49 lines
1.3 KiB
ReStructuredText
49 lines
1.3 KiB
ReStructuredText
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Asynchronous Covariance (Hayashi--Yoshida)
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==========================================
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The module :code:`timeseries_utils::nonsync_covariance` implements the
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Hayashi--Yoshida estimator of the integrated covariance between two
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asynchronously sampled processes :math:`X` and :math:`Y` observed at
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distinct, non-overlapping observation grids
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:math:`\{t^X_i\}` and :math:`\{t^Y_j\}`.
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Estimator
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---------
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Let :math:`I_i = (t^X_{i-1}, t^X_i]` and :math:`J_j = (t^Y_{j-1}, t^Y_j]`.
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The Hayashi--Yoshida estimator is
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.. math::
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\widehat{\langle X, Y\rangle}_{[0,T]}
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\;=\;
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\sum_{i, j}\,
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\big(X_{t^X_i} - X_{t^X_{i-1}}\big)\,
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\big(Y_{t^Y_j} - Y_{t^Y_{j-1}}\big)\,
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\mathbf{1}\!\big[I_i \cap J_j \neq \emptyset\big].
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It is consistent under non-synchronicity and avoids the *Epps effect*
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that plagues naive grid interpolation.
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Implementation
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--------------
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* A two-pointer scan in :math:`O(n_X + n_Y)` collects all overlapping
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pairs.
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* For matrices of size :math:`d \times d` with large per-asset sample
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counts, off-diagonal entries are computed in parallel with Rayon.
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API
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---
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.. code-block:: rust
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pub fn hayashi_yoshida_covariance(
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t1: &[f64], v1: &[f64],
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t2: &[f64], v2: &[f64],
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) -> Result<f64>;
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pub fn hayashi_yoshida_matrix(
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series: &[(Vec<f64>, Vec<f64>)],
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) -> Result<Vec<Vec<f64>>>;
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