RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data 5. Results

This section reports the quantitative results on the importance of temporal disaggregation for exchange rate forecasts. All forecasts are constructed in real time as described in Section 4 using the data documented in Section 3.

Subsection 5.1 compares the performance of the two no-change benchmarks. Subsection 5.2 compares the performance of the recursive and direct forecasting models to no-change benchmarks.

5.1 Comparison of no-change benchmarks

5.1.1 Median performance across countries

We begin by examining the extent to which the end-of-month no-change forecast outperforms the month-average no-change forecast. We report results for the four types of exchange rates and, as a point of comparison, for a simulated random walk at the daily frequency aggregated to monthly data with n = 21.^[8] Table 5 reports the median RMSFE ratios at various forecast horizons.

When the simulated data follows a random walk, the end-of-month no-change forecast substantially outperforms the month-average no-change forecast (Ellwanger and Snudden 2023). The gains in the RMSFE are the largest one month ahead, showing a 17 per cent reduction and, consistent with theory, the differences decline with the forecast horizon. These patterns are also present for directional accuracy. For one-month-ahead forecasts, the median SR is 0.74, which means that the end-of-month no-change predicted the direction in which the month-average exchange rate moved 74 per cent of the time. The SRs also decline at longer horizons, but remain above 0.5 up to 12 months ahead.

The pattern of the forecast gains observed for the simulated random walk are also observed for the alternative exchange rate measures. In particular, the median RMSFE ratios for NER are nearly identical to those obtained from a random walk. The results suggest that the NER exhibits properties most similar to a random walk followed by the RER, NEER, and REER. That said, even for NEER and REER, the end-of-month no-change forecast outperforms the month-average no-change forecast one month ahead by 7 and 3 per cent, respectively. Moreover, the end-of-month no-change does at least as well as the monthly average up to 12 months ahead for all four exchange rate measures.

Regarding directional accuracy, the gains in the SR are also substantial but much more consistent across exchange rate measures. For all exchange rates, at one month ahead, we find gains of around 20 percentage points relative to a coin flip. Moreover, even at the six-month-ahead horizon, gains of 6 to 9 percentage points are found for all exchange rates. The results clearly indicate that the end-of-month no-change is a more accurate naive forecast than the month-average no-change.

5.1.2 Performance and hypothesis tests for all countries

Now we explore how robust these forecast gains are across countries. Figure 1 reports the quantiles of the RMSFE and SRs for the end-of-month no-change forecast relative to the month-average no-change forecast at horizons of 1 to 12 months for the RER and REER. The gains across quantiles indicates that the differences between the end-of-month no-change and the month-average no-change in our sample is widespread, in addition to being substantial.^[9]

Improvements in the forecasts are statisticallye significant for a large fraction of countries, for both mean squared and directional accuracy (Table 6).

The results suggest that the loss in forecast accuracy from temporal aggregation of daily exchange rates to the monthly frequency is sizable. This is due to the high persistence of daily exchange rates (Zellner and Montmarquette 1971; Amemiya and Wu 1972; Tiao 1972), and is consistent with the evidence on other aggregated macroeconomic variables (Ellwanger and Snudden 2023; Ellwanger et al 2023). The substantial and consistent differences in forecast accuracy indicate the importance of using the correct no-change benchmark in practice.

5.2 Comparison of model-based to no-change forecasts

We now quantify the information gains from temporal disaggregation when constructing real-time model-based forecasts of monthly average exchange rates using the three recursive and the three direct methods as described in Section 4. We report on the distribution of RMSFE ratios and SRs over our sample period, and then turn to hypothesis tests.

5.2.1 Performance over the sample period

To be consistent with Subsection 5.1, and the existing literature for EERs, we begin by comparing the forecasts to the month-average no-change forecast.

The median forecast performance of model-based forecasts of the bilateral RERs is reported in Table 7. When recursive and direct forecasts are estimated with monthly average data, the forecasts do worse than the month-average no-change forecast in terms of median RMSFE at all horizons and in terms of median SR at horizons up to one year. The month-average no-change forecast can seem hard to beat even though it is an inefficient naive forecast because model-based forecasts with period-average inputs are also inefficient. When estimated with monthly average data, the recursive and direct forecasts are almost indistinguishable from each other in terms of RMSFE up to a two-year horizon, and in terms of SR at all horizons.

In contrast, for both recursive and direct forecasts, the use of high-frequency data in end-of-month or bottom-up methods results in substantially better real-time forecast performance than using month-average inputs. The gains are very similar to what was observed from the end-of-month no-change forecast one month ahead, with a 12 percentage point improvement in RMSFE and an 18 percentage point improvement in the SR. These findings reinforce that the gains in forecast accuracy are substantial when model-based forecasts use disaggregated daily data.

Interestingly, the results indicate that end-of-month forecasts do about as well as the bottom-up forecasts constructed using daily data for real-time forecasts of the monthly average level. This evidence suggests that methods that have been shown to perform well when forecasting end-of-period exchange rates may perform well for period-average exchange rates.

We now examine the model-based forecast performance relative to the end-of-month no-change forecast, that is, the naive forecast that represents the random walk hypothesis. The distribution of RMSFEs and SRs from the different model-based forecasts at the one-month-ahead horizon for REERs are reported in Figure 2. Model-based forecasts using disaggregated methods have much lower RMSFE ratios compared to models estimated with month-average inputs. The forecasts made with month-average inputs are so poor that the entire interquartile range (IQR) of RMSFE ratios is above the median RMSFE ratio constructed using end-of-month or daily inputs. These results show that, like the gains for no-change forecasts, the differences between the disaggregated model-based forecasts and the models estimated with monthly average data are substantial and near universal.

Even though we observe substantial deterioration in RMSFEs for model-based forecasts estimated with monthly average data, the pattern is less clear for directional accuracy, as shown in Figure 2. This can be seen in the overlap in the IQRs of the SRs for the month-average, end-of-month and daily inputs. However, the UMIDAS forecasts exhibit some of the largest and most robust forecast directional accuracy gains, with the lower bound of the IQR above 0.5. This suggests that mixed-frequency direct forecasts may have notable advantages in forecasting directional accuracy, at least at short horizons.

Qualitatively, the results are very similar for the other exchange rates and are reported in Appendix F. Substantial RMSFE gains are found for all exchange rates and are robust across countries when disaggregated model-based forecasts are employed. These results are all indicative that time-averaging introduces a loss of information for model-based forecasts of monthly average exchange rates. Integrating information from daily or end-of-month inputs into model-based forecasts can substantially enhance forecast accuracy compared to specifications with month-average inputs.

5.3 Hypothesis tests

We now formally test the real-time predictability of month-average exchange rates against the naive forecast that reflects the random walk hypothesis. Previous tests of predictability in the literature tested against the month-average no-change benchmark, which does not reflect the random walk hypothesis (see Section 2). Table 8 reports the share of countries for which we find significant outperformance of the model-based forecasts against both the end-of-month and the month-average no-change benchmarks in terms of mean square accuracy and directional accuracy.

Immediately notable is that comparisons to the month-average no-change result in substantially more statistically significant forecasts when disaggregated methods are employed. For example, for forecasts of the monthly average NER, the disaggregated model-based forecasts significantly outperform the month-average no-change for up to 80 and 95 per cent of countries in terms of mean square accuracy and directional accuracy, respectively. However, this is a perfect example of spurious predictability. There is little evidence of short-term predictability of bilateral NERs when the exact same model-based forecasts are tested against the random walk hypothesis, that it, the end-of-month no-change forecast. For NERs, less than 5 per cent of countries exhibit significant predictability in RMSFE terms. This is substantial evidence that when forecasting a period-average, comparisons relative to the period-average no-change benchmark can lead to a sizable type-I error rate.

Interestingly, evidence of real-time predictability is present for the forecasts of the other exchange rates. For bilateral RERs, significant RMSFE gains relative to the end-of-month no-change forecast are found for up to 31 per cent of countries, and up to 15 per cent of countries for the SR. These are slightly better for NEERs, with significant RMSFE gains relative to the end-of-month no-change forecast found for up to 37 per cent of countries, and up to 33 per cent of countries for the SR. By far, the most predictable exchange rate is the REER, with up to 56 per cent of countries exhibiting significant predictability based on RMSFE and up to 30 per cent based on the SR. We emphasise that this is the first time that forecasts of period-average exchange rates have been compared against the traditional random walk hypothesis. Hence, the finding of statistically significant predictability of period-average exchange rates, relative to the traditional random walk benchmark, is new to the literature.

5.4 Robustness

The use of the same univariate models for all countries in the baseline analysis is intentional. This approach allows us to isolate the informational loss due to temporal aggregation, rather than to make model-specific recommendations for individual countries. Nonetheless, the main results are robust to alternative model specifications and to using a subset of countries.

Appendix E presents forecasts based on pre-sample testing for the order of integration and lag length using the Akaike information criterion (AIC). These tests are applied to the daily ARIMA specification, and the resulting lag structure is imposed on the recursive and direct forecast models in Equations (5) to (10). Forecast performance remains qualitatively unchanged.

We also assess model selection using the automatic ARIMA procedure of Hyndman et al (2022), estimated by maximum likelihood, as well as restricted MIDAS regressions estimated via nonlinear least squares (Ghysels, Sinko and Valkanov 2007). Although these methods produce broadly similar forecasts, they exhibit convergence failure rates that vary by the exchange rate series and forecast method. For this reason, their results are omitted to maintain consistent samples across specifications.

Further, Appendix F confirms that the core findings hold for the subset of countries that maintained flexible exchange rate regimes over the sample period, as defined by Ilzetzki, Reinhart and Rogoff (2019). Forecast performance and significance patterns for these countries closely mirror those of the full sample.

Together, these robustness checks demonstrate that the paper's main conclusions are not sensitive to the precise model parameterisation or country sample. While model assumptions can matter for individual countries, the median forecast performance and the share of countries with significant gains remain stable. Across all specifications, the forecast gains from using disaggregated inputs dominate those from changing other model assumptions, underscoring the first-order importance of temporal aggregation in forecasting period-average exchange rates.

Footnotes

For the simulated random walk, we simulate 30 years worth of data in addition to burning the first 500 daily observations. We then apply our out-of-sample evaluation methodology to the simulated data, and iterate 5,000 times. [8]

The forecast gains are even larger and more robust for the NER and NEER, as is reported in Figure D1. [9]