heter_covariate: Long memory tests for non-stationary time series regression

In mlrv: Long-Run Variance Estimation in Time Series Regression

Long memory tests for non-stationary time series regression

Description

\loadmathjax

Test for long memory of \mjseqne_i in the time series regression

y_i = x_i \beta_i + e_i, 1\le i \le n

where \mjseqnx_i is the multivariate covariate process with first component 1, \mjseqn\beta_i is the functional coefficient, \mjseqne_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 \mjseqnm. 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,\mjseqnm and \mjseqn\tau_n, default FALSE.

Details

param

• B, the number of bootstrap simulation, say 2000 *lrvmethod, the method of long-run variance estimation, lrvmethod = 0 uses the plug-in estimator in Zhou (2010), lrvmethod = 1 offers the debias difference-based estimator in Bai and Wu (2024b), lrvmethod = 2 provides the plug-in estimator using the \mjseqn\breve\beta, the pilot estimator proposed in Bai and Wu (2024b)

• gcv, 1 or 0, whether to use Generalized Cross Validation for the selection of \mjseqnb, the bandwidth parameter in the local linear regression

• neighbour, the number of neighbours in the extended minimum volatility, for example 1,2 or 3

• lb, the lower bound of the range of \mjseqnm in the extended minimum volatility Selection

• ub, the upper bound of the range of \mjseqnm in the extended minimum volatility Selection

• bw_set, the proposed grid of the range of bandwidth selection. if not presented, a rule of thumb method will be used for the data-driven range

• tau_n, the value of \mjseqn\tau when no data-driven selection is used. if \mjseqn\tau is set to \mjseqn0, the rule of thumb \mjseqnn^-2/15 will be used

• type, c( "KPSS","RS","VS","KS") type of tests, see Bai and Wu (2024a).

• ind, types of kernels

• 1 Triangular \mjseqn1-|u|, \mjseqnu \le 1

• 2 Epanechnikov kernel \mjseqn3/4(1 - u^2), \mjseqnu \le 1

• 3 Quartic \mjseqn15/16(1 - u^2)^2, \mjseqnu \le 1

• 4 Triweight \mjseqn35/32(1 - u^2)^3, \mjseqnu \le 1

• 5 Tricube \mjseqn70/81(1 - |u|^3)^3, \mjseqnu \le 1

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)

mlrv documentation built on Sept. 11, 2024, 6:57 p.m.