heter_covariate {mlrv}R Documentation

Long memory tests for non-stationary time series regression

Description

Test for long memory of \(e_i\) in the time series regression

y_i = x_i β_i + e_i, 1≤ i ≤ n

where \(x_i\) is the multivariate covariate process with first component 1, \(\beta_i\) is the functional coefficient, \(e_i\) is the error term which can be long memory. In particular,covariates and the error term are allowed to be dependent.

Usage

heter_covariate(
  data,
  param = list(B = 2000, lrvmethod = 1, gcv = 1, neighbour = 1, lb = 3, ub = 11, tau_n =
    0.3, type = "KPSS"),
  mvselect = -1,
  bw = 0.2,
  shift = 1,
  verbose_dist = FALSE,
  hyper = FALSE
)

Arguments

data

a list with the vector y and the matrix x, for example, list(x=...,y=...).

param

a list of parameters, list(B =..., lrvmethod =...,gcv = ..., neighbour =..., lb = ..., ub = ..., tau_n = ..., type = ..., ind = ...)

mvselect

the value of moving window parameter \(m\). In addition, mvselect=-1 provides data-driven smoothing parameters via Minimum Volatility of the long-run covariance estimator as proposed in Chapter 9 of Politis et al.(1999), while mvselect = -2 provides data-driven smoothing parameters via Minimum Volatility of the bootstrap statistics, see Bai and Wu (2024a).

bw

the bandwidth parameter in the local linear regression, default 0.2.

shift

modify bw by a factor, default 1.

verbose_dist

whether to print intermediate results, i.e., the bootstrap distribution and statistics, default FALSE.

hyper

whether to only print the selected values of the smoothing parameters,\(m\) and \(\tau_n\), default FALSE.

Details

param

Value

p-value of the long memory test

mlrv functions

Heter_LRV, heter_covariate, heter_gradient, gcv_cov, MV_critical

References

Bai, L., & Wu, W. (2024a). Detecting long-range dependence for time-varying linear models. Bernoulli, 30(3), 2450-2474.

Bai, L., & Wu, W. (2024b). Difference-based covariance matrix estimation in time series nonparametric regression with application to specification tests. Biometrika, asae013.

Zhou, Z. and Wu, W. B. (2010). Simultaneous inference of linear models with time varying coefficients.J. R. Stat. Soc. Ser. B. Stat. Methodol., 72(4):513–531.

Politis, D. N., Romano, J. P., and Wolf, M. (1999). Subsampling. Springer Science & Business Media.

Examples

param = list(d = -0.2, heter = 2, tvd = 0,
 tw = 0.8, rate = 0.1, cur = 1,
 center = 0.3, ma_rate =  0, cov_tw =  0.2,
 cov_rate = 0.1, cov_center = 0.1, all_tw  = 1, cov_trend = 0.7)
data = Qct_reg(1000, param)
### KPSS test B
heter_covariate(data, list(B=20, lrvmethod = 1,
gcv = 1, neighbour = 1, lb = 3, ub = 11, type = "KPSS"), mvselect = -2, verbose_dist = TRUE)

[Package mlrv version 0.1.2 Index]