My data is a time series of employed population, L, and the time span, year.
n.auto=auto.arima(log(L),xreg=year)
summary(n.auto)
Series: log(L)
ARIMA(2,0,2) with non-zero mean
Coefficients:
ar1 ar2 ma1 ma2 intercept year
1.9122 -0.9567 -0.3082 0.0254 -3.5904 0.0074
s.e. NaN NaN NaN NaN 1.6058 0.0008
sigma^2 estimated as 1.503e-06: log likelihood=107.55
AIC=-201.1 AICc=-192.49 BIC=-193.79
In-sample error measures:
ME RMSE MAE MPE MAPE
-7.285102e-06 1.225907e-03 9.234378e-04 -6.836173e-05 8.277295e-03
MASE
1.142899e-01
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
why does this happen? Why would auto.arima selects the best model with std error of these ar* ma* coefficients Not a Number? Is this selected model valid after all?
My goal is to estimate the parameter n in the model L=L_0*exp(n*year). Any suggestion of a better approach?
TIA.
data:
L <- structure(c(64749, 65491, 66152, 66808, 67455, 68065, 68950,
69820, 70637, 71394, 72085, 72797, 73280, 73736, 74264, 74647,
74978, 75321, 75564, 75828, 76105), .Tsp = c(1990, 2010, 1), class = "ts")
year <- structure(1990:2010, .Tsp = c(1990, 2010, 1), class = "ts")
L
Time Series:
Start = 1990
End = 2010
Frequency = 1
[1] 64749 65491 66152 66808 67455 68065 68950 69820 70637 71394 72085 72797
[13] 73280 73736 74264 74647 74978 75321 75564 75828 76105
Best Answer
The sum of the AR coefficients is close to 1 which shows that the parameters are near the edge of the stationarity region. That will cause difficulties in trying to compute the standard errors. However, there is nothing wrong with the estimates, so if all you need is the value of $L_0$, you've got it.
auto.arima()
takes a few short-cuts to try to speed up the computation, and when it gives a model that looks suspect, it is a good idea to turn those short-cuts off and see what you get. In this case:This model is a little better (a smaller AIC for example).