hawkesRate: Intensity for the Hawkes process.
In ppstat: Point Process Statistics

Description Usage Arguments Details Value Author(s) See Also

Computes the intensity, or rate, for the non-linear multivariate Hawkes process at a given time point given a history of points.

1 2	hawkesRate(t, T = list(), h, predict = TRUE, Delta = 1, beta0 = rep(1, M), phi = function(x) pmax(x, 0), warn = TRUE, ...)

`t`	a `numeric`. The time point at which the intensity is computed.
`T`	a `list`. The history of the process as a list of vectors, one for each mark, containing the event times preceeding `t`.
`h`	a `list` of `lists` of filter function evaluations.
`predict`	a `logical`. Specifies whether the events in the history `T` have to strictly preceed `t` (`predict = TRUE`, the default), or whether equality is allowed.
`Delta`	a `numeric`. The distance between the equidistant evaluations of the filter functions. Default value is 1.
`beta0`	a `numeric` vector. Default value is a vector of ones.
`phi`	a `function`. Transforms the linear predictor obtained by the filters to the intensity. Default is to take the positive part.
`warn`	a `logical` specifying if warnings should be given. Default is `TRUE`.
`...`	additional arguments

The hawkesRate function computes

phi(beta0_k + sum_k int_0^{t-} h^{mk}(t-s) dN_s^k)

if predict = TRUE. It is an error to allow for event times in the history that don't strictly preceed t when predict = TRUE. If predict = FALSE equality is allowed. The latter option is used to compute bounds on the intensity until the next event occurs, which in turn is used in Ogatas thinning algorithm.

A numeric vector.

Niels Richard Hansen, Niels.R.Hansen@math.ku.dk

Ogata

ppstat documentation built on May 2, 2019, 5:26 p.m.