sim.ARMA | R Documentation |

Simulates an ARMA, AR or MA process according to the arguments given.

sim.ARMA( n, ar = NULL, ma = NULL, sigma = 1, eta = NULL, method = "strong", k = 1, mu = 0, ... )

`n` |
Number of observations. |

`ar` |
Vector of AR coefficients. If |

`ma` |
Vector of MA coefficients. If |

`sigma` |
Standard deviation. |

`eta` |
Vector of white noise sequence. Allows the user to use his own white noise. |

`method` |
Defines the kind of noise used for the simulation. By default, the noise used is strong. See 'Details'. |

`k` |
Integer used in the creation of the noise. See 'Details'. |

`mu` |
Integer for the mean of the series. |

`...` |
Arguments needed to simulate GARCH noise. See 'Details'. |

ARMA model is of the following form :

* X_{t}-μ = e_{t} + a_{1} (X_{t-1}-μ)
+ a_{2} (X_{t-2}-μ) + ... + a_{p} (X_{t-p}-μ) - b_1 e_{t-1} - b_2 e_{t-2} - ... - b_{q} e_{t-q}*

where *e_t* is a sequence of uncorrelated random variables with zero
mean and common variance *σ^{2} > 0* . *ar = (a_{1}, a_{2}, ..., a_{p})* are
autoregressive coefficients and *ma = (b_{1}, b_{2}, ... , b_{q})* are moving
average coefficients. Characteristic polynomials of ar and ma must
constitute a stationary process.

Method "`strong`

" realise a simulation with gaussian white noise.

Method "`product`

", "`ratio`

" and "`product.square`

"
realise a simulation with a weak white noise. These methods employ
respectively the functions `wnPT`

, `wnRT`

and
`wnPT_SQ`

to simulate nonlinear ARMA model. So, the
paramater `k`

is an argument of these functions. See `wnPT`

, `wnRT`

or `wnPT_SQ`

.

Method "`GARCH`

" gives an ARMA process with a GARCH noise. See
`simGARCH`

.

Returns a vector containing the `n`

simulated observations of the
time series.

Francq, C. and Zakoïan, J.M. 1998, Estimating linear representations
of nonlinear processes, *Journal of Statistical Planning and
Inference*, vol. 68, no. 1, pp. 145-165

`arima.sim`

y <- sim.ARMA(n = 100, ar = 0.95, ma = -0.6, method = "strong" ) y2 <- sim.ARMA(n = 100, ar = 0.95, ma = -0.6, method = "ratio") y3 <- sim.ARMA(n = 100, ar = 0.95, ma = -0.6, method = "GARCH", c = 1, A = 0.1, B = 0.88) y4 <- sim.ARMA(n = 100, ar = 0.95, ma = -0.6, method = "product") y5 <- sim.ARMA(n = 100, ar = 0.95, ma = -0.6, method = "product.square")

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.