The method simulate multivariate Hawkes processes.
The object hspec-class
contains the parameter values such as mu
, alpha
, beta
.
The mark (jump) structure may or may not be included.
It returns an object of class hreal
which contains inter_arrival
, arrival
,
type
, mark
, N
, Nc
, lambda
, lambda_component
, rambda
, rambda_component
.
Usage
hsim(
object,
size = 100,
lambda_component0 = NULL,
N0 = NULL,
Nc0 = NULL,
verbose = FALSE,
...
)
# S4 method for class 'hspec'
hsim(
object,
size = 100,
lambda_component0 = NULL,
N0 = NULL,
Nc0 = NULL,
verbose = FALSE,
...
)
Arguments
- object
hspec-class
. S4 object that specifies the parameter values.- size
Number of observations.
- lambda_component0
Initial values for the lambda component \(\lambda_{ij}\). Can be a numeric value or a matrix. Must have the same number of rows and columns as
alpha
orbeta
inobject
.- N0
Starting values of N with default value 0.
- Nc0
Starting values of Nc with default value 0.
- verbose
Logical. If
TRUE
, print progress messages during the simulation. Default isFALSE
.- ...
Further arguments passed to or from other methods.
Value
hreal
S3-object, summary of the Hawkes process realization.
Examples
# example 1
mu <- 1; alpha <- 1; beta <- 2
h <- new("hspec", mu=mu, alpha=alpha, beta=beta)
hsim(h, size=100)
#> -------------------------------------------------------
#> Simulation result of exponential (marked) Hawkes model.
#> An object of class "hspec" of 1-dimensional Hawkes process
#>
#> Slot mu:
#> [,1]
#> [1,] 1
#>
#> Slot alpha:
#> [,1]
#> [1,] 1
#>
#> Slot beta:
#> [,1]
#> [1,] 2
#>
#> Realized path :
#> arrival N1 mark lambda1 lambda11
#> [1,] 0.00000 0 0 1.500 0.50000
#> [2,] 0.04361 1 1 1.458 0.45824
#> [3,] 1.42215 2 1 1.093 0.09256
#> [4,] 1.96504 3 1 1.369 0.36889
#> [5,] 3.18763 4 1 1.119 0.11870
#> [6,] 3.25617 5 1 1.975 0.97539
#> [7,] 4.00690 6 1 1.440 0.44012
#> [8,] 4.11924 7 1 2.150 1.15033
#> [9,] 4.13472 8 1 3.085 2.08480
#> [10,] 4.49366 9 1 2.505 1.50472
#> [11,] 4.76137 10 1 2.466 1.46632
#> [12,] 4.87785 11 1 2.954 1.95377
#> [13,] 4.90706 12 1 3.786 2.78617
#> [14,] 5.22155 13 1 3.019 2.01853
#> [15,] 5.25446 14 1 3.826 2.82625
#> [16,] 5.82846 15 1 2.214 1.21396
#> [17,] 5.84546 16 1 3.140 2.13996
#> [18,] 5.94467 17 1 3.575 2.57481
#> [19,] 6.03999 18 1 3.954 2.95434
#> [20,] 6.23474 19 1 3.679 2.67865
#> ... with 80 more rows
#> -------------------------------------------------------
# example 2
mu <- matrix(c(0.1, 0.1), nrow=2)
alpha <- matrix(c(0.2, 0.1, 0.1, 0.2), nrow=2, byrow=TRUE)
beta <- matrix(c(0.9, 0.9, 0.9, 0.9), nrow=2, byrow=TRUE)
h <- new("hspec", mu=mu, alpha=alpha, beta=beta)
res <- hsim(h, size=100)
print(res)
#> -------------------------------------------------------
#> Simulation result of exponential (marked) Hawkes model.
#> An object of class "hspec" of 2-dimensional Hawkes process
#>
#> Slot mu:
#> [,1]
#> [1,] 0.1
#> [2,] 0.1
#>
#> Slot alpha:
#> [,1] [,2]
#> [1,] 0.2 0.1
#> [2,] 0.1 0.2
#>
#> Slot beta:
#> [,1] [,2]
#> [1,] 0.9 0.9
#> [2,] 0.9 0.9
#>
#> Realized path :
#> arrival N1 N2 mark lambda1 lambda2 lambda11 lambda12 lambda21
#> [1,] 0.000 0 0 0 0.1500 0.1500 3.333e-02 1.667e-02 1.667e-02
#> [2,] 2.800 0 1 1 0.1040 0.1040 2.682e-03 1.341e-03 1.341e-03
#> [3,] 4.872 0 2 1 0.1161 0.1316 4.156e-04 1.571e-02 2.078e-04
#> [4,] 8.116 0 3 1 0.1063 0.1125 2.242e-05 6.240e-03 1.121e-05
#> [5,] 11.637 1 3 1 0.1045 0.1089 9.431e-07 4.470e-03 4.715e-07
#> [6,] 13.573 1 4 1 0.1358 0.1191 3.501e-02 7.826e-04 1.751e-02
#> [7,] 14.563 1 5 1 0.1557 0.1899 1.436e-02 4.134e-02 7.181e-03
#> [8,] 14.632 2 5 1 0.2464 0.3725 1.350e-02 1.329e-01 6.751e-03
#> [9,] 24.985 2 6 1 0.1000 0.1000 1.918e-05 1.193e-05 9.589e-06
#> [10,] 26.830 2 7 1 0.1190 0.1380 3.642e-06 1.899e-02 1.821e-06
#> [11,] 26.955 2 8 1 0.2064 0.3127 3.255e-06 1.064e-01 1.628e-06
#> [12,] 30.109 2 9 1 0.1121 0.1241 1.904e-07 1.207e-02 9.521e-08
#> [13,] 37.449 3 9 1 0.1002 0.1003 2.575e-10 1.516e-04 1.288e-10
#> [14,] 40.774 3 10 1 0.1100 0.1050 1.003e-02 7.605e-06 5.017e-03
#> [15,] 42.009 3 11 1 0.1362 0.1675 3.301e-03 3.290e-02 1.651e-03
#> [16,] 42.762 3 12 1 0.1692 0.2359 1.677e-03 6.752e-02 8.386e-04
#> [17,] 42.789 3 13 1 0.2651 0.4278 1.637e-03 1.635e-01 8.184e-04
#> [18,] 43.519 3 14 1 0.2373 0.3734 8.480e-04 1.365e-01 4.240e-04
#> [19,] 50.020 3 15 1 0.1007 0.1014 2.441e-06 6.807e-04 1.220e-06
#> [20,] 54.162 3 16 1 0.1024 0.1048 5.870e-08 2.421e-03 2.935e-08
#> lambda22
#> [1,] 3.333e-02
#> [2,] 2.682e-03
#> [3,] 3.141e-02
#> [4,] 1.248e-02
#> [5,] 8.940e-03
#> [6,] 1.565e-03
#> [7,] 8.268e-02
#> [8,] 2.657e-01
#> [9,] 2.387e-05
#> [10,] 3.799e-02
#> [11,] 2.127e-01
#> [12,] 2.414e-02
#> [13,] 3.031e-04
#> [14,] 1.521e-05
#> [15,] 6.580e-02
#> [16,] 1.350e-01
#> [17,] 3.270e-01
#> [18,] 2.730e-01
#> [19,] 1.361e-03
#> [20,] 4.843e-03
#> ... with 80 more rows
#> -------------------------------------------------------