Adjusting Currency Time Series for Redenominations
Summary
The document addresses how to make a long exchange-rate history comparable when a currency has been redenominated more than once. It treats each redenomination as a scale change, similar to adjusting historical prices for a reverse stock split. If official conversion ratios are known, those ratios can be applied to earlier observations so the full series uses a consistent unit.
When the ratios are unknown, one response suggests estimating each adjustment from the exchange-rate observations immediately before and after the change, then rescaling all earlier data cumulatively. This provides a practical way to remove discontinuities caused by a change of denomination. The answer is brief and does not discuss whether market moves occurred around the switch, how to handle missing or noisy observations, or how to validate inferred ratios. Those estimates should therefore be treated as assumptions when the official conversion terms cannot be confirmed.
Key ideas
- A redenomination changes the scale of quoted currency values, so historical observations may need adjustment.
- Known conversion ratios can be applied to earlier data to express the series in consistent units.
- If ratios are unavailable, the suggested fallback estimates each factor from observations around the switch date.
- Adjustments across multiple redenominations must account for each earlier scale change.
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Full text
# Modelling currency exchange rates timeseries data across re-denomation dates # 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? ## Answer by GNUser (score 3, accepted) https://quant.stackexchange.com/a/14503 How is this different than a reverse stock split? If you just want the same scale for all the data, you'd just have to update the historic data using the reverse split ratio. ## Answer by rupweb (score 0) https://quant.stackexchange.com/a/14502 why not run the same time series 3 times, once for each data set? ## Answer by Shahar (score 0) https://quant.stackexchange.com/a/14516 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 $k_1$. Good luck!
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