Sampling from interdependent data set I have a simulation model with trains entering at the limits of the simulation part way into their trip.  I have sourced real-world data which provides the variation in the arrival time of these trains relative to their scheduled time. For trains, the lateness of a train is not independent of the previous trains arrival. I have calculated a correlation coefficient of up to 0.50 for some locations, meaning that you can get a pretty good estimate of the next trains lateness based on the lateness of the last train.  If I blindly randomly sample from the data set, this interdependence would vanish, and I could even have very early trains following very late trains, creating an impossible out-of-order situation.
What techniques are there for sampling from interdependent time series data like this?
Should I create a simple linear regression with added randomness as a fit to the data? Should I sample real world clusters of multiple data points instead of sampling one at a time?
I have searched, but I haven't been able to find any literature, perhaps because I do not know the correct terminology. I would expect that this is a common problem in sampling from economics and scientific datasets
 A: Answering my own question:
I will use an autoregression model to generate values.  The autoregression model uses the previous 'lag states', the number of lag states would be 1 if we only care about the previous train, as in the example I asked about.  When the number of lag states is 1, it is a 'random walk' model.  Researching my data set further, I saw that using multiple previous train latenesses could improve the model so it is better than a random walk.  The randomness in the autoregression model comes from adding a white noise or 'shock' term (epsilon) to the regression.  The random values for the epsilon term need to be set to match the distribution of the residuals when the model is applied against the data.  (First plot the residuals and check if the residuals appear to not be random in the plot, that would be a sign that the linear autoregression model is not a good fit. In my case they were random, so the autoregression model is reasonable.)
The equation used to generate values for the random walk case is:
y(t) = C_1 * y(t-1) + epsilon
If more lag states are included, then additional C_n*y(t-n) terms are included.  The epsilon values can be generated for the size of the sample dataset and then used to prime the model.  The earliest values in the dataset less than the number of lag states shoudl be excluded. Once the model has been used to generate values, the distribution should be compared against the original to see how well it matches.
