Fitting IVX-AR Models — ivx

ivx_ar implements the Yang et al (2020) new instrumental variable based Wald statistic (IVX-AR) which accounts for serial correlation and heteroscedasticity in the error terms of the linear predictive regression model.

Usage

ivx_ar(
  formula,
  data,
  horizon,
  ar = "auto",
  ar_ic = c("bic", "aic", "aicc"),
  ar_max = 5,
  ar_grid = function(x) seq(x - 0.3, x + 0.3, by = 0.02),
  na.action,
  contrasts = NULL,
  offset,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  beta = 0.95,
  cz = 1,
  bandwidth = NULL,
  robust = FALSE,
  ...
)

# S3 method for class 'ivx_ar'
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.
horizon: is the horizon (default horizon = 1 corresponds to a short-horizon regression). For horizon > 1 the estimator and modified Wald statistic are those of Kostakis et al. (2023), eqs (15) and (23): K-period sums of the response and of the lagged predictors, a single-lag instrument in the signal matrix and the K-period sum of the instrument in the covariance.
ar: Method to include the autoregressive terms. "auto" find the optimal ar order by using the information criteria. ar = 0 reduces to simple ivx. ar > 1 uses a fixed order to estimate the model.
ar_ic: Information criterion to be used in model selection.
ar_max: Maximum ar order of model to fit.
ar_grid: The ar grid sequence of which to iterate.
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.
offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset
model: logical. If TRUE the model.frame of the fit is returned.
x: an object of class "ivx_ar", usually, a result of a call to ivx_ar.
y: logical. If TRUE the response of the fit is returned.
beta, cz: tuning parameters of the IVX instrument \(z_t = \sum_{j=0}^{t-1} (1 - c_z/n^\beta)^j \Delta x_{t-j}\). Defaults (beta = 0.95, cz = 1) follow Kostakis et al. (2015).
bandwidth: Newey-West bandwidth for the long-run covariance estimate. The default NULL uses \(n^{1/3}\) as in Kostakis et al. (2015).
robust: logical. If TRUE the Eicker-White (heteroskedasticity-robust) form of the IVX covariance matrix is used (Demetrescu et al., 2023). Only available for horizon = 1.
...: additional arguments to be passed to the low level regression fitting functions (see lm).
digits: the number of significant digits to use when printing.

References

Yang, B., Long, W., Peng, L., & Cai, Z. (2020). Testing the Predictability of US Housing Price Index Returns Based on an IVX-AR Model. Journal of the American Statistical Association, 1-22. DOI: 10.1080/01621459.2019.1686392

Examples


ivx_ar(hpi ~ log(res) + cpi, ylpc)
#> 
#> Call:
#> ivx_ar(formula = hpi ~ log(res) + cpi, data = ylpc, horizon = 1)
#> 
#> Lag Selection:
#> Auto (bic) with AR terms q = 4
#> 
#> Coefficients:
#>   log(res)         cpi  
#>  0.0018317  -0.0002078  
#> 

ivx_ar(hpi ~ log(res) + cpi, ylpc, ar_ic = "aic")
#> 
#> Call:
#> ivx_ar(formula = hpi ~ log(res) + cpi, data = ylpc, ar_ic = "aic", 
#>     horizon = 1)
#> 
#> Lag Selection:
#> Auto (aic) with AR terms q = 4
#> 
#> Coefficients:
#>   log(res)         cpi  
#>  0.0018317  -0.0002078  
#> 

ivx_ar(hpi ~ log(res) + cpi, ylpc, ar = 1)
#> 
#> Call:
#> ivx_ar(formula = hpi ~ log(res) + cpi, data = ylpc, ar = 1, horizon = 1)
#> 
#> Lag Selection:
#> Fixed with AR terms q = 1
#> 
#> Coefficients:
#>   log(res)         cpi  
#>  0.0010780  -0.0001155  
#>