Joe.Markov.DATA: Generating Time Series Data Under a Copula-Based Markov Chain...

In Copula.Markov: Copula-Based Estimation and Statistical Process Control for Serially Correlated Time Series

Description

Time-series data are generated under a copula-based Markov chain model with the Joe copula.

Usage

Joe.Markov.DATA(n, mu, sigma, alpha)

Arguments

n	sample size
mu	mean
sigma	standard deviation
alpha	association parameter

Details

alpha>=1 for positive association

Value

Time series data of size n

Author(s)

Takeshi Emura

References

Emura T, Long TH, Sun LH (2017), R routines for performing estimation and statistical process control under copula-based time series models, Communications in Statistics - Simulation and Computation, 46 (4): 3067-87

Long TS and Emura T (2014), A control chart using copula-based Markov chain models, Journal of the Chinese Statistical Association 52 (No.4): 466-96

Examples

n=1000
alpha=2.856 ### Kendall's tau =0.5 ###
mu=2
sigma=1
Y=Joe.Markov.DATA(n,mu,sigma,alpha)
mean(Y)
sd(Y)
cor(Y[-1],Y[-n],method="kendall")

Joe.Markov.MLE(Y,k=2)

Example output

[1] 1.869801
[1] 0.9572086
[1] 0.4607553
$estimates
        mu      sigma      alpha        UCL        LCL 
 1.8958440  0.9983598  2.6785176  3.8925637 -0.1008757 

$out_of_control
 [1]   4  43  71  96 115 116 122 123 124 211 248 264 297 298 300 311 376 430 434
[20] 442 487 553 562 594 603 621 672 701 793 822 839 901 946 947 948 949 950 968
[39] 969 976

$Gradient
[1] -6.821210e-15 -5.306866e-14  6.593837e-15

$Hessian
           [,1]       [,2]       [,3]
[1,] -0.5411087 -0.2183230  0.1971793
[2,] -0.2183230 -2.1813517  0.3915524
[3,]  0.1971793  0.3915524 -0.1371003

$Mineigenvalue_Hessian
[1] -2.289899

$CM.test
[1] 0.1091633

$KS.test
[1] 0.02844239

Copula.Markov documentation built on Nov. 29, 2021, 9:07 a.m.