Using Lagged Correlation and Granger Tests to Study Lead-Lag

Summary

The document introduces statistical methods for investigating whether one time series tends to lead another. Lagged correlation, also called cross-correlation in this context, measures association after shifting one series relative to the other. Examining whether past values of one series are associated with a later value of another can help assess its potential predictive usefulness. The answer also points to lagged regression as a related method.

For a broader analysis, it recommends fitting a vector autoregression (VAR) to the variables and testing Granger non-causality. This tests whether the lagged values of one series add predictive information for another within the model. The response provides no data, test statistics, or guidance on selecting lags. Correlation and Granger tests can identify temporal predictive relationships, but the document does not establish that such relationships are causal or stable out of sample.

Key ideas

• Lagged or cross-correlation measures association between time series shifted relative to one another.
• A shifted series can be examined as a potential predictor of later values in another series.
• Lagged regression is another way to study lead-lag relationships.
• A vector autoregression can be used to test Granger non-causality between variables.
• These methods assess predictive relationships and do not by themselves establish causation or out-of-sample stability.

Tags

# detecting and measuring lead lag effect


# detecting and measuring lead lag effect












Given two time series data. I remember there is one statistics that tells you one is the leading factor while the other is the lagging factor. However, i do not remember the exact details. correlation is part of its name. I wonder if any one here could help me out. Thanks.

## Answer by Simon (score 4, accepted)

https://quant.stackexchange.com/a/14868

You may want to take a look at lagged correlation or cross correlation. Lagged correlation refers to the correlation between two time series shifted in time relative to one another. This measure is useful for studying whether a lagged time series $x_{t-k}$ can be viewed as a good predictor for $y_t$. If you are familiar with R, then you may find the following two links on cross correlation, lagged regression useful: Cross Correlation Functions and Lagged Regressions and Cross-correlation as Leading indicator.

As suggested by Professor Eric Zivot, we can also generalize the approach as follows: one can estimate a vector autoregression involving your variables of interest and then test for Granger non-causality. See the vars package and in particular the causality() function.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.