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Simulate Time Series for Multiple iAR Models

Source: R/02_sim.R
sim.Rd

Simulates a time series for irregular autoregressive (iAR) models, including: 1. Normal iAR model (`iAR`) 2. T-distribution iAR model (`iAR-T`) 3. Gamma-distribution iAR model (`iAR-Gamma`)

Usage

sim(x, ...)

Arguments

x

An object of class iAR, CiAR, or BiAR, containing the model specification and parameters:

  • For iAR (irregular AR models), the model family could be "norm", "t", or "gamma", where:

    • family: The distribution family of the iAR model (one of "norm", "t", or "gamma").

    • coef: The coefficient(s) of the iAR model.

    • times: A numeric vector specifying the time points of the series.

    • df: Degrees of freedom for the t-distribution (only for family = "t").

    • sigma: The scale parameter for the t-distribution (only for family = "t").

    • mean: The mean parameter for the gamma distribution (only for family = "gamma").

    • variance: The variance parameter for the gamma distribution (only for family = "gamma").

  • For CiAR (complex irregular autoregressive models):

    • coef: The real and imaginary parts of the CiAR model's coefficients.

    • times: A numeric vector specifying the time points of the series.

    • rho: The correlation parameter for the CiAR model.

    • c: The scale parameter for the CiAR model.

  • For BiAR (BiAR models):

    • coef: The coefficients of the BiAR model (real and imaginary).

    • times: A numeric vector specifying the time points of the series.

    • rho: The correlation parameter for the BiAR model.

    • series_esd: The series for the error structure (optional, used internally).

...

Additional arguments for generating irregular times. This is used only if no time points have been provided in the times argument:

n

A positive integer. Length of observation times. Default is 100. This is used only if no time points are provided in times.

distribution

A character string specifying the distribution of the observation times. Default is `"expmixture"`. Available options are:

expmixture

A mixture of two exponential distributions.

uniform

A uniform distribution.

exponential

A single exponential distribution.

gamma

A gamma distribution.

lambda1

Mean (1/rate) of the exponential distribution or the first exponential distribution in a mixture of exponential distributions. Default is `130`.

lambda2

Mean (1/rate) of the second exponential distribution in a mixture of exponential distributions. Default is `6.5`.

p1

Weight of the first exponential distribution in a mixture of exponential distributions. Default is `0.15`.

p2

Weight of the second exponential distribution in a mixture of exponential distributions. Default is `0.85`.

a

Shape parameter of a gamma distribution or lower limit of the uniform distribution. Default is `0`.

b

Scale parameter of a gamma distribution or upper limit of the uniform distribution. Default is `1`.

Value

An updated object of class iAR, CiAR, or BiAR, where the series property contains the simulated time series.

Details

This function simulates time series based on the specified model and its parameters. Depending on the class of the input object:

  • For iAR models, it supports three distribution families:

  • "norm" for normal distribution.

  • "t" for t-distribution.

  • "gamma" for gamma distribution.

  • For CiAR models, it uses complex autoregressive processes to generate the time series.

  • For BiAR models, it simulates a BiAR process using specified coefficients and correlation.

The coefficients and any family-specific parameters must be set before calling this function.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487 , https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf. ,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560 . ,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216 , https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

# Example 1: Simulating a normal iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9,hessian=TRUE)
model_norm <- sim(model_norm)
plot(model_norm, type = "l", main = "Simulated iAR-Norm Series")


# Example 2: Simulating a CiAR model
set.seed(6714)
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
plot(model_CiAR , type = "l", main = "Simulated CiAR Series")


# Example 3: Simulating a BiAR model
set.seed(6714)
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
plot(times, model_BiAR@series[,1], type = "l", main = "Simulated BiAR Series")