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Computing the initial state covariance matrix of ARMA

arma_Q0Gardner.Rd

Wrappers for the internals 'stats' functions used by arima() to compute the initial state covariance matrix of ARMA models.

Usage

<!-- % arma_Q0Gardner(phi, theta, tol = .Machine$double.eps) -->

<!-- % arma_Q0bis(phi, theta, tol = .Machine$double.eps) -->

arma_Q0naive(phi, theta, tol = .Machine$double.eps)

arma_Q0gnbR(phi, theta, tol = .Machine$double.eps)

Arguments

phi

autoregressive coefficients.

theta

moving average coefficients.

tol

tollerance.

Details

arima() uses one of two methods to compute the initial state covariance matrix of a stationary ARMA model. Both methods are implemented by internal non-exported C functions. arma_Q0Gardner() and arma_Q0bis are simple R wrappers for those functions. They are defined in the tests (TODO: put in the examples?) bit are not defined in the namespace of the package since they use unexported functions.

arma_Q0Gardner() implements the original method from Gardner et al (1980). arma_Q0bis() is a more recent method that deals better with roots very close to the unit circle.

These functions can be useful for comparative testing. They cannot be put in package 'sarima' since they use `:::` operator and are hence inadmissible to CRAN.

Value

a matrix

References

Gardner G, Harvey AC, Phillips GDA (1980). “Algorithm AS154. An algorithm for exact maximum likelihood estimation of autoregressive-moving average models by means of Kalman filtering.” Applied Statistics, 311--322.

Examples

## arma_Q0Gardner(phi, theta, tol = .Machine$double.eps)
## arma_Q0bis(phi, theta, tol = .Machine$double.eps)