I have a data set which consists of 50 observed years for which I have date and inflow values between a river and a reservoir. The data is formatted as follows:

Day     Inflows
123      4356.0

I have 50 years of observed data which includes daily values for each day. The plotted data looks as follows:

Plot of inflow values for each day of 2005

Ignoring the small outlying patches of green for now, I'm looking for a method of simulating the green portion of the curve (which represents the spring runoff period) so that I can do a series of model runs with simulated spring inflows.

I'm hoping that someone might be able to point me towards a 'standard' method for approaching this kind of problem. There is extensive variation between the years in the data set (drought years show very little change between the blue and green portions of the year). What are some methods for approaching generating data like this?

Let me know if there is any other information that I can provide. I'm quite new to this kind of problem so I'm unsure what would be most useful.


2 Answers 2


One possibility is to fit a time series model to the data you are interested in. Then you can resample the residuals from the fitted model and use them to simulate the data. For example, you can fit an ARIMA model, resample the residuals and then generate new data from the fitted ARIMA model. Instead of generating the innovations from a Gaussian distribution you would use the resampled residuals.

You can find further details searching in the literature about bootstrapping time series. See for example this post and the references mentioned there.

You should take care of events that you mention such as drought years or other particular events. Those events may be exceptional for a particular year or may be cyclical patterns observed in the data. You should choose an appropriate intervention variable to capture these effects in the model. Alternatively, you may fit a model for each subsample where the data remain relatively stable with no breaks or changes in the variance.


I suggest you first determine that you wanna predict for one day, one month or one year, next think about situation that effect in your goal variable, and if you could use variable from external database like temperature, and as our friend says use time-series models. I think preparation data is more important modeling. don't forget that do smoothing on your data.


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