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I am attempting to perform a CCF analysis between a predictor time series(P_a_cm) and a response time series (delta_total_cm) which represent annual precipitation and annual water table elevation change (one observation per year), respectively. My task is to asses if water table elevation change is dependent on precipitation inputs AND if precipitation inputs from antecedent years have any effect on a given years water table elevation change. When looking at the the acf/pacf for the predictor I find no auto-correlation and have also determined the time series to be stationary. The response time series on the other hand produces the following acf/pacf plots...

Response ACF

Response PACF

My understanding is that these plots are indicating auto-correlation at lag 1 for this time series. I have found plenty of information on prewhitening, however it always assumes there is auto-correlation or a trend in the predictor, which you would account for and then use to filter your response variable.

My question is do I need to do anything about the auto-correlation in the response time series or can I safely run the ccf simply using the two original time series? When i do this, it returns...

CCF: Raw Data

I feel the correlation at lag -1 is likely a result of this auto-correlation.

I attempted to apply an AR(1) to the response time series and then filter the predictor using that model, however, it resulted in a CCF that suggested hydrologicly implausible relationships.

Any direction would be greatly appreciated.

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  • $\begingroup$ It depends on what exactly you want to learn from your data. $\endgroup$ Commented Apr 5, 2023 at 10:22
  • $\begingroup$ @Richard Hardy. thanks for the reply. so my task is to asses if there is correlation between the independent (rain) and dependent (water table elevation) variables. Namely, is water table elevation change dependent on the precipitation input in a given year AND does the precipitation input in a given year affect the water table change in the next year. $\endgroup$
    – istheflesh
    Commented Apr 5, 2023 at 16:10
  • $\begingroup$ I think you could build an ARDL model and test for Granger causality. If the past of (change in) the precipitation input explains (change in) the current water table level beyond what is explained by its own past, then the former Granger-causes the latter. $\endgroup$ Commented Apr 13, 2023 at 15:22
  • $\begingroup$ This looks like it might have been a good route. I ended up just using the ccf results and my own background knowledge of the system I am modeling to identify possible lag relationships and built some regression with ARIMA error models using those lags as regressors. My committee was pleased with the results, so I am going to leave it at that for now. Thanks for the information! $\endgroup$
    – istheflesh
    Commented Apr 15, 2023 at 0:25

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My understanding as of now is that no prewhitening is necessary since the dependent variable already lacks auto-correlation or trend; in fact, it may actually wind up masking relevant lag relationships. The CCF is a tool used to help identify possible lags that might be useful in whatever model you are building, it's not the model itself. I think I was simply confused about how I should be using them.

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