advanced-algorithmic-trading

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Figure 11.1: Plot of simulated ARIMA(1,1,1) model with α = 0.6 and β = −0.5
Call:
arima(x = x, order = c(1, 1, 1))
Coefficients:
ar1 ma1
0.6470 -0.5165
s.e. 0.1065 0.1189
sigma^2 estimated as 1.027: log likelihood = -1432.09, aic = 2870.18
The confidence intervals are calculated as:
> 0.6470 + c(-1.96, 1.96)*0.1065
[1] 0.43826 0.85574
> -0.5165 + c(-1.96, 1.96)*0.1189
[1] -0.749544 -0.283456
Both parameter estimates fall within the confidence intervals and are close to the true parameter
values of the simulated ARIMA series. Hence we should not be surprised to see the
residuals looking like a realisation of discrete white noise as given in Figure 11.2.
> acf(resid(x.arima))
Finally, we can run a Ljung-Box test to provide statistical evidence of a good fit:
> Box.test(resid(x.arima), lag=20, type="Ljung-Box")