nerive

hd.nerive(tick_series_list, stp=None, estimator=None, \*\*kwargs)

The nonparametric eigenvalue-regularized integrated covariance matrix estimator (NERIVE) of Lam and Feng (2018). This estimator is similar to the nercome() estimator extended into the hight frequency setting.

Parameters

tick_series_listlist of pd.Series

Each pd.Series contains ticks of one asset with datetime index.

Knumpy.ndarray, default= None

An array of sclales. If None all scales \(i = 1, ..., M\) are used, where M is chosen \(M = n^{1/2}\) acccording to Eqn (34) of Zhang (2006).

stparray-like of datetime.time() objects, default = [9:30, 12:45, 16:00]

The split time points.

estimatorfunction, default = None

An integrated covariance estimator taking tick_series_lists as the first argument. If None the msrc_pairwise() is used.

**kwargsmiscellaneous

Keyword arguments of the estimator.

Returns

outnumpy.ndarray, 2d

The NERIVE estimate of the integrated covariance matrix.

Notes

The nonparametric eigenvalue-regularized integrated covariance matrix estimator (NERIVE) proposed by Lam and Feng (2018) splits the sample into \(L\) partitions. The split points are denoted by $$ 0=\widetilde{\tau}_{0}<\widetilde{\tau}_{1}<\cdots<\widetilde{\tau}_{L}=T $$ and the \(l\)th partition is given by \(\left(\widetilde{\tau}_{l-1}, \widetilde{\tau}_{l}\right].\) The integrated covariance estimator for the \(l\)th partition is \begin{equation} \widehat{\mathbf{\Sigma}}_l=\mathbf{U}_{-l} \operatorname{diag}\left(\mathbf{U}_{-l}’ \widetilde{\mathbf{\Sigma}}_l \mathbf{U}_{-l}\right) \mathbf{U}_{-l}’ \end{equation} where \(\mathbf{U}_{-l}\) is an orthogonal matrix depending on all observations over the full interval \([0, T]\) except the \(l\)th partition. The NERIVE estimator over the full interval \([0, T]\) is given by \begin{equation} \widehat{\mathbf{\Sigma}}=\sum_{l=1}^{L} \widehat{\mathbf{\Sigma}}_l= \sum_{l=1}^{L} \mathbf{U}_{-l} \operatorname{diag}\left(\mathbf{U}_{-l}’ \widetilde{\mathbf{\Sigma}}_l \mathbf{U}_{-l}\right) \mathbf{U}_{-l}’. \end{equation} \(\widetilde{\mathbf{\Sigma}}\) is an integrated covariance estimator that corrects for asynchronicity and microstructure noise, e.g., one of hf. Lam and Feng (2018) choose the TSRC for the sake of tractablility in the proofs. Importantly, NERIVE does not assume i.i.d. observations but weak dependence between the log-price process and the microstructure noise process within partition \(l\), and weak serial dependence of microstructure noise vectors, given \(\mathcal{F}_{-l}\). Similar to NERCOME, NERIVE allows for the presence of pervasive factors as long as they persist between refresh times.

Warning

NERIVE splits the data into smaller subsamples. Estimator parameters that depend on the sample size must be adjusted. Further, the price process must be preprocessed to have zero mean return over the full sample.

References

Lam, C. and Feng, P. (2018). A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data, Journal of Econometrics 206(1): 226–257.