advanced-algorithmic-trading

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Figure 10.20: Correlogram of an ARMA(1,1) Model, with α = 0.5 and β = −0.5
Call:
arima(x = x, order = c(1, 0, 1))
Coefficients:
ar1 ma1 intercept
-0.3957 0.4503 0.0538
s.e. 0.3727 0.3617 0.0337
sigma^2 estimated as 1.053: log likelihood = -1444.79, aic = 2897.58
We can calculate the confidence intervals for each parameter using the standard errors:
> -0.396 + c(-1.96, 1.96)*0.373
[1] -1.12708 0.33508
> 0.450 + c(-1.96, 1.96)*0.362
[1] -0.25952 1.15952
The confidence intervals do contain the true parameter values for both cases but we should
note that the 95% confidence intervals are very wide. This is a consequence of the reasonably
large standard errors.
Let us now try an ARMA(2,2) model. That is, an AR(2) model combined with a MA(2)
model. We need to specify four parameters for this model: α 1 , α 2 , β 1 and β 2 . Let us take
α 1 = 0.5, α 2 = −0.25 β 1 = 0.5 and β 2 = −0.3:
> set.seed(1)
> x <- arima.sim(n=1000, model=list(ar=c(0.5, -0.25), ma=c(0.5, -0.3)))