hspec-class | R Documentation |

This class represents a specification of a marked Hawkes model with exponential kernel. The intensity of the ground process is defined by:

*λ(t) = μ + \int ( α + Ψ ) * exp( -β (t-u)) d N(t).*

For more details, please see the vignettes.

*μ* is base intensity.
This is generally a constant vector but can be extended to stochastic processes.
Currently, piecewise constant mu is also possible. mu is left continous.

*α* is a constant matrix which represents impacts on intensities after events.
It is represented by slot `mu`

.

*Ψ* is for non-constant parts of the impact.
It may depend on any information generated by *N*, *λ*, *k* and so on.
It is represented by slot `impact`

.

*β* is a constant matrix for exponential decay rates.
It is represetned by slot `beta`

.

*k* is mark and represented by slot `rmark`

.

`mu`

, `alpha`

and `beta`

are required slots for every exponential Hawkes model.
`rmark`

and `impact`

are additional slots.

`mu`

numeric value or matrix or function, if numeric, automatically converted to matrix

`alpha`

numeric value or matrix or function, if numeric, automatically converted to matrix, exciting term

`beta`

numeric value or matrix or function, if numeric,, automatically converted to matrix, exponential decay

`eta`

numeric value or matrix or function, if numeric,, automatically converted to matrix, impact by additional mark

`dimens`

dimension of the model

`rmark`

a function that generates mark for counting process, for simulation

`dmark`

a density function for mark, for estimation

`impact`

a function that describe the after impact of mark to lambda

`type_col_map`

used for multiple kernel

MU <- matrix(c(0.2), nrow = 2) ALPHA <- matrix(c(0.75, 0.92, 0.92, 0.75), nrow = 2, byrow=TRUE) BETA <- matrix(c(2.25, 2.25, 2.25, 2.25), nrow = 2, byrow=TRUE) mhspec2 <- new("hspec", mu=MU, alpha=ALPHA, beta=BETA)

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