RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data 2. Literature Survey

This literature review offers a comprehensive survey of research forecasting effective and bilateral exchange rates. We complement other surveys in the exchange rate literature (Frankel and Rose 1995; Rogoff 1996; Engel et al 2007; Rossi 2013) by reporting the temporal assumptions used in each study. We report the frequency and temporal sampling of the data of the forecast target, in estimation, and the benchmark against which forecasts are evaluated. For each paper, we assess the type of exchange rate targeted, including if real or nominal and if in levels or returns. We confine our examination to papers published or accepted for publication as of 2023. We also record if forecast analysis was conducted in ‘real time’, defined as forecasts made with models estimated only on data available at the time of the forecast (e.g. Clarida and Taylor 1997). Specifically, if the exchange rates are expressed in real terms, this requires that they are computed using CPI observations that account for the lag in publication. For EERs, this requires real-time treatment of the trade weights.

As the main focus of the survey is the temporal methods used for the forecasts, our survey separately documents forecasts of point-sampled and period-average exchange rates. We also delineate studies into those that examine EERs (Section 2.1) and bilateral exchange rates (Section 2.2). In cases where papers forecast multiple types of exchange rates, we include them in each section.

2.1 Effective exchange rates

Our initial focus is on forecasts of EERs, which are prominent in macroeconomics. REERs are important because they reveal relative price levels between a nation and its trade partners, which are important for understanding trade flows. NEERs are useful summaries of a country's nominal exchange rate with its trading partners. Among other things, they can be used to forecast the extent to which nominal exchange rate movements will contribute to domestic inflation (Dornbusch 1987; Goldberg and Knetter 1997; Shambaugh 2008; Forbes, Hjortsoe and Nenova 2018).

2.1.1 Forecasts for period-average effective exchange rates

We found 19 papers that examined forecasts of period-average EERs, as summarised in Table 1. Around half of these papers concentrate on forecasts of the level of EERs rather than returns in EERs, with the focus on real versus nominal EERs also approximately split. Most studies forecast month-average EERs, although there is a recent trend towards forecasting quarter-average EERs.

We document three features of papers studying period-average EERs.

First, studies that compare the predictability of period-average EERs to that of a naive forecast have done so using the period-average no-change benchmark. This is potentially problematic, as forecast improvements relative to the period-average no-change forecast are theoretically expected for all autoregressive integrated moving average representations of the levels of daily data, including the special case of the random walk (Telser 1967; Brewer 1973; Weiss 1984; Marcellino 1999). This parallels concerns over spurious predictability for returns: Working (1960) shows that aggregation converts the growth rate of a random walk – an entirely unpredictable process – into a cumulative moving average process that is predictable based on past returns. Hence, forecasts of a period average, whether expressed in levels or returns, are expected to outperform a period-average no-change benchmark even if the underlying exchange rate is a random walk (and hence unpredictable, by definition). Since this predictability arises by construction, it has been typically referred to as ‘spurious predictability’. To avoid such spurious predictability, forecasts of period averages need to be compared against the end-of-period no-change forecast. This is because only the end-of-period no-change reflects the null hypothesis that all future exchange rates, averaged or not, are conditionally unpredictable. This is true whether one is assessing mean square forecast accuracy (Ellwanger and Snudden 2023) or directional accuracy (McCarthy and Snudden forthcoming). Moreover, the differences in the two no-change forecasts are substantial; if the daily series is a random walk, the end-of-month no-change will have mean square accuracy 44 per cent lower than the month-average no-change (Ellwanger and Snudden 2023). This calls into question the validity of the conclusions in studies whose naive no-change forecast used period-average exchange rates.

Second, the literature on period-average EERs has always used models estimated with period-average data. However, this is expected to compromise forecast accuracy due to information loss from temporal aggregation (Zellner and Montmarquette 1971; Tiao 1972; Amemiya and Wu 1972; Wei 1978; Kohn 1982; Lütkepohl 1986). The information loss is expected to be large for daily to monthly data aggregation, given the high persistence of daily exchange rates and the large number of periods aggregated over. Most of the information loss occurs when departing from no aggregation, and occurs over the first few observations (Tiao 1972). Substantial gains in forecast accuracy have been documented in practice for daily to monthly aggregations (Ellwanger and Snudden 2023; Ellwanger, Snudden and Arango-Castillo 2023). In contrast, comparisons of already aggregated frequencies, such as monthly versus quarterly, have found that the effect is small or non-existent (e.g. Zellner and Montmarquette 1971; Lütkepohl 1986; Athanasopoulos et al 2011). Consequently, the loss in forecast accuracy may be substantial for period-average exchange rates, which are based on point-sampled daily prices. The degree of the information loss is an empirical question, quantified in Section 5.

Finally, we find that no study has conducted a real-time forecast evaluation for any period-average EERs. Hence, it remains unclear if the methods proposed in existing studies would be useful in practical applications if adopted by policymakers or other forecasters. The lack of real-time forecast evaluations may reflect the absence of real-time EER data vintages that account for the delay in the publication of trade weights, a gap that we remedy with our dataset in Section 3.

2.1.2 Forecasts for point-sampled effective exchange rates

Only three studies evaluate forecasts for end-of-period EERs, see Table 2. As was the case for period-average EERs, none of the studies use real-time methods. Forecasts for end-of-period NEERs were examined by Kohlscheen et al (2017) and Zhang et al (2016). Zhang et al (2016) specifically discuss the information loss from temporal aggregation in their motivation of daily forecasts of NEERs. Additionally, Ca' Zorzi et al (2022) stand alone in examining forecasts of end-of-period REERs, which they construct for a basket of eight advanced economies. These studies compare forecasts against end-of-period no-change benchmarks and, hence, unlike the studies examining period-average exchange rates, correctly test against the null of no predictability.

The valid hypothesis testing in these papers is potentially informative on the predictability of period-average EERs. This is because, under certain conditions, a forecast for the end-of-period EER can be an excellent forecast of the period average at long horizons and at short horizons when the underlying series is persistent (Ellwanger et al 2023). However, the applicability to exchange rates is a question that can only be answered quantitatively. Due to the interest in the forecastability of period-average EERs in macroeconomics, we examine the efficiency of point-sampled forecasts for period averages for all countries in Section 5.

2.2 Bilateral exchange rates

2.2.1 Forecasts for period-average bilateral exchange rates

We now survey the literature on forecasting period-average bilateral exchange rates. Bilateral exchange rates provide insights into relative price levels between a pair of countries and are therefore relevant to flows between them. The research on period-average bilateral exchange rates comprises eighteen papers (Table 3). Only three papers examine period-average bilateral RERs, and only one of those forecasts the level. In contrast to EERs, a few papers employ real-time methods for period-average bilateral exchange rates in nominal terms (Wright 2008; Molodtsova, Nikolsko-Rzhevskyy and Papell 2008; Carriero, Kapetanios and Marcellino 2009; Abbate and Marcellino 2018) and one in real terms (Kilian and Taylor 2003).

Unfortunately, like for EERs, all papers summarised are found to compare forecasts to the period-average no-change benchmark, and never to the end-of-period no-change benchmark. As with the EER literature, forecasts are expected to outperform the period-average no-change benchmark by construction, even if the daily series is a random walk and hence unpredictable by definition. This reveals that for both bilateral and effective exchange rates, there is a critical gap in the understanding of the forecastability of period-average exchange rates. Moreover, like EERs, these studies universally use period-average inputs in estimation, potentially jeopardising forecast accuracy. In essence, our understanding of the predictability of period-average bilateral exchange rates remains limited.

2.2.2 Forecasts for point-sampled bilateral exchange rates

Lastly, we delve into the literature which has examined point-sampled bilateral exchange rates. Researchers may favour bilateral point-sampled exchange rates over bilateral period-average rates for some applications, such as in asset valuation or trade settlements at specific time intervals. Our survey documents 14 studies examining real rates and 101 studies examining nominal rates. The literature examining point-sampled bilateral RERs is presented in Table 4. We also discuss papers that have examined point-sampled bilateral NERs, for which a summary table is reported in Appendix A.

In all cases, papers are found to construct forecasts using point-sampled data and compare them to point-sampled no-change forecasts. This suggests that conclusions derived from hypothesis testing in these papers are valid, and do not suffer from the concerns of spurious predictability discussed in the previous subsections. Again, the valid hypothesis testing for RERs is potentially quite informative on the predictability of period-average bilateral exchange rates and will be quantified in Section 5.

Finally, no paper has investigated real-time forecasts of point-sampled bilateral RERs. This disparity suggests a knowledge gap regarding real-time forecasts for bilateral RERs. In contrast, since Clarida and Taylor (1997), 14 out of 101 studies of point-sampled bilateral NERs have employed real-time forecasts.

2.3 Identified gaps in the literature

In summary, there are three key findings from the survey. First, we found that the literature has yet to test the predictability of period-average exchange rates by comparing them with the no-change benchmark that reflects the random walk hypothesis. This raises questions, not only regarding the validity of the conclusions in these studies, but also on the predictability of these rates more generally. Second, we found that the literature forecasting period-average exchange rates uses models estimated on period-average inputs rather than end-of-period or daily inputs. This questions the efficiency of the forecasts. Finally, we found that no paper has conducted a real-time evaluation of forecasts for period-average or point-sampled EERs, or for point-sampled bilateral RERs. This calls into question the usefulness of proposed forecasts in practice. Taken together, our findings suggest that researchers know little about the predictability of period-average exchange rates. Our paper aims to fill these gaps.