gamma

hf.gamma(data, h)

The h-th realized autocovariance.

Parameters

datanumpy.ndarray, shape = (p, n)

An array of synchronized and demeaned log_returns. (e.g. with refresh_time()).

hint

The order of the autocovariance.

Returns

gamma_hnumpy.ndarray, shape = (p, p)

The h-th realized autocovariance matrix.

Notes

The h-th realized autocovariance is given by \begin{equation} \boldsymbol{\gamma}^{(h)}\left(\mathbf{Y}\right)= \sum_{s=h+2}^{n+1}\left(\mathbf{Y}(s)-\mathbf{Y}(s-1)\right) \left(\mathbf{Y}(s-h)-\mathbf{Y}(s-h-1)\right)^{\prime}, \quad h \geq 0 \end{equation} and \begin{equation} \boldsymbol{\gamma}^{(h)}\left(\mathbf{Y}\right)= \boldsymbol{\gamma}^{(-h)}\left(\mathbf{Y}\right)^{\prime}, \quad h < 0, \end{equation} where \(\mathbf{Y}\) denotes the synchronized zero-return log-price.