CEPI · Methodology

Canada Economic Pulse Index (CEPI) — Methodology

Version 2.0 · Last Modified: 2026-04-30

Section 1

Overview

The Canada Economic Pulse Index (CEPI) is a daily composite index designed to measure real-time momentum in Canadian economic activity.

CEPI imagines Canada as if it were a tradable asset. It aggregates high-frequency throughput signals — including cross-border flows, transportation activity, currency stability, and monetary policy conditions — into a single, continuously updated index level.

CEPI is not a GDP forecast. It is not a long-term growth model. It is a structured measure of acceleration or deceleration in observable economic activity.

CEPI consists of two distinct layers:

CEPI-D (Daily Pulse Index) — a bounded, mean-reverting daily composite centred on 100. Values above 100 indicate above-trend macro momentum; values below 100 indicate below-trend momentum.
Structural Composite Index — quarterly composite built from core macroeconomic pillars.

All data sources, transformations, and weights are explicitly documented below.

Section 2

Design Principles

CEPI is governed by the following principles:

Transparency — All data inputs and transformations are published.
Reproducibility — A third party can reconstruct CEPI from this document.
Mean Reversion — CEPI-D is a bounded index centred on 100; it naturally reverts toward baseline, producing visible regime shifts and recoveries.
Lag Robustness — Explicit grace-period logic governs publication.
Layer Separation — Daily pulse and structural fundamentals are independent systems.

Section 3

Data Sources

3.1 Daily & High-Frequency Inputs (CEPI-D)

CEPI-D incorporates the following vectors:

Flow Signals

International arrivals by air (daily)
International arrivals by land (daily)
Cross-border truck entries (daily)

Financial Signals

CAD/USD daily average exchange rate
CAD/EUR daily average exchange rate
CAD/GBP daily average exchange rate
CAD/CNY daily average exchange rate
CAD/JPY daily average exchange rate

Monetary Policy

Bank of Canada target overnight rate (daily)

Transportation Activity

Domestic aircraft movements (weekly)
Transborder aircraft movements (weekly)

Freight Activity

National railway carloadings (monthly)

All vectors are version-locked and monitored for availability.

Section 4

CEPI-D Construction

4.1 Daily Spine

Let:

t ∈ {t₀, t₀ + 1, …, T}

Where:

t₀ = canonical start date (2025-07-01)
T = publication end date, determined by grace logic

All vectors are mapped onto a common daily calendar spine.

4.2 Grace Period Logic

Define:

targetEnd = yesterday (UTC calendar date)
seriesMax_i = most recent available date for series i

Each series has a maximum permitted lag:

Series	Grace Window
Arrivals / Trucks (border flows)	45 days
FX (USD, EUR, GBP)	3 days
FX (CNY, JPY)	60 days
Policy Rate	60 days

Lag is defined as:

lag_i = targetEnd − seriesMax_i

If lag_i > grace_i, then:

graceEnd = min(seriesMax_i)

Otherwise:

graceEnd = targetEnd

The index publishes through spineEnd = graceEnd. Any previously computed values beyond spineEnd are pruned.

The border-flow inputs (air and land arrivals, and trucks) are daily observations, but Statistics Canada releases them in monthly batches in arrears — a month’s daily values are typically published roughly two weeks after month-end. Their grace window is therefore set to 45 days so the index keeps publishing between releases, forward-filling these inputs from their last reported day. While this forward-fill is active, cepi_border_data_status is set to forward_filled and cepi_border_data_as_of records the date through which real border-flow data exists; both are surfaced as a note on the index page.

4.3 Forward Fill

Sparse series are forward-filled onto the daily spine:

x_t = v_t if observation exists at t
x_t = x_t−1 otherwise

This avoids artificial zeros during short reporting gaps.

4.4 Flow Transformations

For daily flow-type series:

Step 1 — 7-Day Rolling Sum

RS_t = Σ_k=0⁶ x_t−k

Step 2 — Year-over-Year Growth (Preferred)

YoY_t = (RS_t − RS_t−365) / RS_t−365

Fallback (if insufficient history for YoY):

Momentum_t = (RS_t − RS_t−14) / RS_t−14

Step 3 — Rolling Causal Z-score (120-day window)

Z_t = (signal_t − μ_t−119:t) / σ_t−119:t

A minimum of 60 observations in the window is required before a z-score is emitted. This rolling normalization replaces the former expanding z-score, enabling CEPI-D to adapt to regime changes within approximately four months rather than carrying the full history as a permanent reference.

Step 4 — Winsorization

Extreme values are clamped to reduce tail distortions.

Step 5 — Nonlinear Scaling

S_t = tanh(Z_t / 2)

4.5 FX Stability Signal

Exchange rate stability is computed via rolling realized volatility. Let σ_c,t denote the 30-day rolling volatility for currency c.

Signal:

Signal_c,t = −σ_c,t

Currency weights are derived from export shares:

w_c = exportShare_c

Basket signal:

FX_t = Σ_c w_c · Signal_c,t

Standardization and scaling follow the same Z-score and tanh transformation.

4.6 Policy Rate Signal

The policy rate signal is constructed from daily changes (first differences):

Δr_t = r_t − r_t−1

Rate holds produce a near-zero signal; cuts or hikes produce directional scores. This replaces the former level-based signal, which produced persistent negative drift whenever rates were below their expanding-window mean.

Standardized via rolling z-score and winsorized as above.

4.7 Weekly & Monthly Inputs

Weekly and monthly inputs are forward-filled to the daily spine before transformation. Each applies the same YoY-preferred signal chain with a frequency-appropriate fallback window for the pre-YoY period:

Weekly aircraft (28-day rolling sum): YoY preferred; 42-day momentum fallback.
Monthly rail (90-day rolling sum): YoY preferred; 90-day momentum fallback.

Section 5

CEPI-D Composite Formula

The composite Z is the weighted average of the component z-scores available on a given day (with the trade-exposure multiplier applied to trucks and rail), renormalized by the sum of those available weights. On days when some components do not report — for example the daily border-flow series on weekends — the composite uses only the components that reported rather than treating the missing ones as neutral, so daily values stay comparable across dates. The composite is then transformed to a bounded signal:

S_i,t = tanh(Z_i,t / 2)

The bounded CEPI-D level is:

CEPI_t = 100 + 10 · Σ_i w_i · S_i,t

CEPI-D is centred on 100. Values above 100 indicate above-trend macro momentum; values below 100 indicate below-trend momentum. The practical range is approximately [90, 110]. This bounded construction replaces the former chain-linked cumulative return, which produced irreversible downward drift.

Section 6

Structural Composite Index (Quarterly)

Quarterly pillars:

Real GDP per capita
Business investment per worker
Business R&D intensity
Labour productivity
Export diversification

Structural momentum:

Momentum_structural = slope_3y − slope_10y

Nowcast momentum:

Momentum_nowcast = slope_1y − slope_10y

Standardized and scaled to:

Index = 50 + 25 · score

Section 7

Export Diversification Score

Herfindahl–Hirschman Index:

HHI = Σ s_i²

Diversification score:

D = 1 − HHI

Section 8

Publication Policy

CEPI-D updates daily.
Structural index updates only when all pillars are available.
Trade data may lead the structural composite.
Quarter mismatches are disclosed.

Section 9

Revision Policy

All source revisions propagate automatically.
Composite recalculated on each run.
Methodology changes increment the version number.
All changes are documented within this file.

Section 10

Limitations

High-frequency data exhibits volatility.
Weekend and holiday distortions exist.
Forward-fill assumes short persistence.
Grace logic introduces bounded estimation risk.
Structural data is release-lagged.

Section 11

Change Log

Version 2.0 · 2026-04-30

Methodological upgrade from cumulative chain-linked returns to bounded level index. CEPI-D now uses CEPI_t = 100 + 10 · Σw_i·tanh(Z_i,t/2), producing a mean-reverting index centred on 100.
Expanding z-scores replaced with rolling causal z-scores (120-day window, 60-day minimum warmup). This enables CEPI-D to detect regime changes and recover from deteriorations rather than carrying a permanent negative reference.
Policy rate signal changed from z-score of rate level to z-score of daily rate change (Δr). Rate holds now produce near-zero signals instead of persistent negative drift.
Chain-linking and the daily return function removed. CEPI-D is now a direct bounded level, not a cumulative product of daily returns.
Component contributions now use bounded signals (tanh of z-score) rather than raw z-scores.
Rationale: the v1 chain-linked construction produced monotonic downward drift because negative signals compounded irreversibly while stabilization produced near-zero returns. The bounded level model recovers naturally and produces visible regime shifts, matching CEPI's intended behaviour as a tradable macro pulse index.

Version 1.1 · 2026-03-12

Fallback momentum horizons shortened to improve CEPI responsiveness in the pre-YoY period: daily flows 28d → 14d; weekly aircraft 84d → 42d; monthly rail 180d → 90d.
Rolling aggregation windows, normalization framework, and chain-linking behaviour unchanged.

Version 1.0 · 2026-03-02

Initial public release.
Grace period framework formalized.
Equal-weight CEPI-D composite locked.