mc_ARFIMA {fractalRegression}

Mixed-correlated ARFIMA processes

Description

Simulate various types of correlated noise processes.

Usage

mc_ARFIMA(
  process,
  n,
  rho,
  d1 = NULL,
  d2 = NULL,
  d3 = NULL,
  d4 = NULL,
  alpha = NULL,
  beta = NULL,
  delta = NULL,
  gamma = NULL,
  theta = NULL,
  theta1 = NULL,
  theta2 = NULL
)

Arguments

process

specifies the type of correlated noise process to simulate and includes 'Noise_rho', 'ARFIMA_rho','ARFIMA_AR','AR_rho', 'Mixed_ARFIMA_ARFIMA','Mixed_ARFIMA_AR',and 'Mixed_ARFIMA_noise'.

n

is a numeric value specifying the length of the time-series.

rho

specifies the strength of the correlation with values -1 - 1.

d1

is a numeric fractional difference parameter for x specifying long term memory.

d2

is a numeric fractional difference parameter for x specifying long term memory.

d3

is a numeric fractional difference parameter for y specifying long term memory.

d4

is a numeric fractional difference parameter for y specifying long term memory.

alpha

see Kristoufek (2013) for details.

beta

see Kristoufek (2013) for details.

delta

see Kristoufek (2013) for details.

gamma

see Kristoufek (2013) for details.

theta

see Kristoufek (2013) for details.

theta1

see Kristoufek (2013) for details.

theta2

see Kristoufek (2013) for details.

Details

This function includes multiple options simulating various types of correlated noise processes including mixed-correlated ARFIMA processes with power-law cross-correlations, These functions were originally written by Ladislav Kristoufek and posted on his website. They go with the paper presented in Kristoufek (2013). The 'process' argument specifies the type of noise to be generated.

• 'Noise_rho' - Generates two correlated noise series and requires arguments: n, rho.

• 'ARFIMA_rho' - Generates two ARFIMA processes with correlated innovations and requires arguments: n, d1, d2, rho.

• 'ARFIMA_AR' - Generates ARFIMA and AR(1) processes with correlated innovations and requires arguments: n, d1, theta, rho.

• 'AR_rho' - Generates two AR(1) processes with correlated innovations and requires arguments: n, theta1, theta2, rho.

• 'Mixed_ARFIMA_ARFIMA' - Generates MC-ARFIMA process with long-range correlation and long-range cross-correlation (Kristoufec, 2013 Model 1) and requires arguments: alpha, beta, gamma, delta, n, d1, d2, d3, d4, rho.

• 'Mixed_ARFIMA_AR' - Generates MC-ARFIMA process with long-range correlation and short-range cross-correlation (Kristoufec, 2013 Model 2) and requires arguments: alpha, beta, gamma, delta, n, d1, d2, theta, rho.

• 'Mixed_ARFIMA_noise' - Generates MC-ARFIMA process with long-range correlation and simple correlation (Kristoufec, 2013 Model 3) and requires arguments: alpha, beta, gamma, delta, n, d1, d2, rho.

Value

The object returned is a matrix of length n with a time series (x,y) in column 1 and 2.

References

Kristoufek, L. (2013). Mixed-correlated ARFIMA processes for power-law cross-correlations. Physica A: Statistical Mechanics and its Applications, 392(24), 6484-6493.

Examples

set.seed(987345757)

sim1 <- mc_ARFIMA(process='Mixed_ARFIMA_ARFIMA', alpha = 0.2,
beta = 1, gamma = 1, delta = 0.2, n = 10000, d1 = 0.4, d2 = 0.3,
d3 = 0.3, d4=0.4, rho=0.9)

plot(sim1[,1],type='l', ylab= "Signal Amplitude", xlab='Time',
main = "MC-ARFIMA with LRC and LRCC")

lines(sim1[,2], col='blue')