Documentation for Residual Analysis¶

def calculate_residues(y, yhat):
    """Calculate the residues (errors) between true and predicted values.

    Parameters
    ----------
    y : array-like of shape (n_samples,)
        True values.
    yhat : array-like of shape (n_samples,)
        Predicted values.

    Returns
    -------
    residues : ndarray of shape (n_samples,)
        Residues (errors) between true and predicted values.
    """
    return (y - yhat).flatten()

def compute_cross_correlation(y, yhat, arr):
    """Compute the cross-correlation between the residues and another array.

    Parameters
    ----------
    y : array-like of shape (n_samples,)
        True values.
    yhat : array-like of shape (n_samples,)
        Predicted values.
    arr : array-like of shape (n_samples,)
        Another array to compute the cross-correlation with.

    Returns
    -------
    ccf : ndarray of shape (n_samples,)
        Cross-correlation function.
    upper_bound : float
        Upper bound for the confidence interval.
    lower_bound : float
        Lower bound for the confidence interval.
    """
    e = calculate_residues(y, yhat)
    n = len(e) * 2 - 1
    ccf, upper_bound, lower_bound = _input_ccf(e, arr, n)
    return ccf, upper_bound, lower_bound

def compute_residues_autocorrelation(y, yhat):
    """Compute the autocorrelation of the residues.

    Parameters
    ----------
    y : array-like of shape (n_samples,)
        True values.
    yhat : array-like of shape (n_samples,)
        Predicted values.

    Returns
    -------
    e_acf : ndarray of shape (n_samples,)
        Autocorrelation of the residues.
    upper_bound : float
        Upper bound for the confidence interval.
    lower_bound : float
        Lower bound for the confidence interval.
    """
    e = calculate_residues(y, yhat)
    unnormalized_e_acf = get_unnormalized_e_acf(e)
    half_of_symmetry_autocorr = int(np.floor(unnormalized_e_acf.size / 2))

    e_acf = (
        unnormalized_e_acf[half_of_symmetry_autocorr:]
        / unnormalized_e_acf[half_of_symmetry_autocorr]
    )

    upper_bound = 1.96 / np.sqrt(len(unnormalized_e_acf))
    lower_bound = upper_bound * (-1)
    return e_acf, upper_bound, lower_bound

def get_unnormalized_e_acf(e):
    """Compute the unnormalized autocorrelation function of the residues.

    Parameters
    ----------
    e : array-like of shape (n_samples,)
        Residues (errors).

    Returns
    -------
    unnormalized_e_acf : ndarray of shape (2*n_samples-1,)
        Unnormalized autocorrelation function of the residues.
    """
    return np.correlate(e, e, mode="full")