arma.py 文件源码

def arma_predictor_model(x, y, m, n):
    """
    Return matrix and vector relating (*m*, *n*) ARMA model to the
    input *x* and output *y*. In other words, construct the max(*m*,
    *n*) - 1 by (*m* - 1 + *n* - 1) matrix A such that

    y[k] + a_1 y[k - 1] + ... + a_m y[k - m] = b_1 x[k - 1] + ... + b_n x[k - n]

    and the vector b corresponds to y[k] for k >= max(*m*, *n*).
    """
    assert len(x) == len(y)
    k = max(m, n)
    A1 = SP.linalg.toeplitz(-y[k:-1], r=-y[(k - m):k][::-1])
    A2 = SP.linalg.toeplitz(x[k:-1], r=x[(k - n):k][::-1])
    A = NP.hstack((A1, A2))
    b = y[k+1:]
    return A, b