debias_ivx: Debiased IVX for predictive regression
In zhan-gao/LasForecast: Time series linear predictive regression

debias_ivx

R Documentation

Debiased IVX for predictive regression

Description

y_t = w_{t-1} theta + u_t

where data is already aligned to incorporate the lagged regressor

Usage

debias_ivx(
  w,
  y,
  d_ind,
  intercept = FALSE,
  standardize = TRUE,
  c_z = 5,
  a = 0.9,
  standardize_iv = TRUE,
  iid = TRUE,
  post_inference = TRUE,
  lambda_choice = vector("list", length(d_ind) + 1),
  lambda_seq = vector("list", length(d_ind) + 1),
  train_method = "timeslice",
  nlambda = 100,
  lambda_min_ratio = 1e-04,
  k = 10,
  initial_window = ceiling(nrow(w) * 0.7),
  horizon = 1,
  fixed_window = TRUE,
  skip = 0,
  zhang_zhang = TRUE
)

Arguments

`w`	Matrix of all regressors
`y`	Vector of dependent variable
`d_ind`	Index for inference targets
`intercept`	Whether to include intercept in Lasso regression
`c_z`	Parameter in constructing IV (Phillips and Lee, 2016) `z = \sum_{j=0}^{n-1} (1 - c_z / n^a)^j \Delta d_{t-j}`
`a`	Parameter in constructing IV (Phillips and Lee, 2016)
`standardize_iv`	Whether to standardize the IV
`iid`	boolean indicating whether we want to adjust the long-run variance
`post_inference`	boolean indicating whether to conduct post-lasso inference
`lambda_choice`	Choice of lambda for Lasso regression; List of length length(d_ind) + 1: each element = NULL or = a number if user has a specific choice of tuning parameter
`lambda_seq`	pre-specified sequence of tuning parameter for parameter tuning; Useful in calibration of tuning parameter based on the rate conditions in the asymptotic theory; List of length length(d_ind) + 1: Each element = NULL or a vector of tuning parameters
`train_method`	The parameter tuning method "timeslice"https://topepo.github.io/caret/data-splitting.html#time: By combining initial window, horizon, fixed window and skip, we can control the sample splitting. Roll_block: Setting initial_window = horizon = floor(nrow(x) / k), fixed_window = False, and skip = floor(nrow(x) / k) - 1 Period-by-period rolling: skip = 0. "cv": Cross-validation based on block splits. "cv_random": Cross-validition based on random splits. "aic", "bic", "aicc", "hqc": based on information criterion.
`nlambda`	number of candidate lambdas
`lambda_min_ratio`	# lambda_min_ratio * lambda_max = lambda_min (default: 0.0001): Determines the search range of lambda
`k`	k-fold cv if "cv" is chosen (default: 10)
`initial_window`	length of initial window for "timeslice" method
`horizon`	length of horizon for "timeslice" method
`fixed_window`	whether to use fixed window for "timeslice" method
`skip`	length of skip for "timeslice" method
`zhangzhang`	boolean indicating whether to conduct Zhang and Zhang (2014) debiased IVX

Value

A list contains

`theta_hat_las`	Estimate of delta from Lasso regression
`theta_hat_ivx`	Estimate of delta from debiased IVX
`sigma_hat`	Estimate of standard error of theta_hat_ivx
`lambda_hat`	Chosen tuning parameter for Lasso regression
`phi_hat`	Estimate of the frequency of 0s and L1 norm of std/nonstd coefficients in the second stage