Performs bootstrap statistical tests to validate MSAR models.

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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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