pca_high_freq()

Run high-frequency PCA on a data matrix.

Usage

pca_high_freq(
    X,
    k=None,
    u=None,
    evectors_start=None,
    quiet=False,
)

This function implements the algorithm proposed by Aït-Sahalia and Xiu (2019), returning the time series of principal components, eigenvalues, and eigenvectors.

A summary of the algorithm’s hypothesis and parametrization can be found in this package’s documentation.

Parameters

X: NDArray[np.number]: Input data array with shape (T, d), where T is the number of observations and d is the number of variables. Must not contain npnan or np.inf values.
k: int | None = None: Block size used for the high-frequency PCA routine. If None, it is chosen by a rule-of-thumb. Must be smaller than d
u: NDArray[np.number] | None = None: Jump truncation cutoffs for each variable, with shape (d,). If None, it is chosen by a rule-of-thumb. Must not contain npnan, np.inf, or nonpositive values.
evectors_start: NDArray[np.number] | None = None: Optional initial eigenvector matrix with shape (d, d) used to warm-start the iteration. If not supplied, the first block of the results will be np.nan.
quiet: bool = False: If True, suppress progress prints during computation.

Returns

PCAHighFreqResult

A [PCAHighFreqResult][hfpca.types.PCAHighFreqResult] object containing

the the PCs (.pcs), eigenvalue estimates (.evalues), eigenvector

estimates (.evectors), which can be unpacked into variables. Also

contains: PCAHighFreqResult

the values of k (.k), u (.u), and d (.d); and

PCAHighFreqResult

methods for extracting PCs, eigenvalues, and eigenvectors as polars

dataframes (.pcs_as_polars()). See the class documentation for more

details.

Raises

TypeError: If X, u, or evectors_start are not numpy arrays; if they do not have a numeric dtype; or if k is not an integer.
ValueError: If X is not 2D, or if u or evectors_start do not have the correct dimensions; if any of the inputs contain NaN or Inf values; if u contains nonpositive values; or if k is smaller than d or larger than T.