I have 3 data sets. one is the water level of a lake at 15min intervals, one is the water level of a pond next to the lake (also at 15min intervals) and one is the wind speed over both the lake and the pond.

I want to try and determine if there is a relationship between 1) the changing lake level and the level of the pond. 2) if there is a relationship between the wind speed and the lake height 3) if the wind is effecting the lake weather this is translating to a delayed influence on the pond level. is there anything (like time series analysis) or something beyond plotting a basic r curve that i can do to determine the strength of any relationship present? Any advice would be greatly appreciated Thankyou!


Why don't you try a vector autoregression (VAR) where change in lake level and change in pond level are dependent variables and wind is independent variable?

(I suspect lake level and pond level may be integrated time series, thus I suggest using change rather than level itself. If they are not integrated but stationary, then just use levels. You can test for integration versus stationarity using a unit root test like Elliot, Rotherberg & Stock unit root test or augmented Dickye-Fuller test. Also, there is a third possibility: time series are integrated and cointegrated. You can test that with Johansen's test, for example. In this last case, you would use vector error correction model (VECM) instead of VAR. I am not an expert in water level systems, so I cannot tell upfront whether stationarity, integration or cointegration of your time series is the most likely situation.)

By including multiple lags of your variables in the VAR you will see which lags are significant; this way you will be able to assess how long it takes for one variable (e.g. lake level or wind speed) to affect another variable (e.g. pond level).

The estimated coefficients of the VAR will give you useful information about the strength of the relationships.

Also, try impulse-response analysis given the estimated VAR model. There you will be able to see what happens to the endogenous variable of interest (e.g. change in pond level) over time if there is a shock (an impulse) in one of the equations (e.g. a shock to change in lake level). Try to graph impulse responses to get a flavour of how the effect of the impulse is spreading through across the system.


  • Elliott, Graham, Thomas J. Rothenberg, and James H. Stock. "Efficient Tests for an Autoregressive Unit Root." Econometrica 64.4 (1996): 813-836.

  • Said, Said E., and David A. Dickey. "Testing for unit roots in autoregressive-moving average models of unknown order." Biometrika 71.3 (1984): 599-607.

  • Johansen, Søren. "Statistical analysis of cointegration vectors." Journal of economic dynamics and control 12.2 (1988): 231-254.

  • Zivot, Eric, and Jiahui Wang. Modeling Financial Time Series with S-PLUS®. Vol. 191. Springer, 2007. This nice time series textbook does not require much previous knowledge and is available freely at http://faculty.washington.edu/ezivot/econ589/manual.pdf

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