public void Calc()
{
// we abstracted Tony Finch's code for covariance
// see Tony Finch, Incremental calculation of mean and variance
// https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
//--- average & variance for series
double seriesNew = _series.LogReturn()[0];
double seriesDiff = seriesNew - _avgSeries;
double seriesIncr = _alpha * seriesDiff;
_avgSeries = _avgSeries + seriesIncr;
_varSeries = (1.0 - _alpha) * (_varSeries + seriesDiff * seriesIncr);
//--- average & variance for benchmark
double benchNew = _benchmark.LogReturn()[0];
double benchDiff = benchNew - _avgBench;
double benchIncr = _alpha * benchDiff;
_avgBench = _avgBench + benchIncr;
_varBench = (1.0 - _alpha) * (_varBench + benchDiff * benchIncr);
//--- covariance
_cov = (1.0 - _alpha) * (_cov + seriesDiff * benchIncr);
//--- CAPM
(Beta as TimeSeries <double>).Value = _cov / Math.Max(1e-10, _varBench);
(Alpha as TimeSeries <double>).Value = _avgSeries - Beta[0] * _avgBench;
}
public void Calc()
{
//--- average & variance for series
double seriesNew = _series.LogReturn()[0];
double seriesDiff = seriesNew - _avgSeries;
double seriesIncr = _alpha * seriesDiff;
_avgSeries = _avgSeries + seriesIncr;
_varSeries = (1.0 - _alpha) * (_varSeries + seriesDiff * seriesIncr);
//--- average & variance for benchmark
double benchNew = _benchmark.LogReturn()[0];
double benchDiff = benchNew - _avgBench;
double benchIncr = _alpha * benchDiff;
_avgBench = _avgBench + benchIncr;
_varBench = (1.0 - _alpha) * (_varBench + benchDiff * benchIncr);
//--- covariance
_cov = (1.0 - _alpha) * (_cov + seriesDiff * benchIncr);
//--- CAPM
(Beta as TimeSeries <double>).Value = _cov / Math.Max(1e-10, _varBench);
(Alpha as TimeSeries <double>).Value = _avgSeries - Beta[0] * _avgBench;
}
/// <summary>
/// Calculate historical volatility, based on log-returns.
/// </summary>
/// <param name="series">input time series</param>
/// <param name="n">length</param>
/// <param name="parentId">caller cache id, optional</param>
/// <param name="memberName">caller's member name, optional</param>
/// <param name="lineNumber">caller line number, optional</param>
/// <returns>volatility as time series</returns>
public static ITimeSeries <double> Volatility(this ITimeSeries <double> series, int n = 10,
CacheId parentId = null, [CallerMemberName] string memberName = "", [CallerLineNumber] int lineNumber = 0)
{
var cacheId = new CacheId(parentId, memberName, lineNumber,
series.GetHashCode(), n);
return(series
.LogReturn(cacheId)
.StandardDeviation(n, cacheId));
}
