Class CointegrationTest

java.lang.Object

com.quantfinlib.hedging.CointegrationTest

public final class CointegrationTest
extends Object

Engle-Granger two-step cointegration test: regress one price series on the other, then run an augmented Dickey-Fuller test (no constant) on the residual spread. This is the statistical justification PairsHedger needs before a pairs trade — a high return correlation is not enough; the spread must be stationary.

Critical values: the constants are the Engle-Granger two-variable, no-trend asymptotics -3.90 (1%), -3.34 (5%), -3.04 (10%); criticalValue(double, int) gives MacKinnon's (2010, "Critical values for cointegration tests", Queen's Economics Department WP 1227, Table 2, N = 2, constant) finite-sample response surface τ(T) = τ∞ + τ₁/T + τ₂/T², which engleGranger(double[], double[], int) uses. More negative ADF t-statistics mean stronger evidence of cointegration. The hedge ratio is the OLS slope of A on B, which is not symmetric in the two series (regressing B on A gives a different ratio); total least squares or Johansen would be.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	CointegrationTest.EngleGrangerResult

Field Summary

Fields

Modifier and Type	Field	Description
static final double	CRITICAL_10PCT
static final double	CRITICAL_1PCT
static final double	CRITICAL_5PCT

Method Summary

Modifier and Type	Method	Description
static double	adfTStatistic(double[] series)	Dickey-Fuller t-statistic (no constant, no lags — appropriate for mean-zero regression residuals): regress Δe_t = γ e_{t-1} + u_t and return t = γ̂ / se(γ̂).
static double	adfTStatistic(double[] series, int lags)	Augmented Dickey-Fuller t-statistic without constant (the residuals of a regression with intercept have mean zero): Δe_t = γ·e_{t−1} + Σ_{j=1..p} φ_j·Δe_{t−j} + u_t, OLS over t = p+1 .. n−1; returns γ̂ / se(γ̂).
static double	criticalValue(double level, int observations)	MacKinnon (2010) finite-sample critical value for the two-variable Engle-Granger test with a constant.
static CointegrationTest.EngleGrangerResult	engleGranger(double[] pricesA, double[] pricesB)	Engle-Granger test with no augmentation lags and the asymptotic critical values (the original behaviour); see engleGranger(double[], double[], int).
static CointegrationTest.EngleGrangerResult	engleGranger(double[] pricesA, double[] pricesB, int lags)	Engle-Granger test with lags augmentation lags in the ADF regression and MacKinnon finite-sample critical values.

Methods inherited from class Object

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

Field Details

CRITICAL_1PCT

public static final double CRITICAL_1PCT

See Also:

• Constant Field Values

CRITICAL_5PCT

public static final double CRITICAL_5PCT

See Also:

• Constant Field Values

CRITICAL_10PCT

public static final double CRITICAL_10PCT

See Also:

• Constant Field Values

Method Details

criticalValue

public static double criticalValue(double level,
 int observations)

MacKinnon (2010) finite-sample critical value for the two-variable Engle-Granger test with a constant.

Parameters:

level - 0.01, 0.05 or 0.10

observations - T, the number of residuals used in the ADF regression

engleGranger

public static CointegrationTest.EngleGrangerResult engleGranger(double[] pricesA,
 double[] pricesB)

Engle-Granger test with no augmentation lags and the asymptotic critical values (the original behaviour); see engleGranger(double[], double[], int).

engleGranger

public static CointegrationTest.EngleGrangerResult engleGranger(double[] pricesA,
 double[] pricesB,
 int lags)

Engle-Granger test with lags augmentation lags in the ADF regression and MacKinnon finite-sample critical values.

adfTStatistic

public static double adfTStatistic(double[] series)

Dickey-Fuller t-statistic (no constant, no lags — appropriate for mean-zero regression residuals): regress Δe_t = γ e_{t-1} + u_t and return t = γ̂ / se(γ̂).

adfTStatistic

public static double adfTStatistic(double[] series,
 int lags)

Augmented Dickey-Fuller t-statistic without constant (the residuals of a regression with intercept have mean zero): Δe_t = γ·e_{t−1} + Σ_{j=1..p} φ_j·Δe_{t−j} + u_t, OLS over t = p+1 .. n−1; returns γ̂ / se(γ̂). lags = 0 is adfTStatistic(double[]).