qll_hat: Elliott-Muller Test for Time-Varying Coefficients

In forecastdom: (Un)Conditional Forecast Dominance

Elliott-Muller Test for Time-Varying Coefficients

Description

Computes the \hat{qLL} statistic of Elliott and Muller (2006) for testing the null hypothesis that regression coefficients are constant over time against the alternative of general time variation.

Usage

qll_hat(y, X, Z = NULL, L = 0L)

Arguments

y	Numeric vector of length T; the dependent variable.
X	A T x k matrix of regressors linked to potentially time-varying coefficients.
Z	A T x d matrix of regressors with constant coefficients. Use NULL (default) if all coefficients may vary.
L	Integer; lag truncation for the Newey-West estimator of the variance. Default 0 (no correction).

Details

The test is based on optimal invariant statistics for the null of constant coefficients against local alternatives. The \hat{qLL} statistic has non-standard critical values that depend on k; see Table 1 in Elliott and Muller (2006).

Selected critical values (5\

• k = 1: -5.91

• k = 2: -10.64

• k = 3: -15.78

• k = 4: -20.62

• k = 5: -25.87

Reject the null when \hat{qLL} is below the critical value.

Value

A list with class "qll_hat" containing:

statistic	The \hat{qLL} test statistic.
k	Number of potentially time-varying coefficients.
n	Number of observations.

References

Elliott, G. and Muller, U.K. (2006). Efficient Tests for General Persistent Time Variation in Regression Coefficients. Review of Economic Studies, 73(4), 907-940.

Examples

set.seed(42)
n <- 200
x <- matrix(rnorm(n * 2), n, 2)
y <- x %*% c(0.5, -0.3) + rnorm(n)
qll_hat(y, x)

forecastdom documentation built on Nov. 2, 2026, 1:10 a.m.