# Calculating forecast error with time series cross-validation

I have a forecasting model for a time series and I want to calculate its out-of-sample prediction error. At the moment the strategy I'm following is the one suggested on Rob Hyndman's blog (near the bottom of the page) which goes like this (assuming a time series $y_1,\dots,y_n$ and a training set of size $k$)

1. Fit the model to the data $y_t,\dots,y_{t+k-1}$ and let $\hat{y}_{t+k}$ be the forecast for the next observation.
2. Compute the forecast error as $e_{t} = \hat{y}_{t+k} - y_{t+k}$.
3. Repeat for $t=1,\dots,n-k$
4. Compute the mean square error as $\textrm{MSE}=\frac{1}{n-k}\sum_{t=1}^{n-k} e_t^2$

My question is how much I have to worry about correlations because of my overlapping training sets. In particular, say I want to forecast not only the next value, but the next $m$ values, so that I have predictions $\hat{y}_{t+k},\dots,\hat{y}_{t+k+m-1}$ and errors $e_{t,1},\dots,e_{t,m}$, and I want to construct a term-structure of prediction errors.

Can I still roll the window of the training set forward by 1 each time, or should I roll it forward by $m$? How do the answers to these questions change if there is significant autocorrelation in the series that I'm predicting (conceivably it is a long-memory process, i.e. the autocorrelation function decays as a power law rather than exponentially.)

I'd appreciate either an explanation here, or links to somewhere where I can find theoretical results about the confidence intervals around the MSE (or other error measures).

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Mybe you have a answers with hv block cross validation for autocorrelated data –  grant Nov 4 '11 at 19:00