advanced-algorithmic-trading

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Figure 10.10: Realisation of MA(1) Model, with β 1 = 0.6 and Associated Correlogram
> x.ma <- arima(x, order=c(0, 0, 1))
> x.ma
Call:
arima(x = x, order = c(0, 0, 1))
Coefficients:
ma1 intercept
0.6023 0.1681
s.e. 0.0827 0.1424
sigma^2 estimated as 0.7958: log likelihood = -130.7, aic = 267.39
We receive some useful output from the arima command. Firstly, we can see that the
parameter has been estimated as ˆβ 1 = 0.602, which is very close to the true value of β 1 =
0.6. Secondly, the standard errors are already calculated for us, making it straightforward to
calculate confidence intervals. Thirdly, we receive an estimated variance, log-likelihood and
Akaike Information Criterion (necessary for model comparison).
The major difference between arima and ar is that arima estimates an intercept term because
it does not subtract the mean value of the series. Hence we need to be careful when carrying out
predictions using the arima command. We will return to this point later.
As a quick check we are going to calculate confidence intervals for ˆβ 1 :
> 0.6023 + c(-1.96, 1.96)*0.0827