auto.exact.test {SIMle}

Automated exact form test

Description

This function utilizes L2 test for the automated execution of exact form tests with chosen bases.

Usage

auto.exact.test(
  ts,
  c,
  d,
  b_time,
  b_timese,
  mp_type,
  ops,
  exact_func,
  m = "MV",
  r = 1,
  s = 1,
  per = 0,
  k = 0,
  upper = 10
)

Arguments

ts

ts is the data set which is a time series data typically

c

the maximum value of number of basis for time input

d

the maximum value of number of basis for variate input

b_time

type of basis for time input

b_timese

type of basis for variate input

mp_type

select type of mapping function, "algeb" indicates algebraic mapping on the real line. "logari" represents logarithmic mapping on the real line

ops

Criteria for choosing the number of bases are provided by the package, offering four options: "AIC," "BIC," "CV," and "Kfold," each corresponding to a specific Criteria "AIC" stands for Akaike Information Criterion, "BIC" stands for Bayesian Information Criterion, "CV" represents cross-validation, and "Kfold" corresponds to k-fold cross-validation for time series data

exact_func

A list contains elements that are matrix contain exact functions, which are desired to be tested. The k-th element represents the k-th variable. The matrix contains values of the exact function within its domain

m

the window size for the simultaneous confidence region procedure, with the default being 'MV,' which stands for the Minimum Volatility method

r

indicates number of variate

s

s is a positive scaling factor, the default is 1

per

the percentage for test set used in cross validation option "CV"

k

the number of fold used in k-fold cross validation "Kfold"

upper

upper The upper bound for the variate basis domain. The default value is 10. When "algeb" or "logari" is chosen, the domain is automatically set from -upper to upper

Details

In the parameter type, this package provides 32 types of bases, including options such as 'Legen' for Legendre polynomials, 'Cheby' for the first kind of Chebyshev polynomials, 'tri' for trigonometric polynomials, 'cos' for cosine polynomials, 'sin' for sine polynomials, and 'Cspli' for the class of spline functions. In the 'Cspli' option, the first input 'c' represents knots plus 2, which correspond to 0 and 1. The term 'or' indicates the order of splines, so the number of basis elements is the number of knots + 2 - 2 plus the number of the order. When functions automatically choose the number of basis elements for splines, the number is not less than the order of the spline. The package provides 'db1' to 'db20' for Daubechies1 wavelet basis to Daubechies20 wavelet basis, and 'cf1' to 'cf5' for Coiflet1 wavelet basis to Coiflet5 wavelet basis. The wavelet tables provided by the Sie2nts package are generated by the Cascade algorithm using a low-pass filter. If exact values of wavelets are required, the Recursion algorithm should be used.

Value

A list whose elements are p value of exact form test. Each element in the list represents p-values in the order of variates.

References

[1] Ding, Xiucai, and Zhou, Zhou. “Estimation and inference for precision matrices of nonstationary time series.” The Annals of Statistics 48(4) (2020): 2455-2477.

[2] Ding, Xiucai, and Zhou, Zhou. “Auto-regressive approximations to non-stationary time series, with inference and applications.” Available online, 2021.

[3] Ding, Xiucai, and Zhou Zhou. "Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression." Available online, 2021.