Fit the fARMA(p,q) model.

farma_fit(
  Xt,
  dt,
  order,
  drift = c("linear", "none", "quadratic"),
  vcov = TRUE,
  ad_only = TRUE
)

Arguments

Xt: Matrix of trajectory positions, where each row is an observation and each column is a measurement coordinate. The trajectory is assumed to be sampled at a constant frequency.
dt: Interobservation time \(\Delta t\) = 1/fps (positive scalar).
order: A specification of the farma model: the two integer components (p, q) are the AR order and the MA order.
drift: Character string specifying one of the preset drift types "linear", "none", or "quadratic". Custom drift functions are not supported through this simplified interface. See csi_model for details.
vcov: Logical; if TRUE, also estimate the variance matrix.
ad_only: Whether to return estimates of (alpha, log(D)) only, or the entire parameter vector omega in the computational basis.

Value

A vector of estimated parameters on the transformed scale. If vcov == TRUE, a list with components:

coef: A vector of estimated parameters on transformed scale.
vcov: A matrix of estimated covariance of parameters on transformed scale.

If ad_only == TRUE, instead of the transformed scale parameters, returns an estimate (and possibly the estimated convariance) of (alpha, D).

Examples

# simulate data from a farma(1,1) model
alpha <- .8
phi <- .1
rho <- .1

dt <- 1/60
N <- 1800
ndim <- 2

Xt <- csi_sim(drift = matrix(0, N-1, ndim),
              acf = farma_acf(alpha, phi = phi, rho = rho, dt, N-1),
              Sigma = diag(ndim),
              X0 = rep(0, ndim))


# Fit the farma(1,1) model
farma_fit(Xt, dt = dt, order = c(1,1), vcov = TRUE)
#> $coef
#>      alpha       logD 
#>  0.7431171 -0.7739260 
#> 
#> $vcov
#>             alpha        logD
#> alpha 0.004078114 0.005831055
#> logD  0.005831055 0.011943318
#>

Fit the fARMA(p,q) model.

Arguments

Value

See also

Examples