UQO Working Paper No. 22· v1.1· November 2026· 93 pages
SHARP-HPI: A Spatially Hierarchical, Adaptive and Robust Framework for Quality-Adjusted Housing Price Indices
Monthly municipal indices for Quebec from 769,995 registered sales, 2021–2026
In simulations that follow its own model, SHARP-HPI brings the municipal monthly-change RMSE to 1.58 log points against 3.06 for the production-architecture benchmark, and most of that gain is robust innovation weighting (1.88 with that step alone).
The framework integrates known components: a robust pooled hedonic regression and nested state-space deviations calibrated by empirical Bayes, estimated on 769,995 registered Quebec sales. Outside its own model, at the innovation regime fitted on Quebec or with unobserved seasonal composition, it is not more accurate than the robust benchmark. Its intervals reach nominal coverage only in simulation and must be inflated by 1.41 (houses) to 1.77 (condominiums) for municipalities with 200–600 sales.
Simon-Pierre Boucher — contact@spboucher.ai
1.58 vs 3.06
Municipal monthly-change RMSE (log points) of SHARP-HPI against the production-architecture benchmark, in the nine Monte Carlo designs that follow the model; 12.14 for a cell-level time dummy and 24.32 for the median
3.06 → 1.88 → 1.63 → 1.58
Stepwise ladder from the benchmark to SHARP-HPI: Huber weights on the benchmark's innovations alone give 1.88, SHARP-HPI without empirical-Bayes calibration 1.63; the gain is mostly robust innovation weighting
10.37 vs 10.02
Municipal RMSE of SHARP-HPI against the robust benchmark when innovation variances are drawn at the fitted Quebec regime; with unobserved seasonal composition the robust benchmark (4.24) and an unnested variant (4.09) beat it (5.55)
93 % / 83–86 %
Coverage of 95 % intervals under the published normalisation: baseline design, and misspecified designs; the 98 % of the earlier version was coverage of demeaned errors
×1.41 / ×1.77
Cluster-bootstrap standard error relative to the model standard error on Quebec data, houses / condominiums, municipalities with 200–600 sales; published intervals must be inflated
154.9
Provincial house index in September 2026 (2021 = 100); condominiums 136.4, plexes 151.2
1.64 vs 3.53
Mean absolute revision of first-release municipal house changes against the size of monthly changes, log points; provincial first releases are revised by 0.27
Abstract
SHARP-HPI combines a robust pooled hedonic regression with fine-scale location effects and nested local-level state-space deviations (province, region, regional county municipality, municipality) whose innovation variances are calibrated by empirical Bayes across cells. Applied to 769,995 registered Quebec sales (2021–2026) matched to the assessment roll, it delivers monthly constant-quality indices for 2,654 geography–class cells with counts, effective sample sizes, intervals, reliability grades, real-time vintages and measured revisions. In a Monte Carlo that follows the model, the municipal monthly-change RMSE is 1.58 log points against 3.06 for the production-architecture benchmark; the gain comes mostly from robust innovation weighting (1.88 with that step alone), little from the empirical-Bayes calibration (1.63 without it). At the fitted Quebec innovation regime, or with unobserved seasonal composition, SHARP-HPI is not more accurate than the robust benchmark. Nominal coverage is a simulation result: on Quebec data a cluster bootstrap is 1.41 (houses) to 1.77 (condominiums) times the model standard error for municipalities with 200–600 sales, so published intervals must be inflated. Metropolitan aggregates match Teranet and CREA in cumulative change in Québec City but not in monthly dynamics; the provincial gap to CREA is largely a population difference. The contribution is the integration and the reliability accounting, including where the estimator fails.
JEL: R31, C43, C11, C21, C55
Key Results
An audited population with real-time vintages
769,995 registered sales matched to the provincial assessment roll, an exclusion ledger leading to a headline sample of 632,006 sales, a measured publication lag of 10 to 13 days and monthly vintages with the data cut-off 13 days before each publication date, so that revisions are a measured quantity.
An integration of known components, not a new model class
A single-sale hedonic observation equation with fine location control, a four-level administrative hierarchy, innovation variances calibrated by empirical Bayes across cells, and a reliability bundle for every cell-month. The hierarchical trend model is named as the closest predecessor and no component is claimed to be new.
A component ladder that attributes the gain
Adding the differences from the production architecture one step at a time shows that the accuracy advantage is mostly robust weighting of innovations, little the empirical-Bayes calibration and nothing the administrative nesting; true municipality-level location effects (1.46) would do better still.
Designs that depart from the model, and the failures they reveal
Six further designs draw innovation variances from the priors fitted on Quebec, add unobserved seasonal composition, autoregressive deviations, wrong parents and region-specific quality prices. The ranking survives autoregressive deviations (1.25 against 1.54) and wrong parents (1.22 against 1.48) but not the fitted Quebec regime or seasonal composition; under heavy tails a variant with coarser MRC-level location effects is the most accurate (2.83 against 4.93).
Calibration of the intervals on real data
Coverage is reported under four definitions, and a cluster bootstrap on the Quebec data gives the factor by which model intervals are too narrow, tabulated by sales band and class. A re-anchoring of the reliability grades that would move 30.3 % of municipal cell-months across the A–B boundary is reported, not applied.
External comparison stated with its limits
In the Québec City metropolitan area the house aggregate rises 47.9 log points from 2021 to 2026 on annual means against 45.5 for CREA and 43.7 for Teranet, but the correlation of 12-month changes with Teranet is 0.63. The provincial house index exceeds the CREA single-family benchmark by +14.1 log points; on sub-populations closer to brokered resales the gap falls to +6.9.
Quality control
This paper went through a multi-stage quality control: 7 quality-control reports and 93 points checked. The version presented on this page is the revised manuscript. Scores are on a 0–100 scale and are a diagnostic of the manuscript, not an acceptance probability.
Score after revision
69.5/100
58.6 before quality control · +10.9
Quality control dated November 7, 2026
- Quality-control decision
- major revision
- Scientific integrity
- PASS
- Reproducibility
- R1reproduced from documented analysis data
- Maturity
- Bone revision cycle from submission
- Quality-control reports
- 7
- Points checked
- 93
Scores by dimension
Before quality controlAfter revision
- Originality & contribution57.1 → 60.0
- Scientific rigor54.7 → 70.0
- Identification & methodology56.1 → 68.0
- Data & reproducibility60.0 → 75.0
- Robustness & validation66.0 → 76.0
- Writing68.1 → 70.0
- Figures & tables53.9 → 72.0
- Literature positioning65.7 → 78.0
Revised manuscript93 pages17 figures57 tables4 equations83 references40,493 words
What quality control changed
Quality control turned the paper into an integration study with an honest component ladder. The accuracy gain is now attributed to robust innovation weighting rather than to the empirical-Bayes hierarchy, designs that depart from the model show where the estimator is not better, and nominal interval coverage is restated as a simulation result that does not hold on the Quebec data.
- "The adaptive hierarchy halves the error of per-cell estimation" (1.58 vs 2.91) → 1.58 vs 3.06 against the production-architecture benchmark, with the gain attributed to robust innovation weighting (1.88) and little to empirical Bayes (1.63 without it)
- Nine Monte Carlo designs under the model → fifteen designs, six of which depart from the model; at the fitted Quebec innovation regime (10.37 vs 10.02) or with unobserved seasonal composition (5.55 vs 4.24) SHARP-HPI is not more accurate than the robust benchmark
- 98 % coverage of 95 % intervals → 93 % under the published normalisation and 83–86 % in misspecified designs; on Quebec data the bootstrap is 1.41 (houses) to 1.77 (condominiums) times the model standard error for municipalities with 200–600 sales
- "Aggregates agree closely with Teranet and CREA in Québec City" → agreement in cumulative change only; the correlation of 12-month changes with Teranet is 0.63 and the series starts 16.2 log points below Teranet in January 2021
- Provincial gap to CREA of +14.1 log points → narrows to +6.9 on sub-populations closer to brokered resales; the remainder is a population difference the registry cannot resolve
- Real-time vintages now cut the data 13 days before each publication date: first-release revisions are 0.27 log points at the province and 1.64 for municipal house changes
Limitations stated in the paper
- The published intervals are too narrow: they omit hedonic-parameter and hyper-parameter uncertainty and the covariance between levels, and the reliability grades inherit this; the re-anchoring of the grades is reported, not applied.
- Characteristics come from a single current roll vintage, no sale below $50,000 is collected, the single date per sale conflates signing and registration, and the thin first months of the feed leave a start-up artefact in the metropolitan aggregates of early 2021.
- The hierarchy is administrative and seasonality is not modelled; unobserved seasonal composition is the mechanism under which the nested design loses to a flat one.
- The production-architecture benchmark is an unvalidated re-implementation, and several planned checks were not run, including a sale-price-appraisal-ratio benchmark and a comparison on Statistics Canada metropolitan boundaries.
Data
Quebec registered sales snapshot
One immutable snapshot, taken on 21 October 2026, of the transaction table of the Vrai Prix platform, which ingests the land-registry deeds republished by the Journal de Québec / Journal de Montréal feed: 769,995 sales dated 4 January 2021 to 7 October 2026 and 3,747,008 assessment-roll units, of which 613,153 are matched to at least one sale. The headline sample is 632,006 sales. The author operates the platform.
Earlier extractions and boundaries
Four earlier extractions of the same table (6 and 9 August, 10 and 17 October 2026) measure the publication process: more than 99.96 % of sales already present, no row deleted, no price revised. Geography follows the provincial administrative boundaries (SDA, version 2026-07): the province, 103 regional county municipalities and 1,109 municipalities with roll-matched sales.
External indices
Teranet–National Bank, CREA MLS HPI and Statistics Canada NHPI and RPPI series downloaded on 21 October 2026, used for provincial and metropolitan comparisons in Québec City and Montréal.
Methodology
Stage one: robust pooled hedonic regression
Log prices explained by structural characteristics, fine-scale location fixed effects on a nested metric grid whose resolution adapts to the density of sales, provincial month effects and quality prices that drift smoothly over time.
Stage two: nested state-space deviations
Each geography's monthly mean residual is a noisy observation of a latent deviation from its parent's path, estimated with a heteroskedastic local-level state-space model with robust innovations; the innovation variance of each cell is calibrated by empirical Bayes across the cells of a level.
Eleven benchmarks on the same samples
Median and stratified median, pooled and rolling time dummies, hedonic imputation, rolling-window GEKS, HMTS, repeat sales, static empirical-Bayes pooling, an out-of-time gradient-boosting residual index and a re-implementation of the author's production index architecture, which has not been validated against the production series.
Monte Carlo in two sets of designs
80 replications per scenario on synthetic markets with known quality-constant price paths: nine designs that follow the model, including two pre-specified counter-examples, and six designs that depart from it. RMSE, lag and interval coverage are scored, on own and common sets of cells.
Real-time vintages and validation
Monthly releases simulated from July 2022 to October 2026 with features, location partition, priors and both stages rebuilt at each cut-off; placebo, composition-shock, cluster-bootstrap, ablation and repeat-sales checks; comparison with Teranet and CREA.
Reproducibility
- Every aggregate used in the paper is committed in the repository, together with the index panel and the vintage panel.
- Every table, figure and in-text number is regenerated from those aggregates by a single build target; the pipeline consists of numbered scripts 01 to 62, with a program-to-exhibit map in the README.
- The transaction microdata and the earlier extractions are not redistributed, because the upstream feed does not permit redistribution of record-level data; the raw snapshot, identified by its SHA-256, can be made available for verification on request.
- The external indices and the municipal register are committed; the administrative boundaries are a public download.
- The licence texts of the transaction feed and of the roll compilation are not recorded in the repository, and the replacement of the archived raw artefact by a reduced extract is pending.
Cite this paper
Boucher, S.-P. (2026). SHARP-HPI: A Spatially Hierarchical, Adaptive and Robust Framework for Quality-Adjusted Housing Price Indices. UQO Working Paper No. 22, Université du Québec en Outaouais.
@techreport{boucher2026wp22,
author = {Simon-Pierre Boucher},
title = {SHARP-HPI: A Spatially Hierarchical, Adaptive and Robust Framework for Quality-Adjusted Housing Price Indices},
institution = {Université du Québec en Outaouais, Département des sciences administratives},
number = {22},
type = {UQO Working Paper},
year = {2026},
month = {nov},
url = {https://www.spboucher.ai/research/wp22},
}More in Real Estate & Urban Economics