 and ending at 2009/09/02. The exercice is performed in transcend.
There are terzetto objectives of the exercise:
1.To estimate 3 early ACF values and dissolve importee seek for them;
2.To visualize the variance ratio for q=2, test RW1 hypothesis by applying test statistics and show the level of significance for that statistics;
3.To estimate a GARCH (1,1) model with the mean and variance equations defined.

blow up 1
The first task of the exercise is the estimation of the first three values of the sample autocorrelation function (ACF), which can be estimated using the sample autocovariances:
(1)
, (2)
Then sample ACF is equal to
(3)
In order to get the first three values of ACF, we fall upon additional series: , which includes all returns at lag 1, with returns at lag 2 and with returns at lag 3. Then, using outperform function Data Analysis Correlation we make autocorrelation ground substance between returns and lagged returns ( , , , ).



The results obtained are shown in the following table:
r(t)r(t-1)r(t-2)r(t-3)
r(t)1
r(t-1)0,01341
r(t-2)-0,11370,01151
r(t-3)-0,0329-0,11510,01021

Numbers in the first tugboat show the three first values of the sample ACF. In order to perform a significance test we calculate Z value by formula , where is autocorrelation function, p-value using Excel function p-value=2*(1-normsdist(abs(Z)) and 95% confidence interval using formulas:
(4)
(5)
The results obtained can be seen in the table below:
ACFZp-valueconfidence interval 95%
Rho10,01340,35360,7236-0,06090,08776
Rho2-0,1137-2,99850,0027-0,1881-0,0394
Rho3-0,0329-0,86810,3853-0,10720,0414
If p-valueIf you want to get a full essay, order it on our website: Orderessay



If you want to get a full essay, wisit our page: write my essay .