What are the simplest methods to check for the lead and lag relationship between two variables?
I mean.. how to see, between two variables, which leads the other (and which follows) ?
Contents
hide
Best Answer
Calculate the cross correlation
$$frac{Eleft[ [f(m) – mu_f] [g(m + n) – mu_g] right]}{sqrt{Eleft[ [f(m) – mu_f]^2right]Eleft[ [g(m + n) – mu_g]^2 right]}}$$.
where $mu_f$ and $mu_g$ are the means of $f$ and $g$, respectively.
Note that this is a function of $n$, the relative lag, and that $n$ can be both positive or negative. If $f$ is leading (lagging) over $g$, then this should be significantly positive for some positive (negative) value of $n$.
This is a common first step in econometric lead-lag analysis.
Similar Posts:
- Solved – Variance of the modulus of a random variable
- Solved – Convergence of expectation
- Solved – Constructing example showing $mathbb{E}(X^{-1})=(mathbb{E}(X))^{-1}$
- Solved – Negative relationship but regression analytics gives positive correlation coefficient
- Solved – Interpreting output from cross correlation function in R