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I've been learning about time series analysis because I want to understand how much groundwater level changes in an aquifer affect land subsidence (land sinking). I have two time series: (1) measurements of aquifer water levels and (2) measurements of relative land surface movement. Both series are regularly sampled; monthly measurements for 40 years (480 observations).

First, I decomposed each of the time series for exploratory purposes (the series seemed like "trend stationary"). Then conducted ADF tests to check for stationarity, for which I found they're not. Proceeded to run ADF tests on the 1st differences for each time series and found that the differences are stationary. Finally, I ran a cross-correlation on the differences and got that the series are correlated at different lags.

From the literature, I know that groundwater levels influence land surface elevation. Just by looking at the plots, I can see that the rate at which the land was sinking has slowed down and reversed as the aquifer water levels recovered over time.

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After all the time series analysis research I've done, I still cannot grasp how to get at an estimate of the percent of the variation in land surface movement explained by groundwater level.

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  • $\begingroup$ You could continue your analysis by regressing the growth-rates (first differences of the logarithms) of the dependent variable on the growth-rates of the other variable. The estimated coefficient will give you a measure of the linear relationship between the variables and an estimate of how the dependent variable changes when the explanatory variable increases in one infinitesimal unit. $\endgroup$ – javlacalle Dec 20 '14 at 10:40

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