ensure_causality_invertibility: ensure_causality_invertibility

In hlennon/copulaIVTS: Dependence modelling of a digitised Gaussian ARMA(p,q) copula model for Integer-Valued Time Series

Description

Test to ensure AR parameters are causal and MA parameters are invertible. If the AR parameters are used, the function converts them to casual If the MA parameters are used, the function converts them to invertible parameters If ar parameters, (phi_1, phi_2, ..., phi_p) If ma parameter, (theta_1, theta_2, ..., theta_q)

Usage

ensure_causality_invertibility(parameters)

Arguments

parameters

vector of AR or MA parameters, in the order of

Details

Test to ensure AR parameters are causal and MA parameters are invertible It converts them to casual/incertible parameters if not

Value

parameter values that are causal or invertible, ensureing unique solutions.

Author(s)

Hannah Lennon <[e-mail]>

References

Jingsong Yuan, Time Series Lecture Notes, https://www.ma.man.ac.uk/~jy/tsaf/

See Also

Brockwell and Davis (1987)

Examples

library(polynom)

ensure_causality_invertibility(c(0.5, 1.3))

p    <- 3
q    <- 3
para <- c(0.2, 1, 0.2, 1, -0.5, 0.3)

para[1:p] <- ensure_causality_invertibility(para[1:p])
para[(p + 1):(p + q)] <- -ensure_causality_invertibility(-para[(p + 1):(p + q)])

## The function is currently defined as
function (parameters)
{
    L <- length(parameters)
    ps <- polynomial(c(-parameters[L:1], 1))
    ps <- solve(ps)
    if (all(abs(ps) < 1))
        return(parameters)
    else {
        j <- numeric(L)
        k <- 0
        vec <- numeric(L)
        ps[abs(ps) >= 1] <- 1/ps[abs(ps) >= 1]
        while (k < L) {
            j <- add_1(j)
            k <- sum(j)
            vec[k] <- vec[k] + (-1)^(k + 1) * prod(ps^j)
                      }
        return(as.numeric(vec))
           }
}

hlennon/copulaIVTS documentation built on Dec. 20, 2021, 4:45 p.m.