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_{(-∞,t)\times E} ( α + g(u, z) ) e^{-β (t-u)} M(du \times dz).*

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 continuous.

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

.

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

.

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

.

*z* 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 whose first argument is always

`param`

.`type_col_map`

Mapping between type and column number of kernel used for multi-kernel model.

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) mhspec2

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