IVX-Wald Test for Predictive Regressions — ivx

Computes the IVX-Wald statistic of Kostakis, Magdalinos, and Stamatogiannis (2015) for testing predictability in a regression of returns on persistent predictors. The IVX approach is robust to the degree of persistence of the regressors (stationary, local-to-unity, or unit root).

Usage

ivx_wald(y, X, K = 1L, M_n = 0L, beta = 0.95)

Arguments

y: Numeric vector of length T; the dependent variable (e.g., returns).
X: A T x r matrix of predictor observations.
K: Integer; forecast horizon. Default 1.
M_n: Integer; bandwidth parameter for the long-run covariance estimator. Default 0 (no correction). Use floor(T^(1/3)) as a rule of thumb.
beta: Numeric in \((0, 1)\); controls the rate of the IVX instrument. Values close to 1 yield best performance. Default 0.95.

Value

A list with class "ivx_wald" containing:

statistic: The IVX-Wald test statistic.
pvalue: P-value from the chi-squared distribution.
coefficients: IVX coefficient estimates.
K: Forecast horizon.
n: Number of observations.
r: Number of predictors.

Details

The IVX-Wald test constructs an endogenous instrument \(\tilde{Z}_t\) by filtering the predictor increments through a mildly integrated process with autoregressive root \(R_{nz} = 1 - 1/n^\beta\). The resulting Wald statistic is asymptotically chi-squared with r degrees of freedom, regardless of the persistence of the predictors.

References

Kostakis, A., Magdalinos, T., and Stamatogiannis, M.P. (2015). Robust Econometric Inference for Stock Return Predictability. Review of Financial Studies, 28(5), 1506-1553.

Examples

set.seed(42)
n <- 200
x <- cumsum(rnorm(n))
y <- 0.02 * x + rnorm(n)
ivx_wald(y, as.matrix(x))
#> 
#> ╭────────────────────────────────────────────────────╮
#> │      IVX-Wald Test for Predictive Regressions      │
#> │  (Kostakis, Magdalinos, and Stamatogiannis, 2015)  │
#> ├────────────────────────────────────────────────────┤
#> │ H0: No predictability (all coefficients = 0)       │
#> │ H1: At least one predictor is significant          │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results:                                      │
#> │  IVX-Wald statistic: 1.4730                        │
#> │  P-value: 0.2249                                   │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Details:                                           │
#> │  Observations (T): 200                             │
#> │  Predictors (r): 1                                 │
#> │  Forecast horizon (K): 1                           │
#> │  Reference distribution: Chi-sq(1)                 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ IVX Coefficients:                                  │
#> │    beta_1: 0.0181                                  │
#> ╰────────────────────────────────────────────────────╯
#>