test.model.MSAR: Performs bootstrap statistical tests to validate MSAR models.

In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

Description

Performs bootstrap statistical tests to validate MSAR models. Marginal distribution, auto correlation function and up-crossings are considered. For each of them the tests statistic computed from observations is compared to the distribution of the satistics corresponding to the MSAR model.

Usage

test.model.MSAR(data,simu,lag=NULL,id=1,u=NULL)

Arguments

data	observed (or reference) time series, array of dimension T*N.samples*d
simu	simulated time series, array of dimension T*N.sim*d. N.sim have to be K*N.samples with K large enough (for instance, K=100)
lag	maximum lag for auto-correlation functions.
id	considered component. It is usefull when data is multivariate.
u	considered levels for up crossings

Details

Test statistics Marginal distribution:

S = \int_{-∞}^{∞} ≤ft| F_n(x)-F(x) \right| dx

Marginal distribution, based on Anderson Darling statistic:

S = \int_{-∞}^{∞} ≤ft| \frac{F_n(x)-F(x)}{F(x)(1-F(x))} \right| dx

Correlation function:

S = \int_0^L≤ft|C_n(l)-C(l)\right|dl

Number of up crossings:

S = \int_{-∞}^{∞}≤ft|E_n(N_u)-E(N_u)\right|du

Value

Returns a list including

StaDist	statistics of marginal distributions, based on Smirnov like statistics
..$dd	test statistic
..$q.dd	quantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.value	p value
Cor	statistics of correlation functions
..$dd	test statistic
..$q.dd	quantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.value	p value
ENu	statistics of intensity of up crossings
..$dd	test statistic
..$q.dd	quantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.value	p value
AD	statistics of marginal distributions, based on Anderson Darling statistics
..$dd	test statistic
..$q.dd	quantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.value	p value

Author(s)

Valerie Monbet, [e-mail]

See Also

valid_all, test.model.MSAR

NHMSAR documentation built on Feb. 9, 2022, 9:06 a.m.