Description Usage Arguments Details Value References Examples
Perform simulation of a self-exciting point process whose intensity also includes a component triggered by another given point process data and a non-stationary Poisson trend.
1 |
data |
point process data. |
interval |
length of time interval in which events take place. |
c |
exponential coefficient of lgp corresponding to simulated data. |
d |
exponential coefficient of lgp corresponding to input data. |
ax |
lgp coefficients in self-exciting part. |
ay |
lgp coefficients in the input part. |
at |
coefficients of the polynomial trend. |
ptmax |
an upper bound of trend polynomial. |
This function performs simulation of a self-exciting point process whose intensity also includes a component triggered by another given point process data and non-stationary Poisson trend. The trend is given by usual polynomial, and the response functions to the self-exciting and the external inputs are given the Laguerre-type polynomials (lgp), where the scaling parameters in the exponential functions, say c and d, can be different.
in.data |
input data for |
sim.data |
self-exciting simulated data. |
Ogata, Y., Katsura, K. and Zhuang, J. (2006) Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2. The Institute of Statistical Mathematics.
Ogata, Y. (1981) On Lewis' simulation method for point processes. IEEE information theory, vol. it-27, pp. 23-31.
Ogata, Y. and Akaike, H. (1982) On linear intensity models for mixed doubly stochastic Poisson and self-exciting point processes. J. royal statist. soc. b, vol. 44, pp. 102-107.
Ogata, Y., Akaike, H. and Katsura, K. (1982) The application of linear intensity models to the investigation of causal relations between a point process and another stochastic process. Ann. inst. statist math., vol. 34. pp. 373-387.
1 2 3 |
$in.data
[1] 379.980 462.150 527.722 589.106 679.200 1281.589 1936.376
[8] 1978.485 2005.724 2046.084 2396.726 3363.897 3391.844 3415.762
[15] 3437.722 3574.983 3944.206 4343.578 5012.513 5183.430 5930.347
[22] 5979.053 6478.570 7166.254 7766.953 7770.460 7880.454 8053.839
[29] 8228.121 8832.647 9032.490 9643.708 10040.988 10361.319 11932.021
[36] 12116.334 12649.290 12694.823 13249.371 13274.072 14324.904 14333.882
[43] 14419.576 14649.989 15200.213 15724.547 15796.184 15805.969 15993.236
[50] 16010.848 16258.003 16311.447 16567.033 17070.861 17393.063 17400.454
[57] 17525.027 17857.488 18513.795 18961.702 19058.008 19157.142 19274.173
[64] 19416.957 19505.986 19569.694 19741.299 19812.689 19895.271
$sim.data
[1] 272.6740 288.4796 289.4585 429.1059 569.3960 703.0780
[7] 765.8105 775.2845 806.5467 807.3006 861.7112 913.8867
[13] 1081.6380 1153.2642 1327.6080 1364.3403 1482.2084 1536.6699
[19] 1746.0608 1992.6499 2021.0105 2084.2810 2287.4811 2545.4863
[25] 2744.1549 2989.9092 3068.9358 3252.1822 3374.9241 3382.6042
[31] 3449.4929 3919.4678 3964.4710 4827.2374 5210.1790 5281.0843
[37] 5539.6956 5663.3850 5737.6040 6057.9333 6061.3940 6061.9298
[43] 6063.8387 6431.3542 6857.6799 6860.0080 6988.2674 6992.4195
[49] 7033.4842 7065.9623 7111.2394 7570.6837 7599.4876 7967.5065
[55] 8187.7243 8383.7132 8599.2303 8952.5807 9799.5396 10086.7045
[61] 10107.3036 10218.8555 10292.9053 10592.4653 11322.5214 11329.7593
[67] 11665.7319 11666.9163 12587.1471 12621.8663 12718.9385 13106.7651
[73] 13290.0210 13362.3787 13860.0081 13996.2822 14498.0605 14651.9229
[79] 14738.0583 14924.6213 15473.6836 15595.5387 15817.0662 15878.9656
[85] 15905.5431 15905.6837 16288.6194 16346.8540 16573.4838 16695.3875
[91] 17450.9296 17485.1872 17486.4130 17554.9584 17657.4724 17894.3734
[97] 18261.6920 18871.8166 19094.4277 19945.5896
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