# 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

 1 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, [email protected]