I have been trying to simulate from a time series with trend but I don't see
how to include the trend in the arima.sim() call. The following code
illustrates the problem:
# Begin demonstration program
x <- c(0.168766559, 0.186874000, 0.156710548, 0.151809531, 0.144638812,
0.142106888, 0.140961714, 0.134054659, 0.138722419, 0.134037018,
0.122829846, 0.120188714, 0.122060497, 0.137424358, 0.113311269,
0.125051374, 0.103707302, 0.089999121, 0.094848588, 0.100941354,
0.096845633, 0.072098064, 0.081167803, 0.068140319, 0.063988361,
0.053722446, 0.051986886, 0.044317196, 0.032021664, 0.023656304,
0.025620223, 0.012297433, -0.003523446, -0.005782116, -0.027448303,
-0.034745961, -0.042594172, -0.058662672, -0.072392916, -0.089123923,
-0.093551415, -0.105782822, -0.117481560, -0.126549691, -0.141332587,
-0.158428491, -0.166864452, -0.167363354, -0.177367386, -0.198326344,
-0.218109541, -0.232391155, -0.237220250, -0.244477140, -0.255906978,
-0.279480229)
# Fit arima(p=1,d=2,q=1)
Arima <- arima(x, order = c(1,2,1))
Arima$coef
# Simulate from the fitted model:
set.seed(1)
x.sim <- arima.sim(list(order = c(1,2,1), ar = Arima$coef[1], ma =
Arima$coef[2]), n = 1000, sd = sqrt(Arima$sig))
Arima2 <- arima(x.sim, order = c(1,2,1))
Arima2$coef
# We recover the ar and ma coefficients but we haven't included the drift
# in the simulation so the simulated series is well wide of the mark. The
# following plots demonstrate how wide:
par(mfrow = c(1,2))
plot(ts(x), main = "Data")
plot(x.sim, main = "Simulated data")
# End demonstration program
The documentation for arima.sim() isn't terribly clear on this area. Any
ideas?
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