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## VOLATILITY PREDICTION OF AGGREGATE EQUITY MARKET VOLATILITY

What is the core of what is nontrivially predictable in the financial markets?  In other words, what should we expect to be predictable?  My answer to the question is that volatility should be predictable and the most accurately predictable volatility should be the composite volatility of the entire equities market rather than those of individual stocks.  This is a perspective that is not unusual.  In order to justify this claim here are results of 1-day forecast of aggregate volatility defined as $mean_{1900 stocks} ( \log( r_{stock daily}^2) )$ using an AR(15) model for a simple baseline taking into account long memory features.

```>>> print results.summary()
OLS Regression Results
==============================================================================
Dep. Variable:        -9.399464650204   R-squared:                       0.801
Method:                 Least Squares   F-statistic:                 2.998e+04
Date:                Thu, 17 Dec 2015   Prob (F-statistic):               0.00
Time:                        17:34:16   Log-Likelihood:                 6080.3
No. Observations:                7465   AIC:                        -1.216e+04
Df Residuals:                    7463   BIC:                        -1.214e+04
Df Model:                           1
Covariance Type:            nonrobust
=====================================================================================
coef    std err          t      P>|t|      [95.0% Conf. Int.]
-------------------------------------------------------------------------------------
const                -1.5853      0.044    -36.009      0.000        -1.672    -1.499
-9.28718141559285     0.8278      0.005    173.140      0.000         0.818     0.837
==============================================================================
Omnibus:                      849.393   Durbin-Watson:                   1.523
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1858.764
Skew:                          -0.698   Prob(JB):                         0.00
Kurtosis:                       5.006   Cond. No.                         331.
==============================================================================
```

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