tslarsP: (Robust) least angle regression for time series data with fixed lag length

Description

(Robustly) sequence groups of candidate predictors and their respective lagged values according to their predictive content and find the optimal model along the sequence. Note that lagged values of the response are included as a predictor group as well.

Usage

tslarsP(x, ...)
# S3 method for formula
tslarsP(formula, data, ...)
# S3 method for default
tslarsP(
  x,
  y,
  h = 1,
  p = 2,
  sMax = NA,
  fit = TRUE,
  s = c(0, sMax),
  crit = "BIC",
  ncores = 1,
  cl = NULL,
  model = TRUE,
  ...
)
rtslarsP(x, ...)
# S3 method for formula
rtslarsP(formula, data, ...)
# S3 method for default
rtslarsP(
  x,
  y,
  h = 1,
  p = 2,
  sMax = NA,
  centerFun = median,
  scaleFun = mad,
  regFun = lmrob,
  regArgs = list(),
  combine = c("min", "euclidean", "mahalanobis"),
  winsorize = FALSE,
  const = 2,
  prob = 0.95,
  fit = TRUE,
  s = c(0, sMax),
  crit = "BIC",
  ncores = 1,
  cl = NULL,
  seed = NULL,
  model = TRUE,
  ...
)

Value

If fit is FALSE, an integer vector containing the indices of the sequenced predictor series.

Otherwise an object of class "tslarsP" (inheriting from classes "grplars" and "seqModel") with the following components:

active: an integer vector containing the sequence of predictor series.
s: an integer vector containing the steps for which submodels along the sequence have been computed.
coefficients: a numeric matrix in which each column contains the regression coefficients of the corresponding submodel along the sequence.
fitted.values: a numeric matrix in which each column contains the fitted values of the corresponding submodel along the sequence.
residuals: a numeric matrix in which each column contains the residuals of the corresponding submodel along the sequence.
df: an integer vector containing the degrees of freedom of the submodels along the sequence (i.e., the number of estimated coefficients).
robust: a logical indicating whether a robust fit was computed.
scale: a numeric vector giving the robust residual scale estimates for the submodels along the sequence (only returned for a robust fit).
crit: an object of class "bicSelect" containing the BIC values and indicating the final model (only returned if argument crit is "BIC" and argument s indicates more than one step along the sequence).
muX: a numeric vector containing the center estimates of the predictor variables.
sigmaX: a numeric vector containing the scale estimates of the predictor variables.
muY: numeric; the center estimate of the response.
sigmaY: numeric; the scale estimate of the response.
x: the matrix of candidate predictor series (if model is TRUE).
y: the response series (if model is TRUE).
assign: an integer vector giving the predictor group to which each predictor variable belongs.
w: a numeric vector giving the data cleaning weights (only returned for a robust fit).
h: the forecast horizon.
p: the number of lags in the model.
call: the matched function call.

Arguments

x: a numeric matrix or data frame containing the candidate predictor series.
...: additional arguments to be passed down.
formula: a formula describing the full model.
data: an optional data frame, list or environment (or object coercible to a data frame by as.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 tslarsP or rtslarsP is called.
y: a numeric vector containing the response series.
h: an integer giving the forecast horizon (defaults to 1).
p: an integer giving the number of lags in the model (defaults to 2).
sMax: an integer giving the number of predictor series to be sequenced. If it is NA (the default), predictor groups are sequenced as long as there are twice as many observations as predictor variables.
fit: a logical indicating whether to fit submodels along the sequence (TRUE, the default) or to simply return the sequence (FALSE).
s: an integer vector of length two giving the first and last step along the sequence for which to compute submodels. The default is to start with a model containing only an intercept (step 0) and iteratively add all series along the sequence (step sMax). If the second element is NA, predictor groups are added to the model as long as there are twice as many observations as predictor variables. If only one value is supplied, it is recycled.
crit: a character string specifying the optimality criterion to be used for selecting the final model. Currently, only "BIC" for the Bayes information criterion is implemented.
ncores: a positive integer giving the number of processor cores to be used for parallel computing (the default is 1 for no parallelization). If this is set to NA, all available processor cores are used. For obtaining the data cleaning weights and for fitting models along the sequence, parallel computing is implemented on the R level using package parallel. Otherwise parallel computing for some of of the more computer-intensive computations in the sequencing step is implemented on the C++ level via OpenMP (https://www.openmp.org/).
cl: a parallel cluster for parallel computing as generated by makeCluster. This is preferred over ncores for tasks that are parallelized on the R level, in which case ncores is only used for tasks that are parallelized on the C++ level.
model: a logical indicating whether the model data should be included in the returned object.
centerFun: a function to compute a robust estimate for the center (defaults to median).
scaleFun: a function to compute a robust estimate for the scale (defaults to mad).
regFun: a function to compute robust linear regressions that can be interpreted as weighted least squares (defaults to lmrob).
regArgs: a list of arguments to be passed to regFun.
combine: a character string specifying how to combine the data cleaning weights from the robust regressions with each predictor group. Possible values are "min" for taking the minimum weight for each observation, "euclidean" for weights based on Euclidean distances of the multivariate set of standardized residuals (i.e., multivariate winsorization of the standardized residuals assuming independence), or "mahalanobis" for weights based on Mahalanobis distances of the multivariate set of standardized residuals (i.e., multivariate winsorization of the standardized residuals).
winsorize: a logical indicating whether to clean the data by multivariate winsorization.
const: numeric; tuning constant for multivariate winsorization to be used in the initial corralation estimates based on adjusted univariate winsorization (defaults to 2).
prob: numeric; probability for the quantile of the \(\chi^{2}\) distribution to be used in multivariate winsorization (defaults to 0.95).
seed: optional initial seed for the random number generator (see .Random.seed), which is useful because many robust regression functions (including lmrob) involve randomness. On parallel R worker processes, random number streams are used and the seed is set via clusterSetRNGStream.

Author

Andreas Alfons, based on code by Sarah Gelper

References