test.model.MSAR: Performs bootstrap statistical tests to validate MSAR 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
Value
Returns a list including
StaDiststatistics of marginal distributions, based on Smirnov like statistics
..$ddtest statistic
..$q.ddquantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.valuep value
Corstatistics of correlation functions
..$ddtest statistic
..$q.ddquantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.valuep value
ENustatistics of intensity of up crossings
..$ddtest statistic
..$q.ddquantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.valuep value
ADstatistics of marginal distributions, based on Anderson Darling statistics
..$ddtest statistic
..$q.ddquantiles .05 and .95 of the distribution of the test statistic under the null hypothesis
..$p.valuep value
Details
Test statistics
Marginal distribution: {$$S = \int_{-\infty}^{\infty} \left| F_n(x)-F(x) \right| dx$$ }
Marginal distribution, based on Anderson Darling statistic: {$$S = \int_{-\infty}^{\infty} \left| \frac{F_n(x)-F(x)}{F(x)(1-F(x))} \right| dx$$ }
Correlation function: {$$S = \int_0^L\left|C_n(l)-C(l)\right|dl$$ }
Number of up crossings: {$$S = \int_{-\infty}^{\infty}\left|E_n(N_u)-E(N_u)\right|du$$}