Cross Correlation Analysis (CCF)

Cross-correlation analysis measures the correlation between one series and lagged values of another, usually after prewhitening, to identify lead-lag relations between them.

교차상관 분석은 한 시계열과 다른 시계열의 시차 값 사이의 상관을, 대개 사전백색화 후에 측정해 두 시계열의 선행·후행 관계를 찾는 방법이다.

Does advertising spending lead sales, and by how many weeks?

광고비가 매출을 몇 주 앞서 움직이는지 알고 싶어요.

The cross-correlation function gives the correlation of the input at time t with the output at time t + k for each lag k. Prewhitening both series with an AR filter fitted to the input removes spurious correlations caused by autocorrelation.

When to use Cross Correlation Analysis (CCF)

• You want to find the lag at which one series relates to another.
• You are building a transfer-function or distributed-lag model.
• Both series are measured at the same equally spaced times.

When to use something else

• You want to test whether one series improves prediction of another; use the Granger Causality Test.
• You need the long-run effect of one series on another; use an Autoregressive Distributed Lag Model (ARDL).

Assumptions and requirements

• Both series are stationary.
• Prewhitening or white-noise input for the ±z/√n bounds.
• Linear relation between the series.
• Only the first feature is used as the input series.

What the analysis reports

• Cross-correlation at each lag with bounds
• Lag with the largest absolute correlation
• AR order of the prewhitening filter

How to report it

The prewhitened cross-correlation peaked at lag [value] (r = [value]; 95% bound ±[value]).

Related methods

• Granger Causality Test
• Autocorrelation Analysis (ACF, PACF, Ljung-Box)
• Autoregressive Distributed Lag Model (ARDL)

Run Cross Correlation Analysis (CCF) on Quorant