Multiplicative ARIMA model

Question

Given this ARIMA model:

(1-0.8B)*(1-0.2B^6)*(1-B)Y_t = epsilon_t

Where the multiplicative model is (1,1,0*(1,1,0)_6 (seasonal component=6). Is there any tool to predict new values from this model (such as the 10th or 11th values) given some initial set of values such as :

y <- c(1,4,5,2,0,8,9,4,-3,-3)

I tried

arima(y,order=c(1,1,0),seasonal=list(order=c(1,1,0),period=6))

 error: initial value in 'vmmin' is not finite

Answer 1

You can predict ahead with the predict() function:

> y=c(1,4,5,2,0,8,9,4,-3,-3)
> mymodel = arima(c(1,4,5,2,0,8,9,4,-3,-3) ,order=c(1,1,0),seasonal=list(order=c(1,1,0), period=2))
> mymodel

Call:
arima(x = c(1, 4, 5, 2, 0, 8, 9, 4, -3, -3), order = c(1, 1, 0), seasonal = list(order = c(1, 
    1, 0), period = 2))

Coefficients:
         ar1     sar1
      0.7368  -0.9169
s.e.  0.3696   0.1089

sigma^2 estimated as 11.25:  log likelihood = -20.23,  aic = 46.46


> predict(mymodel, n.ahead = 5)
$pred
Time Series:
Start = 11 
End = 15 
Frequency = 1 
[1]  -7.763438 -16.104376 -25.686464 -28.419524 -35.086436

$se
Time Series:
Start = 11 
End = 15 
Frequency = 1 
[1]  3.354151  6.722215 10.392430 14.061929 19.640317

I reduced the period so that your model has a sufficiently long data vector.