Interpolation prediction error of missing data in time series using interp1

I am using linear interpolation to fill in the missing data in my 1D time series. The consecutive missing samples comprise only 3% of the whole time series. Using interp1 to fill in the missing gaps I would like to say something of the accuracy of the method. Is there a way to tell how good my estimated values are, i.e. the prediction error of the estimated values or an upper error bound that tells how much the estimated samples can vary maximally?

Answer 1

[Star Strider]

I doubt it would be possible to predict with any accuracy the values interp1 provides, unless you know the process that created your data and have a model for it. However in that instance, you could just fit the model and not have to use interp1. Several Statistics Toolbox functions provide specific estimates for the prediction error. (One that provides it explicitly is nlpredci.)

The problem in doing this with interp1 is that it only fits a small number of points (generally from 2 to 4). Estimating the prediction error would likely be difficult, because with so few data, the residual errors and thus the covariances would be very small or zero, producing a very small or zero prediction error. How accurate this prediction error estimate would be in terms of your entire time series would be impossible to determine without modeling the entirety of your time series, and of course in that instance, you would not need interp1.