Data | RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data

RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data 3. Data

Martin McCarthy and Stephen Snudden

December 2025

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The dataset includes real-time monthly vintages of daily bilateral and effective exchange rates, both nominal and real. While daily bilateral exchange rates are widely available, and the BIS publishes daily NEERs for a subset of countries, our dataset is the first to include daily REERs and to construct real-time vintages of EERs that account for the publication delays of trade weights. The daily EERs are computed consistently across countries using IMF trade weights and formulas.

For each type of exchange rate and country, we construct one real-time vintage of daily frequency per month, intended to reflect all information that would have been available to a forecaster at the end of the month. Our decision to construct real-time vintages is not motivated by data revisions, since NERs, CPIs, and trade weights are rarely revised. Rather, our aim is to reflect the typical delays in the publication of CPI and trade weight data.

From each vintage of daily data, we construct corresponding vintages of month-average and end-of-month exchange rates. These are derived directly from the daily observations available in each vintage.

3.1 Monthly vintages of daily frequency exchange rates

Section 3.1.1 describes the calculation of bilateral NERs and bilateral RERs. Section 3.1.2 describes the calculation of NEERs and REERs. Detail on the inputs into these calculations (bilateral NERs, CPIs and trade weights) is provided in Appendix B.

3.1.1 Bilateral exchange rates

Constructing monthly vintages of bilateral NERs is straightforward. Bilateral NERs are available daily and observed in real time. As such, a bilateral NER vintage for a month is simply the daily NER on each day until the end of that month. For example, the March 2023 vintage of Canada's bilateral NER is simply its daily bilateral NER on each day up to 31 March 2023.

To construct monthly vintages of daily bilateral RERs we need data on both daily bilateral NERs and monthly CPI. To describe the calculations precisely, we introduce some notation. Let $N E R_{t}^{i}$ denote the bilateral NER of country i on day t. This is the value of the currency in terms of US dollars. Let $C P I_{m}^{i}$ denote the CPI level in country i in month m. Finally, let $R E R_{t}^{i}$ denote the bilateral RER of country i on day t. This is the cost of goods and services in country i relative to the cost of goods and services in the United States.

The daily bilateral RER on day t of month m is the daily bilateral NER of that country multiplied by the ratio of country i's CPI level to the US CPI level:

(1)

R E R_{t}^{i} \equiv N E R_{t}^{i} \times \frac{C P I_{m}^{i}}{C P I_{m}^{US}}

An alternative approach would have been to combine the daily nominal price with daily CPI levels, where the daily CPI levels have been estimated by interpolating monthly levels. We constructed the daily bilateral RER using Equation (1) because it is more transparent than the alternative, since it avoids needing to take a stand on how to perform the interpolation. The forecast results are qualitatively robust to alternative CPI assumptions, since fluctuations in CPI are typically dwarfed by movements in exchange rates.

A complication is that CPI data is published with a lag that differs by country. For example, as at the end of March 2023, the latest CPI data for the United States or Canada is for February 2023, which is a one-month lag. In contrast, some low- or middle-income countries may only publish their CPI two or three months later. When constructing a monthly vintage, we only use the monthly CPI data likely to have been known at the time. The CPI data are from the World Bank dataset; see Appendix B.2 for complete details. For consistency, we construct our own real-time vintages and nowcast the missing monthly CPI levels by assuming that CPI inflation remains constant at the latest rate known at the time.

3.1.2 Effective exchange rates

We also construct monthly vintages of daily EERs. This is more complex, both because a number of EER formulas are available, and because we only want each vintage to be constructed using CPI and trade weight data available at the time.

We compute daily EERs by adapting the formulas used for monthly EERs by the IMF. We use the IMF's method because we want our method to be consistent with our choice of weights, and we use the IMF weights because they are the most comprehensive in terms of countries and time periods. Other institutions use different formulas for computing EERs.^[4]

To describe our method, we must define some terms. We use the term ‘reporter’ to refer to the country whose EER we are computing, and we use the term ‘partner’ to refer to any other country included in the calculation. The ‘weight reference period’ is the period of a few years with which a set of weights is associated. For example, there is a set of weights based on the trade flows during the ‘2010–2012’ weight reference period (see Appendix B.3 for details). Let $w_{r, j}^{b}$ denote the weight that reporter r puts on partner j in weight reference period b.

If we only have data for a single weight reference period, then we can compute the daily EER using a ‘fixed weight’ formula. Equation (2) is used to compute the daily REER of a reporter r on a day t in month m and weight reference period b. The numerator is the reporter's NER in US dollars multiplied by the reporter's price level. To compute the denominator, we multiply each partner's NER in US dollars with that partner's price level, and then aggregate across partners. To compute the NEER, simply set the CPI terms equal to 1.

(2)

R E E R_{t}^{r, b} = \frac{N E R_{t}^{r} \times C P I_{m}^{r}}{\exp (\sum_{j = 1}^{J} w_{b}^{r, j} \ln (N E R_{t}^{j} \times C P I_{m}^{j}))}

For each weight reference period, we only use partners whose exchange rates are available on all days in the period.^[5] Additionally, if over half of partners by weight have missing exchange rates for a weight reference period, then we don't compute the REER for that period.

Typically, we want to compute the EER over a longer time period that spans multiple weight reference periods. In this case, we compute an EER by ‘chaining’ the fixed-weight indices, as described in Appendix C.

3.2 Monthly vintages of monthly exchange rates

We derive month-average and end-of-month series from the daily series. For each vintage of daily exchange rates (of any type), we make a corresponding vintage of month-average exchange rates (by averaging the daily rates over each month) and a vintage of end-of-month exchange rates (by extracting the last daily rate of each month).

For bilateral RERs, an alternative would be to apply the bilateral RER formula to a month-average NER and a monthly CPI. However, this is exactly equivalent to our approach of computing an average of daily bilateral RERs. To see this, let t = 1,..., n index the days in a month.

R E R_{m}^{i} = \frac{1}{n} \sum_{t = 1}^{n} R E R_{t}^{i} = \frac{1}{n} \sum_{t = 1}^{n} (N E R_{t}^{i} \times \frac{C P I_{m}^{i}}{C P I_{m}^{US}}) = (\frac{1}{n} \sum_{t = 1}^{n} N E R_{t}^{i}) \times \frac{C P I_{m}^{i}}{C P I_{m}^{US}}

Similarly, one could instead compute NEERs by applying the EER formula to month-average NERs, or compute REERs by applying the formula to month-average NERs and monthly CPI. This alternative approach gives EERs whose growth rates are very close to those from our chosen approach, except during periods of hyperinflation.

Footnotes

For REERs, the formulas differ in how they combine NERs and prices. For example, the approach used by the BIS is to aggregate the bilateral nominal exchange rates to obtain an NEER, separately aggregate the price levels, and then compute the REER by adjusting the NEER by aggregate price levels (Turner and Van ‘t dack 1993; Klau and Fung 2006). The IMF's previous approach was to directly aggregate the bilateral RERs (Bayoumi, Lee and Jayanthi 2006). In contrast, the IMF's current approach is to compute the REER as a ratio of products of bilateral NERs and CPIs. Moreover, for both NEERs and REERs, the formulas differ in how they aggregate across countries, which affects the properties of the series. For example, Vartia and Vartia (1984) show that the NEER used by the Bank of Finland at the time had an upward bias, unlike alternative index number formulas such as a Fisher index or Tornqvist index. [4]

An exception is that, when computing EERs over the 1990–1995 weight reference period, we compute EERs from 1990 to 1992 using partners whose exchange rates are available from 1990 to 1992, and then compute REERs from 1993 to 1995 using partners whose exchange rates are available from 1993 to 1995. This materially increases the number of partners included in the 1993 to 1995 calculations, because the number of countries with NER data increases materially from the start of the IMF NERs on 1 January 1993. [5]