Volatility
Overview
When a time series is
stationary,
or even weakly stationary,
the
variance (or standard deviation)
is well defined and constant over time. In the context of time series, the standard deviation is
known as the volatility.
Even though {% StdDev(X_i) %} is constant, {% StdDev(X_i|X_{i-1},X_{i-2},...) %} may not be.
That is, the volatiltiy of a time series can change over time, given the previous data points.
More generally, the volatility can be defined within the context of
Ito Processes,
the volatility is the coefficient of Brownian Motion term.
Calculating
The challenge to calculating a volatility is to deal with fact that the theoretical volatility of the time series
changes over time. If this were not the case, we would just take the entire time series and calculate a standard deviation.
In we are presented with a trade off, which is, how many points of the time series should we take in our calculation.
Implementation
