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Statistical Properties of Stock Returns

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Submitted By elyza
Words 324
Pages 2
In exercise we use daily AFGX stock index observations starting at 2006/12/29 and ending at 2009/09/02. The exercice is performed in Excel.
There are three objectives of the exercise:
1. To estimate 3 first ACF values and run significance test for them;
2. To calculate 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.

Part 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 make additional series: , which includes all returns at lag 1, with returns at lag 2 and with returns at lag 3. Then, using Excel function Data Analysis – Correlation we make autocorrelation matrix 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) 0,0134 1 r(t-2) -0,1137 0,0115 1 r(t-3) -0,0329 -0,1151 0,0102 1

Numbers in the first column 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: ACF Z p-value confidence interval 95%
Rho1 0,0134 0,3536 0,7236 -0,0609 0,08776
Rho2 -0,1137 -2,9985 0,0027 -0,1881 -0,0394
Rho3 -0,0329 -0,8681 0,3853 -0,1072 0,0414
If

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