InstrumentEstimateEmpiricalCovariance

This program estimates the empirical auto- and cross-covariance of selected data columns per arc of inputfileInstrument. The maximum computed lag is determined by the number of outputfileCovarianceMatrix specified (for a single output file only the auto-covariance is determined, for two output files auto- and cross-covariance is computed and so on).

Stationarity is assumed for the input time series, which means the temporal covariance matrix has Toeplitz structure. \[ \begin{bmatrix} \Sigma & \Sigma_{\Delta_1} & \Sigma_{\Delta_2} & \Sigma_{\Delta_3} & \Sigma_{\Delta_4} \\ & \Sigma & \Sigma_{\Delta_1} & \Sigma_{\Delta_2} & \Sigma_{\Delta_3} \\ & & \Sigma & \Sigma_{\Delta_1} & \Sigma_{\Delta_2} \\ & & & \Sigma & \Sigma_{\Delta_1} \\ & & & & \Sigma \\ \end{bmatrix} \] The matrix for lag $h$ describes the covariance between $x_{t-h}$ and $x_{t}$, i.e. $\Sigma(t-h, t)$.

To get a reliable estimate, InstrumentDetrend should be called first.

Name	Type	Annotation
outputfileCovarianceMatrix	filename
inputfileInstrument	filename
startDataFields	uint	start
countDataFields	uint	number of data fields (default: all after start)

This program is parallelized.