I am working on some exchange rates data. I have two series:
- $X_t$ with the official exchange rate (e.g. forex)
- $Y_t$ with the exchange rate on the "black market" (e.g. currency exchange houses at airports).
I am interested in modelling the relationship between these two series. It is reasonable to model $Y_t$ as a function of $X_t$ and lagged values of this series (because the black market kinda follows the official market). I would like to get insight on two questions:
- Average lag in the response of the black market (how long does it take for currency exchange houses to react to changes in the official market).
- The magnitude of the reaction (do currency exchange houses overreact?, or they kind of smooth the movements in the official market?)
Here's how the data looks like:
I've read that the "cross correlation function (CCF) is helpful for identifying lags of the $X$-variable that might be useful predictors of $Y_t$". (link)
So I produced such plots for 20, 50 and 150 lags (I have in total 520 obs) with the following code in R .
ccf(x = toy$xa, y = toy$ya, lag.max = 20) ccf(x = toy$xa, y = toy$ya, lag.max = 50) ccf(x = toy$xa, y = toy$ya, lag.max = 250)
And here's how they look:
Does it mean that up to 170 lags might be useful predictors?, or am I doing something wrong?