RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data Appendix C: Calculation of Chained EER

Section 3.1.2 explains how we calculate an EER for a period with a single weight reference period. However, typically, we want to compute the EER over multiple weight reference periods. In this case, we compute an EER by ‘chaining’ the fixed-weight indices. The chained EER is set equal to 1 on the first day of our sample. For each subsequent day, the growth in the chained EER is set equal to the growth in the relevant fixed-weight EER. Formally:

where b is the weight reference period that contains day t.

This formula ensures that the numerator and denominator both use the same set of weights. For example, if we compute growth in the United Kingdom's chained EER on 1 January 1996, which is the first day of the ‘1996–2003’ weight reference period, we would compute:

To compute the chained REER on 31 December 1995, which the last day of the ‘1990–1995’ weight reference period, we would compute:

For each monthly vintage, we compute daily EERs by applying the above formulas to the data that a forecaster would have had access to as at the end of each month. This includes daily NERs that are published without delay, and the nowcasted vintage of monthly CPI. Trade weights are assumed to be unavailable for five years after the end of the period to which the weights relate (see Appendix B.3). For example, the trade weights based on 2013–2015 trade flows are assumed to become available from the January 2021 vintage onwards. We assume a five-year lag to emulate current practice at the IMF, since they are our source of trade weights.