I have time-dependent data from experiments done by two different labs. Lab1 has measurements at 60 different time-points. Lab2 has measurements at 40 different time-points (within the same range as Lab1 but not exactly the same time-points). I fitted the splines for data from Lab1 and Lab2. The curves look very similar. I would like to test if the fits/data are significantly different. I would like to answer the question if the difference between the results from both labs is statistically significant. What type of test I should use?
Well one really helpful answer has been already given here. However I am not sure that you have gaussian modeling in your time series. A known test you can use is the Granger Causality test, however it seems that you do not want to predict Lab2 from Lab1, so I just state it to be safe.
Otherwise, study these two posts: 1, 2. I would standardize the time series (by scale) and then use interpolation in order to split each series in the same time-points in order to use an ARIMA model. ARIMA models can describe each series separately as stated here.