# sim.ARMA: Simulation of ARMA(p,q) model. In weakARMA: Tools for the Analysis of Weak ARMA Models

 sim.ARMA R Documentation

## Simulation of ARMA(p,q) model.

### Description

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

### Usage

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

### Arguments

 `n` Number of observations. `ar` Vector of AR coefficients. If `NULL`, the simulation is a MA process. `ma` Vector of MA coefficients. If `NULL`, the simulation is a AR process. `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'.

### 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`.

### Value

Returns a vector containing the `n` simulated observations of the time series.

### References

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`

### Examples

```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")

```

weakARMA documentation built on April 5, 2022, 1:16 a.m.