# What's statistic should I use to determine if Time Series A (economic) is a leading indicator of Time Series B (Sales)

I'm trying to utilize economic and industry data to forecast sales of industrial companies. I have numerous economic and industry indices and as a first step I would like to indentify those indices that are good leading indicator for sales. I have already utilized graphing, but I was hoping there was a statistic that would also provide some insight.

Some preliminary research has uncovered the Granger Causality statistic, but I was hoping to see if there were any other recommended alternatives or to confirm that Granger Causality is the current best practice.

Any input or suggestions would be greatly appreciated.

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For the record: the concept of Granger causality is introduced in the context of vector autoregression models, and aims at linking two (or more) time-series. If for two series $y_t$, $z_t$, $t=1,\ldots,T$, an AR model is built as $$y_t = a_0 + \sum_{j=1}^k b_j y_{t-j} + \epsilon_t$$ and then lags of $z_t$ are added to this model as $$y_t = a_0 + \sum_{j=1}^k b_j y_{t-j} + \sum_{l=1}^m c_l z_{t-l} + \epsilon_t$$ then $z_t$ is said to Granger-cause $y_t$ if the test $H_0: c_1 = \ldots = c_m$ against a non-directional alternative $H_1: c_1^2 + \ldots + c_m^2 > 0$ rejects the null. To put it simply, the lagged values of $z_t$ help predicting the current value of $y_t$ on top of its own autoregression, so there must be something in $z_t$ that affects $y_t$. This can be (and has been) cast more formally in the context of filtrations and probability spaces, but most books would give this basic autoregression version of the concept. Hamilton (1994), Time Series Analysis is a standard econometric reference, although it is cumbersome to read.