# Modelling currency exchange rates timeseries data across re-denomation dates

I am working with data for an exotic currency, that has been re-denominated a couple of times during the twenty years of data that I have.

What is the best way of 'normalising' the data, so that I can work with the data, although it contains two 'switch over' dates on which the currency was re-denominated?

• Belarusian ruble ? :)) – IharS Aug 22 '14 at 12:48

You are working with a time series $x(t)$ which has been re-denominated at times $t_1$ and $t_2$. You want to rescale the time series for all times $t < t_2$.
First, do you know what the rescaling factors ($k$) should be (e.g. did 1000 units turn into one unit)? If not, I would set $k_2:= t_2^+ / t_2^-$, where $t_2^-$ is the last currency rate before the last rescale, and $t_2^+$ is the first data point after the rescale. For all $t < t_2$, multiply all $x(t)$ by $k_2$. Do the same thing around $t_1$: set $k_1:= t_1^+ / t_1^-$ (if you have no other information on $k_1$) and then for all $t < t_1$, multiply all $x(t)$ by $k_1$.