An Adaptive Moving Average for Macroeconomic Monitoring

Karin Klieber; Philippe Goulet Coulombe

REVIEW 3 major objections 4 minor 30 references

An Adaptive Moving Average for Macroeconomic Monitoring

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A Random Forest trained on only a time trend produces an adaptive moving average, and in US data it reads the post-pandemic disinflation as a sharp July 2022 break rather than a gradual slowdown.

desk verdict A clean, useful idea with clear simulations, but the real-time (one-sided) claim is under-specified and the empirical hyperparameters are unreported; worth refereeing, not worth citing in its current form. read the letter →

arxiv 2501.13222 v1 pith:5E5LKJB6 submitted 2025-01-22 econ.EM stat.AP

Philippe Goulet Coulombe , Karin Klieber This is my paper · ORCID

classification econ.EMstat.AP MSC 62M1062G0862P20

keywords adaptivemovingaveragerandomforestbaggedtreestime-varyingweightsinflationmonitoringstructuralbreaksone-sidedfilteringmacroeconomic

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes AlbaMA, an adaptive moving average built from a Random Forest whose only predictor is a time trend, and argues that it addresses the time-varying bias-variance trade-off of fixed-window moving averages. The estimator is a weighted average of past observations in which the weights are read off the forest's leaves, so the effective look-back window shortens around abrupt breaks and lengthens in calm periods. Applying it to US and euro-area inflation, core inflation, and real activity series, the authors find that the post-pandemic US inflation path is not a gradual slowdown but a sharp drop in July 2022 followed by a plateau near 3 percent. They also report that AlbaMA's one-sided, real-time estimates line up with its two-sided, hindsight estimates more closely than standard moving averages and the Savitzky-Golay filter across their nine series.

What carries the argument

The central object is AlbaMA, a Random Forest (specifically bagged regression trees) fitted with a single deterministic regressor, the time trend $t$. Each tree partitions time into leaves; the prediction for date $t$ is the average of the in-sample targets in the leaf containing $t$, and averaging over trees yields a weighted average $\hat y_t = \sum_\tau w_{\tau t} y_\tau$. The weights $w_{\tau t}$ are the moving-average coefficients, recovered by counting, across trees, how often observation $\tau$ shares a leaf with $t$ (with weight $1/\text{leaf size}$ each time). The mechanism that carries the argument is the distinction between herd behavior and dispersion: an abrupt break produces near-identical split dates across trees, while a smooth trend produces scattered splits whose average is a straight line. These weights let the estimator shorten its effective window at turning points and revert to a longer window in calm times.

What would settle it

Re-estimate AlbaMA on the same US CPI series over a grid of minimum leaf sizes (say 5 to 200), tree counts, and bootstrap seeds; if the July 2022 sharp decline and the subsequent 3% plateau disappear or shift by several months under nearby settings, the central narrative is a tuning artifact rather than a property of the estimator.

Watch

Extended reading notes

Core claim

The central claim is that a simple bagged-trees smoother can turn a fixed moving average into a fully data-adaptive one. When a clear break exists, most trees split on the same date and the ensemble reproduces the break sharply; when change is gradual, trees split at scattered dates and averaging recovers a smooth slope. The paper shows that this behavior carries over to real data: for US headline CPI, AlbaMA peaks at 11.2% in June 2022 and drops below 4% within two months, identifying July 2022 as the disinflation break, whereas the twelve-month moving average displays a slow convergence lasting until June 2023. For core inflation, AlbaMA jumps in April 2021 and then declines gradually, with weights temporarily abandoning a twelve-month average structure for a near three-month structure. Across nine series, its median one-sided/two-sided $R^2$ is the highest in all three evaluation samples (0.81, 0.78, and 0.75).

Load-bearing premise

The empirical AlbaMA paths in Figures 4 to 7 depend on forest hyperparameters (depth, leaf size, tree count, bootstrap seeds) that the paper does not report, so the central narrative presumes those settings were not chosen to make breaks stand out.

Editorial extensions

If this is right

If AlbaMA is right, the standard twelve-month moving-average narrative of a gradual post-pandemic disinflation in the US is an artifact of fixed smoothing; the actual turning point is a sharp July 2022 break.
AlbaMA's recovered weights give a transparent, time-varying window: around 90% of weight on the last five months for US headline inflation, with the weight on the most recent month doubling from 19% to 41% at the July 2022 juncture.
Because the one-sided estimate tracks the two-sided estimate well, real-time monitoring with AlbaMA is less subject to the boundary problem than fixed moving averages or Savitzky-Golay.
The same adaptive behavior appears across euro-area HICP, US PMI, and industrial production, so the mechanism is not specific to US CPI.
The estimator can be implemented in a few lines with standard random-forest packages, making the adaptive window available to practitioners without bespoke filtering code.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The authors leave implicit that a sharper July 2022 break in measured inflation changes how the 'last mile' of disinflation is narrated: the disinflation itself was fast, but the subsequent plateau near 3% was long, so policy discussion might focus on the persistence of the plateau rather than a gradual slide.
A natural testable extension is to run AlbaMA recursively on real-time CPI vintages and compare its turning-point nowcasts with actual ex-post revisions, which would separate genuine timeliness from tuning luck.
The forest-weights representation connects AlbaMA to time-varying parameter and unobserved-components models; unlike UC-SV, AlbaMA needs no distributional assumptions, so its weighting scheme could serve as a model-free diagnostic for other inflation filters.
A broader implication is that any noisy series with occasional structural breaks, not just inflation, could benefit from the same adaptive weighting, and the paper's one-sided/two-sided consistency metric is a reusable way to evaluate other real-time filters.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The simple idea here is genuinely good: a bagged regression tree using only a time trend gives you a moving average whose effective window shortens around breaks, and the authors show how to back out the implied weights. The simulations in Section 2.3 are clear and do illustrate the intended herd-vs-dispersion behavior. The weight dynamics in the empirical sections are also a nice way to see how the filter adapts. That is the real contribution, and it is new as an applied packaging even though the building blocks (Lin and Jeon 2006, Goulet Coulombe et al. 2024) are established.

But the paper has a load-bearing soft spot that the stress-test picked up. The empirical results and the headline "sharp decline in July 2022" all come from one-sided AlbaMA, yet the paper never defines the algorithm that enforces one-sidedness. The Figure 3 note says only past data can be utilized, but a standard tree trained on the full sample uses future observations to choose split points. If the one-sided estimates are full-sample fits with leaf restrictions, then the break date is informed by post-July 2022 data, and the real-time monitoring claim collapses. The Section 3.3 R2 comparison would then be evaluating full-sample fits, not real-time filtering. This is not a minor omission; it is the difference between a descriptive smoother and a real-time monitoring tool.

Second soft spot: the empirical hyperparameters are not reported. The paper gives min node size 40 for the simulation only. We do not know what was used for Figures 4-7, whether they were tuned, or how sensitive the break narrative is to those choices. Given that the central narrative is about sharpness versus gradualness, that sensitivity matters. No code or data repository is provided either.

Smaller concerns: there is no uncertainty quantification, which is forgivable for a descriptive tool; and the one-sided-vs-two-sided R2 is an unusual metric, though the authors explain its construction honestly. The benchmark comparison against UC-SV and EMA is fine but mostly visual.

The simulations and the weight-extraction idea are solid enough that the paper deserves a serious referee, not a desk reject. But the referee should demand: (1) an exact description of the one-sided estimation procedure, ideally with recursive expanding-window fits; (2) reported empirical hyperparameters and a sensitivity analysis; (3) code or a detailed replication appendix. If the one-sided procedure turns out to be full-sample-trained trees, the post-pandemic narrative should be downgraded to an illustration, not a real-time finding.

For my own work, I would not cite this in its current form. I would bring it to a reading group, mainly to discuss the lookahead issue. My bottom line: referee it, but expect heavy revision on the one-sided definition.

Referee Report

3 major / 4 minor

Summary. The paper proposes AlbaMA, an adaptive moving average constructed from a bagged regression tree (Random Forest) using only a time trend as predictor, and shows how to recover the implied time-varying weights on past observations. The authors illustrate with simulations that abrupt changes produce concentrated tree splits while gradual changes produce dispersed splits that average to a smooth path. They then apply the one-sided version to US and Euro Area inflation, core inflation, industrial production, unemployment, and PMI, claiming that AlbaMA gives a different and timelier post-pandemic inflation narrative, notably a sharp decline in July 2022 rather than a gradual slowdown. The paper also evaluates the one-sided/two-sided consistency of AlbaMA against standard moving averages and the Savitzky-Golay filter.

Significance. If the one-sided construction is properly defined and the empirical results are stable, AlbaMA is a simple and attractive tool for macroeconomic monitoring: it automatically varies its effective look-back window, and the weight decomposition makes the adaptivity transparent. The simulation design is well chosen to demonstrate the mechanism, and the application to nine series is a useful empirical illustration. The main limitation is that the paper's central real-time claim rests on a one-sided estimator whose algorithm is never specified, and the sensitivity of the empirical narrative to unreported tuning choices is not assessed. With those points addressed, the paper could be a valuable contribution to the practical time-series filtering literature.

major comments (3)

[Section 2.2 / Figure 3 note] The one-sided AlbaMA never receives a formal definition. Equation (2.2) defines T_b(t) as an average over the leaf P_b(t), and the note to Figure 3 states that "in the one-sided case only past data can be utilized by the RF," but no algorithm is given that enforces this. A regression tree fitted on the full sample chooses split points using observations on both sides of t, and the leaf P_b(t) containing t generally includes future observations; averaging over such leaves is not a one-sided filter. Because all estimates labeled one-sided in Figures 4–7, including the headline July 2022 drop in Section 3.1, rely on this unidentified construction, the paper does not establish that the reported break is available in real time. The authors should either define and implement a genuine expanding-window or recursive estimation, or state explicitly that trees are fitted on the full sample and assess how much of the break is due to lookahead in split selection.
[Sections 2.3 and 3.1] The simulation in Section 2.3 reports the settings B=500 and min node size=40, but Sections 3.1–3.2 and Figures 4–7 do not report the hyperparameters used for the empirical AlbaMA estimates (min node size, maximum depth, number of trees, bootstrap seed). The implied weights and the inferred break locations, e.g., the weight on y_t changing from 19% in May 2022 to 41% in July 2022, are direct outputs of these choices. The authors should report the exact empirical settings and provide a sensitivity analysis over min node size and B to show that the qualitative post-pandemic narrative is not an artifact of one particular configuration.
[Section 3.3 / Figure 8] The R2 comparison between one-sided and two-sided estimates is only meaningful if the one-sided AlbaMA is genuinely computed without future information. As written, the high R2 values in Figure 8 and Tables 1–2 may simply reflect that the same full-sample tree ensemble underlies both the "one-sided" and two-sided paths, so the metric would not measure real-time revision error. The section should also justify why R2 between a model's own one-sided and two-sided versions is the appropriate yardstick against fixed-window moving averages; as it stands, the criterion conflates filter consistency with forecast accuracy.

minor comments (4)

[Section 2.1, Eq. (1)] The notation k ∈ K, c ∈ I_R is confusing: I_R is not defined, and K = [t] is introduced only afterwards. Please define all symbols at first use.
[Appendix A.1 and throughout] There are several typos: "Bechnmark" in the appendix title, "adpative" in Section 2.2, "Savitzgy-Golay" in Tables 1–2, "paramter" in Appendix A.2, and "trippling" in Section 3.2. A careful proofread is needed.
[Figure 8 note] The label "MA" in the boxplot legend is ambiguous because the figure reports MA(3), MA(6), and MA(12) separately; please specify which fixed-window average the unlabeled "MA" box refers to.
[Section 3.3] The sentence "the highest-ranked R2 boxplot indicates the best overall model performance across all variables" is imprecise, since the boxplots aggregate over series with different variances and the R2 is not an inferential measure. A more careful wording, such as "descriptively highest median R2," would avoid overstating the result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: AlbaMA's weights are derived algebraically from the estimator's definition, and the adaptive behavior is validated on independent simulations and external benchmarks.

full rationale

The central derivation is self-contained. AlbaMA is defined as a bagged regression-tree ensemble with a single time-trend predictor (Section 2.1), and the weight representation ŷ_t = Σ_τ w_τt y_τ is derived algebraically from the leaf-averaging operation (Section 2.2), not assumed. The claimed adaptive behavior—abrupt changes concentrate splits near the break, gradual changes produce dispersed splits—is demonstrated on explicit simulated DGPs in Section 2.3 and Appendix A.2. The empirical narratives are read off fitted one-sided paths and compared against external benchmarks (MA(3/6/12), Savitzky-Golay, UC-SV, EMA) on public data, so the narrative is not fitted into the estimator by construction. The one-sided versus two-sided R2 evaluation in Section 3.3 is an internal consistency check, not a claim that a fitted parameter predicts the very data it was fit to. The citations to Goulet Coulombe (2024) and Goulet Coulombe et al. (2024) motivate the use of trend variables and weight extraction, but the paper re-derives the weights and independently validates the behavior in simulations, so these self-citations are not load-bearing. Concerns about whether the one-sided estimates are truly real-time (no explicit algorithm enforcing one-sidedness is given, and empirical hyperparameters are not reported) are implementation and correctness issues, not circularity. No equation or claim in the paper reduces to its own input by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The adaptive claim rests on the statistical property that bagged trees behave as adaptive nearest-neighbor smoothers, on hand-chosen random forest hyperparameters (reported only for simulations), and on the assumption that one-sided versus two-sided self-consistency is meaningful for evaluating a real-time filter. No new physical or economic entities are introduced.

free parameters (2)

RF minimum leaf size (min node size) = 40 in simulations; unreported for empirical
Controls the smoothness of AlbaMA and directly affects whether breaks appear abrupt or gradual. Reported only for the simulation in Section 2.3, not for the empirical application in Section 3.
Number of trees (B) = 500 in simulations; unreported for empirical
Ensemble size affects variance and the stability of weights. Reported only in the simulation setup in Section 2.3.

assumptions (3)

domain assumption Random Forest is an adaptive nearest-neighbor smoother whose splits concentrate at structural breaks and scatter otherwise.
Invoked in Sections 2.1 and 2.3 and based on Lin and Jeon (2006); without this property, the adaptive-window claim lacks mechanism.
standard math Bagging reduces variance and turns hard threshold splits into smooth averages.
Cites Bühlmann and Yu (2002) in Section 2.3; used to justify smoothness in gradual-change scenarios.
domain assumption The one-sided RF estimate is comparable to the two-sided RF estimate as a measure of real-time usefulness.
Section 3.3 evaluates one-sided versus two-sided R2; this assumes the two-sided estimate is a meaningful ex-post target, not just a different smoother.

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Cite this review

Pith. "Pith review of An Adaptive Moving Average for Macroeconomic Monitoring." pith.science (2026). https://pith.science/paper/5E5LKJB6

@misc{pith2026250113222,
  author       = {Pith},
  title        = {Pith review of: An Adaptive Moving Average for Macroeconomic Monitoring},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5E5LKJB6}},
  note         = {Machine review of arXiv:2501.13222}
}

read the original abstract

The use of moving averages is pervasive in macroeconomic monitoring, particularly for tracking noisy series such as inflation. The choice of the look-back window is crucial. Too long of a moving average is not timely enough when faced with rapidly evolving economic conditions. Too narrow averages are noisy, limiting signal extraction capabilities. As is well known, this is a bias-variance trade-off. However, it is a time-varying one: the optimal size of the look-back window depends on current macroeconomic conditions. In this paper, we introduce a simple adaptive moving average estimator based on a Random Forest using as sole predictor a time trend. Then, we compare the narratives inferred from the new estimator to those derived from common alternatives across series such as headline inflation, core inflation, and real activity indicators. Notably, we find that this simple tool provides a different account of the post-pandemic inflation acceleration and subsequent deceleration.

Figures

Figures reproduced from arXiv: 2501.13222 by the authors.

**Figure 9.** Comparing MA and Filtering Techniques on Simulated Data [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗

**Figure 10.** Two-sided Measures for US CPI Inflation (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower panels present the weights the RF assigns to past observations. All measures are two-sided. 26 [PITH_FULL_IMAGE:figures/full_fig_p02… view at source ↗

Figures from the paper (8 more)

**Figure 11.** Figure 11: Two-sided Measures for US CPI Core Inflation [PITH_FULL_IMAGE:figures/full_fig_p028_11.png]

**Figure 12.** Figure 12: EA HICP Inflation (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower pane…

**Figure 13.** Figure 13: EA HICP Core Inflation (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower…

**Figure 14.** Figure 14: US PMI (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower panels present …

**Figure 15.** Figure 15: EA Industrial Production (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The low…

**Figure 16.** Figure 16: US Industrial Production (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The low…

**Figure 17.** Figure 17: US Unemployment Rate (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower p…

**Figure 18.** Figure 18: EA Unemployment Rate (a) Great Recession (b) Post-Covid Notes: The upper panel shows AlbaMA and the MA(12). The middle panels compare AlbaMA to standard moving averages and the Savitzky-Golay filter for (a) the Great Recession and (b) the post-Covid surge. The lower p…

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Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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Barun \' k, J. and Vacha, L. (2023). The dynamic persistence of economic shocks. arXiv preprint arXiv:2306.01511

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work page 1996

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Breiman, L. (2001). Random forests. Machine learning , 45(1):5--32

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Breiman, L., Friedman, J., Stone, C. J., and Olshen, R. A. (1984). Classification and regression trees . CRC press

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