Free Canadian Food Inflation Index — Methodology

Version 1.1 — Hybrid Storage + Multi-Basket + X-13 SA Published at canadianfoodindex.ca

1. Scope

The Free Canadian Food Inflation Index is a publicly accessible measure of Canadian food price inflation, computed as a confidence-weighted blend of three independent sources. Version 1.1 stores raw monthly index levels per snapshot and derives multiple views (basket × adjustment × window × period range) at request time; see § 2.4 for the derivation matrix.

Coverage at v1.1:

• Geography: National Canada (no provincial or per-retailer banner breakdown at this version; per-banner readings ship as a separate published surface in a future release)
• Baskets: food_combined (default; the StatsCan combined Food rollup — the headline reading), food_stores (groceries; food purchased from stores), and food_restaurants (eating out; food purchased from restaurants). Each basket carries its own snapshot file with NSA and SA series; SA is StatsCan-published for food_combined and X-13ARIMA-SEATS-derived for the sub-baskets (see § 2.4)
• Periods: Canonical grammar is YYYY-MM (monthly; e.g., 2026-04), because Statistics Canada and Bank of Canada both publish CPI series at monthly cadence. Quarterly aggregates (YYYY-Qn) and yearly aggregates (YYYY) are also supported. Weekly and daily periods are not published — weekly belongs to the per-banner surface (a separate release); daily has no upstream signal to publish
• Cadence: Refreshes on the publication schedule of the upstream Statistics Canada CPI Food Component and Bank of Canada CPI all-items series (monthly; typically third Tuesday of the following month)

Out of scope at v1.1:

• Per-retailer banner-level or sub-category breakdowns (a separate per-banner weekly snapshot is published in a future release)
• Real-time intra-day pricing data
• Provincial decomposition
• Imputation for missing categories within the StatsCan or BoC series

2. Data Sources

Three independent sources contribute to the blended reading. Each is documented with its upstream attribution, methodology link, and licence.

2.1 Statistics Canada — CPI Food Component

• Source: Statistics Canada Table 18-10-0004-01 (Consumer Price Index, monthly, not seasonally adjusted, food component)
• Licence: Statistics Canada Open Licence
• Attribution: "Adapted from Statistics Canada, Consumer Price Index, Table 18-10-0004-01 (Open Licence). Statistics Canada does not endorse this product."
• Methodology pedigree: Published methodology, peer-reviewed, audited by the National Statistician. The benchmark consumers and regulators recognize for Canadian food price inflation.
• Cadence: Monthly publication, typically third Tuesday of the following month
• Authoritativeness rank in this blend: Highest (base weight 0.45)

2.2 Bank of Canada — CPI All-Items (Valet Web Service)

• Source: Bank of Canada Valet Web Service, series V41690973 (Consumer Price Index, all-items)
• Licence: Bank of Canada Valet Terms of Use
• Attribution: "Adapted from Bank of Canada Valet Web Service, series V41690973 (CPI all-items). Bank of Canada does not endorse this product."
• Methodology pedigree: Strong central-bank pedigree. Covers ALL items in the CPI basket — not specifically food. Included as a cross-check on the directional accuracy of the StatsCan food-component reading; deviation between BoC all-items and StatsCan food indicates whether food prices are tracking the broader CPI or diverging
• Cadence: Monthly publication (released alongside or shortly after StatsCan CPI release)
• Authoritativeness rank in this blend: High (base weight 0.35; lower than StatsCan because the basket alignment is weaker)

2.3 Internal Price-History Source

• Source: Project-internal price_history table populated by the daily-collection pipeline (parser-driven shelf-price observations across the products the pipeline currently tracks)
• Licence: Internal (no third-party constraint)
• Attribution: "Computed from the grocery_pipeline project's own price-history observations. Not a substitute for Statistics Canada's published CPI."
• Methodology pedigree: Transparent observation methodology. The "value" is a basket-weighted average of per-product month-over-month percentage changes. Per-product baselines at or below zero are skipped (would produce divide-by-zero). At least one product must have both a baseline and a current observation for a non-fallback reading
• Cadence: Daily collection capability; aggregated to the period the consumer queries
• Authoritativeness rank in this blend: Lowest (base weight 0.20). Future cycles that validate the internal basket composition against StatsCan food-component weights may raise this weight

2.4 Multi-view derivation matrix

Per ADR-0013 v4, the producer stores raw monthly index levels in every snapshot rather than only a pre-computed YoY value. Consumers derive views from those levels at request time. Four orthogonal dimensions span the view space:

Per-basket vector ids. Each basket maps to a StatsCan vector id from table 18-10-0004-01:

SA provenance. Each SA series declares one of two sa_provenance values:

The /yoy and /levels endpoints surface sa_provenance on every response so a consumer can audit whether the SA they're reading is StatsCan's own or our X-13 derivation.

Storage windows. Each snapshot's levels block carries the most recent 15 months of NSA + SA points (LEVELS_STORAGE_WINDOW_MONTHS = 15). The producer fetches 60 months from upstream per refresh (LEVELS_FETCH_INPUT_WINDOW_MONTHS = 60) so X-13 has enough input history for stable seasonal estimates; only the last 15 land in storage. The 15-month window covers both the standard YoY lookback (12 months) and the 3-month-trailing YoY window (15 months total).

Revision tracking. When the producer re-fetches a period that already has a snapshot, deltas per level point that exceed REVISION_DETECTION_EPSILON = 0.005 are appended to a per-(basket, period) JSONL revision log. Anything below the epsilon is round-trip float noise (StatsCan publishes levels to 1 decimal place; 0.005 is half the smallest publishable digit).

3. Blending Formula

Each source's effective weight in the blend is the product of three multiplicative factors:

3.1 Base weights

Weights sum to 1.0 for readability; the blender re-normalizes by the actual contributing weights, so the absolute scale does not matter — only the ratios.

3.2 Fallback factor

When a source could not fetch fresh data, the fetcher returns a fallback sentinel rather than raising. The blender retains the source in the per-source transparency surface but scales its contribution by:

A fallback source contributes 5% of its base weight. This bounds the contamination from a wild sentinel value: with the three sources defined here, if two are fresh at 3.0% and one falls back to 0.0%, the blend lands in the range 2.88–2.96% depending on which source fell back — within 0.12 percentage points of the all-fresh 3.0% reading regardless.

3.3 Freshness decay

Older readings contribute less. The decay is exponential with a 30-day half-life:

A source refreshed today contributes at full effective weight (factor = 1.0). A source 30 days stale contributes at half effective weight (factor = 0.5). A source 60 days stale contributes at one quarter (factor = 0.25). The 30-day half-life is anchored to the monthly publication cadence of StatsCan and BoC: a source one publication cycle stale deserves half its weight.

3.4 Weighted average

If all effective weights sum to zero, the blended value is 0.0. With the published base weights (0.45, 0.35, 0.20), even an all-fallback scenario still produces a defined blend at 5% effective contribution per source. The zero-weight branch is reachable only when a source's source_name is not in SOURCE_BASE_WEIGHTS (an unknown source rolled in from a corrupted snapshot), in which case its base weight resolves to 0.0 and contributes nothing.

3.5 Source agreement scalar

A 0.0-to-1.0 transform of the variance across NON-FALLBACK sources. Let $F$ be the set of sources with $\text{fallback\_used}=\text{False}$:

• variance = 0 → agreement = 1.0 (full agreement)
• variance = 100 → agreement = 1/e ≈ 0.37
• variance → ∞ → agreement → 0.0

If fewer than 2 non-fallback sources are present, agreement is 1.0 by definition (nothing to disagree with).

3.6 YoY derivations from stored levels

Given a stored level series $\{L_t\}$ for a (basket, adjustment) tuple, the supported window derivations are:

Standard YoY — point-to-point year-over-year:

3-month-trailing YoY — smooths short-run noise by averaging three consecutive months on each side of the 12-month lookback:

where ${\bar{L}}_{a..b}=\frac{1}{b-a+1}{\sum }_{i=a}^b{L}_i$ — for the trailing-3 average, $b-a+1=3$.

Single-source derivation. Both /yoy and /levels derive from per_source.statscan_cpi_food.levels exclusively (vector 41690974 NSA / vector 41690915 SA for food_combined; sub-basket vector ids per the per-basket table in § 2.4). The three-source blend (StatsCan + BoC + internal) in §§ 3.1–3.5 above applies ONLY to the headline value served at /series for a single (period, basket). Multi-period derivations cannot blend because BoC publishes all-items CPI (not food specifically) and the internal source reports change-rates rather than a monthly level series. This is a methodology choice surfaced as a transparency note on the filter UI; every reading is labelled with its source.

Both derivations require contiguous monthly periods across the lookback window and a strictly positive anchor (denominator). If either guard fails, the /yoy endpoint returns 422 YOY_DERIVATION_FAILED rather than a misleading number.

The same stored levels back BOTH window choices for BOTH adjustment series — no pre-computation, no separate storage, no rebuild required when a new window definition is added.

4. Worked Example

Suppose for period 2026-04 basket food_combined, the three sources return:

Effective weights

• StatsCan: 0.45 × 1.00 × 2^(-5/30) = 0.45 × 1.00 × 0.891 ≈ 0.401
• BoC: 0.35 × 1.00 × 0.891 ≈ 0.312
• Internal: 0.20 × 1.00 × 2^(-1/30) = 0.20 × 1.00 × 0.977 ≈ 0.195
• Sum: ≈ 0.908

Blended value

(3.20 × 0.401 + 2.80 × 0.312 + 4.10 × 0.195) / 0.908 = (1.283 + 0.874 + 0.800) / 0.908 = 2.957 / 0.908 ≈ 3.26%

Source agreement

• mean = (3.20 + 2.80 + 4.10) / 3 = 3.367
• variance = ((3.20-3.367)² + (2.80-3.367)² + (4.10-3.367)²) / 3 = (0.028 + 0.321 + 0.537) / 3 ≈ 0.295 (values rounded to 3 decimals; exact arithmetic against the unrounded mean 3.3667 yields the same 0.997 agreement)
• agreement = exp(-0.295 / 100) ≈ 0.997

A reading where sources agree to within 1 percentage point yields an agreement scalar near 1.0 — high confidence the blended value is methodology-stable.

5. Source Agreement Interpretation

The source_agreement scalar is the headline trustworthiness signal. Consumers use it to gauge whether to act on the blended value or to dig into per-source contributions before making a decision:

The per-source contribution dictionary in the API response always carries every source (including fallbacks) with its raw value and freshness timestamp so consumers can audit the blend at any agreement level.

6. Coverage Gaps

This section documents what v1.1 does NOT do, so consumers and reviewers know the boundaries.

• Not banner-level: This index is national. Per-retailer banner readings (Loblaw vs Sobeys vs Save-On) ship as a separate published surface with its own methodology document, different ToS profile, and weekly cadence
• Not provincial: No Quebec / Ontario / Atlantic / Prairie / BC decomposition. The StatsCan provincial CPI tables exist and a future cycle can incorporate them
• Not category-level within food: No dairy vs produce vs protein decomposition within this index. StatsCan publishes sub-component CPIs for these and a future version can incorporate
• Internal source basket not yet validated against StatsCan weights: The internal price-history aggregator currently uses the set of products the daily-collection pipeline tracks. The composition of that set does not yet attempt to mirror the StatsCan food-component basket weights. A future cycle that validates and re-weights the internal basket will be reflected in an updated base-weight entry for the internal source
• No imputation for missing months: If StatsCan or BoC have not published for a given period, that source contributes via the fallback sentinel + 5% effective weight — not via imputation
• Cache-only read path: The public endpoint reads from a cached snapshot. The refresh is operator-driven. A 404 response means the operator has not yet refreshed for that (period, basket); not that the underlying upstream data is missing

7. Refresh Cadence

The recorded_at field on every snapshot timestamps when the blend was computed. A consumer reading the API can compute snapshot staleness directly.

8. Reproducibility — How to Recreate One Blended Value

A third-party reviewer should be able to reproduce a single blended value from the three raw upstream sources within 30 minutes using only:

• A web browser
• A simple spreadsheet (Excel, Google Sheets, or equivalent)
• Standard calculator-grade math

Step-by-step

1. Pick a period. Choose a month in canonical grammar (e.g., 2026-04) for which the published snapshot is available at canadianfoodindex.ca/api/v1/inflation-index/series?period=2026-04&basket=food_combined
2. Pull the StatsCan reading. Navigate to Statistics Canada Table 18-10-0004-01. Filter to the food component for the chosen period. Record the value
3. Pull the BoC reading. Navigate to Bank of Canada Valet Web Service, series V41690973. Filter to the chosen period. Record the value
4. Pull the internal reading. Read the value field at the path per_source.internal_price_history.value in the /series JSON response. (This is the transparent disclosure — the internal source is documented in this methodology and the per-product contributing data is available on request to peer reviewers)
5. Compute lag in days between each source's freshness_timestamp and the snapshot's recorded_at timestamp
6. Compute effective weights for each source using the formula in section 3
7. Compute the weighted average using the formula in section 3.4
8. Compare to the published blended_value. Should match to within rounding (4 decimal places of agreement)

Discrepancies between your reproduction and the published blended_value indicate either a bug in the blender (please report) or a stale snapshot (re-fetch).

9. Versions

• Version 1.0 (initial public methodology): Single national value per (period, basket) tuple. Stored as pre-computed value field on each snapshot.
• Version 1.1 (current — hybrid storage + multi-basket + X-13 SA): Stores raw monthly index levels per snapshot; derives views (basket × adjustment × window × period range) at request time. Adds three baskets (food_combined, food_stores, food_restaurants), NSA + SA series per basket, and X-13ARIMA-SEATS SA derivation for sub-baskets where StatsCan does not publish SA cubes. See § 2.4.
• Version 1.2 (planned): Per-retailer banner-level weekly snapshot. Separate methodology document; separate ToS profile; weekly cadence.
• Version 2.0 (planned): May add provincial decomposition, sub-category breakdowns within the national index, internal-basket re-weighting against StatsCan food-component weights, and additional non-food adjacent series (e.g., commodity input cost passthrough).

10. Contact + Peer Review

• Contact: hello@canadianfoodindex.ca
• Designated Privacy Officer: Privacy Office — privacy@canadianfoodindex.ca
• Methodology critique + suggestions: welcomed via the contact email. Material improvements will be acknowledged in subsequent version notes

Reproducibility commitment

Per section 8, any reader should be able to reproduce a published blended value from raw upstream sources within 30 minutes using a browser and a spreadsheet. The methodology constants used by the production blender (per-source base weights, fallback factor, freshness half-life, agreement variance scale) are documented in section 3 and re-derivable against the per-source contribution dictionary on every API response.

\text{blended} = \frac{3.20 \cdot 0.401 + 2.80 \cdot 0.312 + 4.10 \cdot 0.195}{0.908} = 3.2563\%

## Interactive worked example

| Source | Value | Lag (days) | Fallback | Effective weight |
|---|---|---|---|---|
| statscan_cpi_food | 3.20% | 5 | no | 0.4009 |
| bank_of_canada_cpi | 2.80% | 5 | no | 0.3118 |
| internal_price_history | 4.10% | 1 | no | 0.1954 |

**Blended value:** 3.2563%
**Source agreement:** 0.9970