Class Ols

java.lang.Object

com.quantfinlib.alpha.Ols

public final class Ols
extends Object

Ordinary least squares by Householder QR, with classical and Newey-West HAC standard errors.

QR rather than the normal equations: solving XᵀX b = Xᵀy squares the condition number of X, which matters for factor return streams that are 0.6 to 0.9 correlated. The coefficient covariance uses (XᵀX)⁻¹ = R⁻¹R⁻ᵀ from the same factorisation.

• Classical: V = σ̂² (XᵀX)⁻¹, σ̂² = e'e/(n − p).
• HAC (Newey and West 1987): V = (XᵀX)⁻¹ S (XᵀX)⁻¹ with S = Σ_t e_t² x_t x_tᵀ + Σ_{l=1..L} w_l Σ_t e_t e_{t−l} (x_t x_{t−l}ᵀ + x_{t−l} x_tᵀ), w_l = 1 − l/(L+1). No small-sample degrees-of-freedom correction is applied.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Ols.Fit

Method Summary

Modifier and Type	Method	Description
static Ols.Fit	fit(double[][] x, double[] y, int hacLag)	Fits y = X b + e.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

fit

public static Ols.Fit fit(double[][] x,
 double[] y,
 int hacLag)

Fits y = X b + e. The caller includes an intercept column if one is wanted.

Parameters:

x - design matrix, x[t][j], n rows by p columns, n > p

y - response, length n

hacLag - Bartlett lag for the HAC errors (0 = White heteroskedasticity-robust errors)

Throws:

IllegalArgumentException - on misaligned input, non-finite values or a rank-deficient design