ThotDjehuty
d780ed81d7
Adds 9 new top-level / sub-modules to the Rust API only (no Python
bindings yet), with at least one analytic unit test per module.
New Rust modules:
- optimal_control::matrix_riccati (RK4 backward solver)
- timeseries_utils::nonsync_covariance (Hayashi-Yoshida)
- timeseries_utils::wavelet (Haar / Daubechies DWT and MODWT)
- risk_measures (VaR, CVaR, projected sub-gradient CVaR minimisation)
- graph::laplacian + graph::spectral_clustering (Jacobi + k-means++)
- topology (Vietoris-Rips persistent homology, bottleneck distance)
- volterra (Caputo Adams, Markovian lift, second-kind Volterra,
Fourier inversion of characteristic functions)
- signatures (truncated tensor signature, log-sig, random reservoir,
Salvi-Cass-Lyons signature kernel, shuffle product)
All previously stable APIs untouched; abi3-py38 ABI preserved.
New module tests: 29/29 passing. Pre-existing 5 unrelated failures
unchanged.
49 lines
1.3 KiB
ReStructuredText
49 lines
1.3 KiB
ReStructuredText
Asynchronous Covariance (Hayashi--Yoshida)
|
|
==========================================
|
|
|
|
The module :code:`timeseries_utils::nonsync_covariance` implements the
|
|
Hayashi--Yoshida estimator of the integrated covariance between two
|
|
asynchronously sampled processes :math:`X` and :math:`Y` observed at
|
|
distinct, non-overlapping observation grids
|
|
:math:`\{t^X_i\}` and :math:`\{t^Y_j\}`.
|
|
|
|
Estimator
|
|
---------
|
|
|
|
Let :math:`I_i = (t^X_{i-1}, t^X_i]` and :math:`J_j = (t^Y_{j-1}, t^Y_j]`.
|
|
The Hayashi--Yoshida estimator is
|
|
|
|
.. math::
|
|
|
|
\widehat{\langle X, Y\rangle}_{[0,T]}
|
|
\;=\;
|
|
\sum_{i, j}\,
|
|
\big(X_{t^X_i} - X_{t^X_{i-1}}\big)\,
|
|
\big(Y_{t^Y_j} - Y_{t^Y_{j-1}}\big)\,
|
|
\mathbf{1}\!\big[I_i \cap J_j \neq \emptyset\big].
|
|
|
|
It is consistent under non-synchronicity and avoids the *Epps effect*
|
|
that plagues naive grid interpolation.
|
|
|
|
Implementation
|
|
--------------
|
|
|
|
* A two-pointer scan in :math:`O(n_X + n_Y)` collects all overlapping
|
|
pairs.
|
|
* For matrices of size :math:`d \times d` with large per-asset sample
|
|
counts, off-diagonal entries are computed in parallel with Rayon.
|
|
|
|
API
|
|
---
|
|
|
|
.. code-block:: rust
|
|
|
|
pub fn hayashi_yoshida_covariance(
|
|
t1: &[f64], v1: &[f64],
|
|
t2: &[f64], v2: &[f64],
|
|
) -> Result<f64>;
|
|
|
|
pub fn hayashi_yoshida_matrix(
|
|
series: &[(Vec<f64>, Vec<f64>)],
|
|
) -> Result<Vec<Vec<f64>>>;
|