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I'll set this question up as a simplified example:

We hypothesize that there is a causal relationship between average gasoline prices and road traffic in a particular city. The data cover the same time period at the same frequency (e.g.: weekly) and contain no missing values. We'll put aside the idea that there could be confounding variables at work, presume that we've made the time series stationary (via differencing), and determine there is no autocorrelation in the series.

What are reliable methods to determine that if a shock occurs in the price data that a corresponding shock occurs in the traffic data at some time lag?

I've looked a ;little bit into Dynamic Time Warping, but I suspect that this is better suited to determining how to map one series to another rather than for determining causality.

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I find two possible solutions: Granger Causality and Convergent Cross Mapping (CCM).

Granger Causality is based on the t-test of lagged value of first variable with the second variable. The limitation is that it could not eliminate the confounding effect.

The CCM first build the manifold for the first variable X. Then for each time point, weights of neighbors are estimated, and used to estimate Y. Then correlation between estimated Y and Y are tested.

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