Standard errors for estimates of smoothing parameters My question is based on the "forecast"  package for R used in Forecasting with Exponential Smoothing. The State Space Approach - Hyndman et al. 2008. I am using the ets function to estimate the parameters of a model. 
Is there a way to obtain standard errors for the estimates of the smoothing parameters? 
 A: Not all methods lead to analytic expressions (preferably based on proper asymptotic results) that provides this.
But the bootstrap allows you to approximate this via simulation. In essence, you generate (lots of) surrogate 'fake' data sets, employ your estimator on each of these and then use the population of your estimates to make inferences.  However, doing bootstrapping in a time series context has its own challenges...
A: The ets() function uses maximum likelihood estimation. So it would be possible to obtain standard errors based on the Hessian matrix in the usual way. However, in forecasting, the value of the model parameters is usually of very limited interest -- what we care about are the forecasts and their variances. 
I can't think of a situation where you might want a confidence interval for a smoothing parameter, for example. What could you do with the information that the "true" value of alpha (whatever that means) lies between 0.2 and 0.4? 
Consequently, I have not included the calculation of the standard errors of parameters in the package.
