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REVIEW 3 major objections 4 minor 74 references

Forecasting UK Consumer Price Inflation with RaGNAR: Random Generalised Network Autoregressive Processes

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A network autoregression that averages forecasts over many random graphs predicts UK CPI inflation more accurately than the Bank of England's four-to-six-month projections.

desk verdict Solid empirical application of random-graph GNAR models to UK CPI, but the headline BoE outperformance rests on a comparison that is not clearly apples-to-apples and needs more work before it can be believed. read the letter →

arxiv 2505.04423 v1 pith:4MZ42W44 submitted 2025-05-07 stat.AP

Guy P. Nason , Henry Antonio Palasciano This is my paper · ORCID
classification stat.AP MSC 62M1062P2091B84
keywords inflationforecastingUKCPIGeneralisedNetworkAutoregressiveprocessesrandomgraphsErdős–Rényi–Gilbertmodelaveragingforecastcomparisondisaggregatedpriceindices
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 claims that UK CPI inflation can be forecast more accurately than conventional benchmarks and the Bank of England's published medium-term projections by a simple ensemble called RaGNAR. The method generates thousands of random graphs on the 114 disaggregated CPI component series, fits a Generalised Network Autoregressive (GNAR) process to each, keeps the graphs that predicted best over the past thirty months, and averages forecasts across the top five graphs and several model orders. The authors report that this ensemble beats autoregressive, random-walk, and Chronos benchmarks at every horizon from one to twelve months, with the largest gains at six months and beyond, and that it beats the Bank of England's four-to-six-month forecasts on the overlapping sample. A sympathetic reader would care because the results suggest that medium-term inflation forecasting does not require a large judgmental model suite: rapid, replicable forecasts from public data can compete with a central bank's published numbers.

What carries the argument

The load-bearing object is the GNAR(p,s) process, an autoregression in which each node's value depends on its own past values plus, for each lag, the average of values from nodes at graph-distance stages one and two, with neighbour sets defined by the graph and averaged with uniform weights. The second ingredient is the random-network ensemble: because selecting among all $2^{6441}$ possible graphs on 114 nodes is infeasible, graphs are sampled from the Erdős–Rényi–Gilbert model with edge probability $\pi=0.03$, which yields small stage-1 neighbour sets (typically three to four nodes). Each month the graph selection uses the CPI node's one-step-ahead RMSE over the previous thirty months, and the final forecast averages the top five graphs and several model orders, which reduces variance and improves robustness; the paper also derives exact distributions for neighbour-set sizes as a function of $\pi$.

What would settle it

Using the public ONS component series and the authors' released code, recompute RaGNAR forecasts on aligned data vintages and compare them month-by-month with the Bank of England's published four-to-six-month forecasts; if the RMSE advantage disappears when vintages and target definitions are matched, the central claim collapses. Alternatively, apply the identical procedure to US or euro-area CPI components and compare against the respective central bank's published forecasts.

Watch

Extended reading notes

Core claim

The central claim is that RaGNAR — selecting and averaging GNAR processes fitted to Erdős–Rényi–Gilbert random graphs — delivers more accurate UK CPI inflation forecasts than standard benchmarks at all horizons and than the Bank of England's four-to-six-month forecasts. Each month, 10,000 random graphs with edge probability $\pi=0.03$ are generated on 114 CPI component series, GNAR(p,s) models are fitted at the CPI node using 150 training observations, and graphs are ranked by the root mean squared error of their last thirty one-step-ahead forecasts. The top five graphs are re-fitted and iterated forward to twelve months, with forecasts averaged across graphs and across model orders such as {1,13,25} with neighbour stages {1}, {2}, or {1,2}. Relative to the AvAR(P2) benchmark, relative RMSEs reach 0.87–0.90 at one month and fall to about 0.83–0.85 at six months for the local-$\alpha\beta$ class; against the Bank of England, several AvGNAR models improve on the published four-to-six-month RMSEs, with a median improvement near 19% for the global-$\alpha$ class. The authors also claim that the neighbour sets of the best graphs identify economically interpretable leading components, such as oils and fats, fuels and lubricants, and liquid fuels, which anticipate CPI movements.

Load-bearing premise

The claim of beating the Bank of England assumes the two sets of forecasts predict the identical thing over the identical window with the same data available to both.

Editorial extensions

If this is right

  • Central banks could produce competitive medium-term inflation forecasts from public disaggregated price data alone, in hours on a single processor, without expert judgement.
  • Averaging forecasts across multiple random graphs — rather than searching for a single 'true' network — is a cheap way to stabilise network-based forecasts and outperforms any single graph.
  • The method flags a small set of CPI components (oils and fats, fuels and lubricants, liquid fuels) as leading indicators, which could be monitored in real time for early inflation signals.
  • Because the gains over benchmarks are largest at six to twelve months, RaGNAR is best suited to the policy horizon where the Bank of England's own forecasts are weakest.

Reading between the lines

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

  • My inference: the headline comparison with the Bank of England likely depends on aligning forecast vintages and target definitions; if the Bank's published numbers are quarterly averages or use data available later than the RaGNAR information set, the measured gap could narrow, and the paper does not report such an alignment.
  • My inference: the dominance of single components such as liquid fuels in the selected neighbour sets suggests that the method's edge may come mainly from tracking a few volatile item prices; a sparse factor model or a small VAR on the top five components might recover much of the gain at lower cost.
  • My inference: applying the same random-network ensemble to CPI component data from other countries, where the Bank of England comparison is replaced by the local central bank's published forecasts, would directly test whether the result is a UK-specific artefact or a general property of network autoregressions on disaggregated price data.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces RaGNAR, a forecasting procedure that fits Generalised Network Autoregressive (GNAR) models to many random Erdős–Rényi–Gilbert graphs defined on 114 UK CPI component series. Each month the graphs are ranked by rolling one-step-ahead RMSE at the CPI node, the best networks are retained, and forecasts up to 12 months ahead are produced either from a single best network or by averaging over networks and model orders. The empirical sections report RMSE and MAPE performance over 2010–2024 against AR, random-walk, averaged-AR, and Chronos benchmarks, and compare 4–6 month forecasts with Bank of England forecasts from the quarterly Monetary Policy Reports. The paper also proves two propositions about neighbour-set size distributions and interprets the most frequent edges in the best networks.

Significance. If the results are valid, the paper makes a useful practical contribution: it provides a very fast, parsimonious, reproducible forecasting method that appears to beat simple univariate benchmarks at medium horizons, and it offers a constructive way to exploit disaggregated CPI information through random networks. Strengths include a genuinely out-of-sample network-selection protocol, transparent reporting of Monte Carlo variability over random graph draws, proofs of the random-graph propositions, and a public code repository. The main unresolved issue is whether the headline comparison with the Bank of England measures the same forecast target and horizon; currently that claim is not sufficiently supported.

major comments (3)
  1. [Section 5.3, Tables 5 and 7] The Bank of England comparison is not an apples-to-apples comparison as presented. The paper never states whether the BoE numbers are month-specific year-on-year CPI forecasts, quarterly average CPI forecasts, or projections of some other object; it also does not define forecast origins or data vintages. Since BoE Monetary Policy Reports publish quarterly projections, the monthly horizons 4, 5, and 6 in Table 5 may be compared with a different target than RaGNAR's monthly year-on-year forecasts. Please specify the exact BoE forecast object and align horizons, target definitions, and information sets, or restrict the abstract claim to a properly aligned subsample.
  2. [Section 5.3] The claim that RaGNAR is 'materially more accurate' than the Bank of England has no inferential support. The evaluation window since end-2019 contains only a small number of quarterly observations, and the reported ±1 standard deviations are Monte Carlo variation across the 100 random graph draws, not sampling uncertainty of forecast-error differences. Please add a small-sample equal-predictive-accuracy test (e.g., Diebold–Mariano or a bootstrap over the dated forecast errors) and state the number of observations used at each horizon.
  3. [Section 5.4, Eq. (15)] The MAPE definition in Eq. (15) uses a nonstandard denominator |X_t| + 1. Because the reported MAPE comparisons with the Bank of England in Table 7 depend on this modified metric, differences may partly reflect the offset rather than forecast accuracy. Please justify the modification and report results under the conventional MAPE definition, or explicitly discuss the sensitivity of the conclusions to the denominator choice.
minor comments (4)
  1. [Abstract] There is a typo in the abstract: 'Bank of Englan's' should be 'Bank of England's'.
  2. [Section 5.3] Tables 5 and 7 should state the exact dates and number of BoE observations available at each horizon, and clarify how the BoE series was constructed from the Monetary Policy Reports, including whether modes, means, or fan-chart ranges were used.
  3. [Appendix B] The PACF windows used to motivate the P1/P2 order sets include 2005–2024, which overlaps the 2010–2024 evaluation period; please clarify whether the averaging sets were chosen before the evaluation window or discuss this as a limitation of the benchmark construction.
  4. [Section 6] The labels 'liquid fuels' and 'fuels & lubricants' in Figures 6–8 may be confusing without ONS series codes; adding the series identifiers would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RaGNAR forecasts are genuine out-of-sample predictions and the cited GNAR machinery is independent, code-reproduced prior work.

full rationale

The derivation chain is self-contained. RaGNAR forecasts are produced by fitting GNAR(p,s) models (Eq. 3) to Erdős–Rényi–Gilbert graphs, ranking graphs by the rolling 30-month one-step-ahead RMSE at the CPI node (Eq. 11), and iterating Eq. 10 out of sample; the evaluation RMSEs in Tables 1-9 are computed on forecasts made from origins up to t with no use of target values beyond t. Propositions 1 and 2 are derived from the ER model and do not import the inflation data or the forecast target. The GNAR model itself is cited to Knight et al. (2020) and Leeming (2019), which are published, code-reproduced sources; citing them is ordinary method attribution, not a circular justification of the empirical claim. The reported outperformance over AvAR(P2) and the Bank of England is an empirical comparison, not an identity: the benchmark RMSEs are independent of the RaGNAR fitting procedure. The only mild concern is Appendix B's choice of averaging orders P1/P2 using PACF windows that extend to 2024, which is a potential look-ahead in hyperparameter selection; however, this is not a fitted parameter renamed as a prediction, and it does not make any forecast equal to its training input. Therefore no step in the paper's derivation reduces to its own inputs.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The method depends on several hand-chosen tuning parameters (pi, G, ntrain, nval, K, n, order sets), on the random-graph search space being rich enough, and on the comparability of Bank of England forecasts. None of these are derived from theory; they are empirical choices that affect the results.

free parameters (9)
  • pi = 0.03
    Edge probability for Erdős–Rényi–Gilbert graphs; chosen after testing 0.05 and 0.07 with no improvement.
  • G = 10000
    Number of random graphs generated; increasing to 100000 gave no meaningful gain.
  • ntrain = 150
    Rolling training window of 150 months (12.5 years).
  • nval = 30
    Validation window of 30 months for ranking networks; alternatives 12 and 60 gave slightly worse results.
  • K = 2500
    Top 25% of networks used to average BIC for model order selection.
  • n_best_networks = 5
    Number of best-performing networks averaged for forecasts; performance improves as n increases up to 5.
  • model_order_sets = P1={1,13,25}, P2={2,13,25}
    Selected from PACF spikes at lags 1,2,13,25 in the inflation rate.
  • neighbour_stage_sets = S1={1}, S2={2}, S3={1,2}
    Maximum neighbour stage sets averaged over; s>2 found no benefit.
  • MAPE_denominator_offset = 1
    Denominator |X_t|+1 to avoid division by zero when inflation is zero.
assumptions (6)
  • domain assumption GNAR(p,s) model (Knight et al., 2020) provides a valid representation of the multivariate time series dynamics
    The paper assumes the GNAR specification with global or local coefficients captures the predictive relationships among CPI components and aggregate CPI.
  • domain assumption Erdős–Rényi–Gilbert random graphs with edge probability pi=0.03 form a sufficient search space for useful network structures
    The authors rely on G=10000 random graphs to approximate the space of 2^6441 possible graphs; if important structures are unlikely under this model, the method will miss them.
  • domain assumption Past 30-month rolling one-step-ahead RMSE is a reliable criterion for selecting networks that will perform well over the next 12 months
    Network selection is based on recent one-step-ahead errors, but the evaluation is on longer horizons; this assumes the relative performance of networks persists across horizons and time.
  • domain assumption The Bank of England's published 4-6 month CPI inflation forecasts are directly comparable to RaGNAR forecasts on target variable, horizon, and information set
    If BoE forecasts refer to quarterly averages or use a different information set, the comparison in Tables 5 and 7 may be misleading.
  • standard math The i.i.d. zero-mean error assumption in Definition 1 holds for the fitted GNAR models
    Standard regression assumption inherited from GNAR definition; not tested in the paper.
  • domain assumption Year-on-year percentage change transformation removes trends and seasonality sufficiently for the series to be modeled as stationary
    The authors apply this transformation to all 114 series and fit autoregressive-type models without explicit unit-root tests.

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Cite this review

Pith. "Pith review of Forecasting UK Consumer Price Inflation with RaGNAR: Random Generalised Network Autoregressive Processes." pith.science (2026). https://pith.science/paper/4MZ42W44

@misc{pith2026250504423,
  author       = {Pith},
  title        = {Pith review of: Forecasting UK Consumer Price Inflation with RaGNAR: Random Generalised Network Autoregressive Processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4MZ42W44}},
  note         = {Machine review of arXiv:2505.04423}
}
read the original abstract

This article forecasts CPI inflation in the United Kingdom using Random Generalised Network Autoregressive (RaGNAR) Processes. More specifically, we fit Generalised Network Autoregressive (GNAR) Processes to a large set of random networks generated according to the Erd\H{o}s-R\'enyi-Gilbert model and select the best-performing networks each month to compute out-of-sample forecasts. RaGNAR significantly outperforms traditional benchmark models across all horizons. Remarkably, RaGNAR also delivers materially more accurate predictions than the Bank of Englan's four to six month inflation rate forecasts published in their quarterly Monetary Policy Reports. Our results are remarkable not only for their accuracy, but also because of their speed, efficiency and simplicity compared to the Bank's current forecasting processes. RaGNAR's performance improvements manifest both in terms of their root mean squared error and mean absolute percentage error, which measure different, but crucial, aspects of the methods' performance. GNAR processes demonstrably predict future changes to CPI inflation more accurately and quickly than the benchmark models, especially at medium- to long-term forecast horizons, which is of great importance to policymakers charged with setting interest rates. We find that the most robust forecasts are those which combine the predictions from multiple GNAR processes via the use of various model averaging techniques. By analysing the structure of the best-performing graphs, we are also able to identify the key components that influence inflation rates during different periods.

Figures

Figures reproduced from arXiv: 2505.04423 by the authors.

Figure 1
Figure 1. Year-on-year percentage change time series of the Consumer Price Index divisions. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Probability distribution of the number of nodes in each neighbour set when [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Model orders selected by the Bayesian Information Criterion (BIC) over time. The [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Comparison of some of our inflation forecasts computed by averaging the predictions [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: Scatter plots comparing the Bank of England’s forecast percentage errors to those of [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]
Figure 6
Figure 6. Figure 6: Percentage of times each component appears in the CPI node’s neighbour set for the [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]
Figure 7
Figure 7. Figure 7: Time series of the components that most frequently appear in the CPI node’s [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]
Figure 8
Figure 8. Figure 8: Time series of the stage-1 neighbour set contributions for some of the best-performing [PITH_FULL_IMAGE:figures/full_fig_p026_8.png]
Figure 9
Figure 9. Figure 9: Partial autocorrelations for the inflation rate time series across different time periods. [PITH_FULL_IMAGE:figures/full_fig_p034_9.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.