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

Description Usage Arguments Details Value Author(s) See Also

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

1

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, valerie.monbet@univ-rennes1.fr

See Also

valid_all, test.model.MSAR



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