advanced-algorithmic-trading

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We can start with the simplest possible non-trivial ARMA model–the ARMA(1,1) model.
This is an autoregressive model of order one combined with a moving average model of order
one. Such a model has only two coefficients, α and β, which represent the first lags of the time
series itself and the "shock" white noise terms. The model is given by:
x t = αx t−1 + w t + βw t−1 (10.20)
We need to specify the coefficients prior to simulation. Let us take α = 0.5 and β = −0.5:
> set.seed(1)
> x <- arima.sim(n=1000, model=list(ar=0.5, ma=-0.5))
> plot(x)
The output is given in Figure 10.19.
Figure 10.19: Realisation of an ARMA(1,1) Model, with α = 0.5 and β = −0.5
Let us also plot the correlogram, as given in Figure 10.20.
> acf(x)
We can see that there is no significant autocorrelation, which is to be expected from an
ARMA(1,1) model.
Finally, let us try and determine the coefficients and their standard errors using the arima
function:
> arima(x, order=c(1, 0, 1))