public static double[,] DiscretePartialAutocorrelation(double[,] x)
{
int length = x.Length;
double[,] r = new double[1, length];
r[0, 0] = 1; r[0, 1] = DiscreteAutocorrelation(x)[0, 1];
for (int k = 2; k < length; k++)
{
double[,] Px = new double[length - k, k - 1];
double[,] PyL = new double[length - k, 1];
double[,] PyR = new double[length - k, 1];
for (int i = 0; i < length - k; i++)
{
for (int j = 0; j < k - 1; j++)
{
Px[i, j] = x[0, j + 1 + i];
}
PyL[i, 0] = x[0, i];
PyR[i, 0] = x[0, i + k];
}
r[0, k] =
Matrix.Product(
Matrix.Trans(Matrix.Subtract(PyL, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyL)))),
Matrix.Subtract(PyR, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyR)))
)[0, 0] / Math.Sqrt(
Matrix.Product(
Matrix.Product(
Matrix.Trans(Matrix.Subtract(PyL, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyL)))),
Matrix.Subtract(PyL, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyL)))
),
Matrix.Product(
Matrix.Trans(Matrix.Subtract(PyR, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyR)))),
Matrix.Subtract(PyR, Matrix.Product(Px, OrdinaryLeastSquares.Beta(Px, PyR)))
)
)[0, 0]);
}
return(r);
}