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Augmented Regression Method (Amihud, Hurvich & Wang)

Source: R/arm.R
arm.Rd

arm implements the multipredictor augmented regression method (mARM) of Amihud, Hurvich and Wang (2009), a reduced-bias OLS alternative to IVX for stationary but persistent predictors. A VAR(1) is fitted to the predictors, its coefficient matrix is bias-corrected with the Nicholls and Pope (1988) expansion (iterated), and the predictive regression is augmented with the corrected VAR residuals, which removes the Stambaugh (1999) bias from the slopes. Standard errors and the joint Wald statistic use the covariance estimator of the paper (eqs 7-8), which adds the estimation uncertainty of the VAR coefficients to the augmented-regression OLS variance.

Usage

arm(
  formula,
  data,
  iter = 10,
  na.action,
  contrasts = NULL,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  ...
)

# S3 method for class 'arm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

n optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

iter

maximum number of bias-correction iterations (K = 10 in the paper); iteration stops earlier if the corrected VAR becomes non-stationary.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

model

logical. If TRUE the model.frame of the fit is returned.

x

an object of class "arm".

y

logical. If TRUE the response of the fit is returned.

...

additional arguments to be passed to the low level regression fitting functions (see lm).

digits

the number of significant digits to use when printing.

Value

an object of class c("arm", "ivx"), so the ivx methods apply. Additional components: phi (coefficients on the augmentation residuals), Phi (bias-corrected VAR(1) coefficient matrix, equations by row) and Phi_ols.

Details

Unlike IVX the method assumes stationary predictors (all eigenvalues of the VAR coefficient matrix inside the unit circle) and Gaussian innovations; it is the natural benchmark for the "control function" approach of Elliott (2011). Short horizon only.

References

Amihud, Y., Hurvich, C. M., & Wang, Y. (2009). Multiple-predictor regressions: Hypothesis testing. The Review of Financial Studies, 22(1), 413-434.

Amihud, Y., & Hurvich, C. M. (2004). Predictive regressions: A reduced-bias estimation method. Journal of Financial and Quantitative Analysis, 39(4), 813-841.

Nicholls, D. F., & Pope, A. L. (1988). Bias in the estimation of multivariate autoregressions. Australian Journal of Statistics, 30A, 296-309.

Examples

arm(Ret ~ DP, data = kms)
#> 
#> Call:
#> arm(formula = Ret ~ DP, data = kms)
#> 
#> Augmented regression method (reduced-bias OLS)
#> 
#> Coefficients:
#>       DP  
#> 0.002463  
#> 

summary(arm(Ret ~ DP + TBL, data = kms))
#> 
#> Call:
#> arm(formula = Ret ~ DP + TBL, data = kms)
#> 
#> Coefficients:
#>      Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP   0.002050   0.003797   0.540    0.292     0.589
#> TBL -0.046509   0.055999  -0.831    0.690     0.406
#> 
#> Joint Wald statistic:  1.068 on 2 DF, p-value 0.5862
#> Multiple R-squared:  0.02415,	Adjusted R-squared:  0.0194
#>