P04-L02 · P04 · P04-M01
Compare the same price series across time aggregations
Prerequisites: P04-L01
Learning objectives
- Aggregate one frozen print series into two different bucket widths.
- Reconcile OHLC and volume across aligned buckets.
- Distinguish scale, alignment and coverage from predictive superiority.
EN source master • P04 — Trading Foundations • needs_review.
Educational boundary: mechanisms and evidence only. No BUY/SELL/HOLD signal, trade recommendation, personalized investment advice, guaranteed setup, price target, expected profit, guaranteed win rate or guaranteed risk/reward outcome. All examples are ILLUSTRATIVE / FICTIONAL; no real money or live trade is required.
Why this matters
Two charts of the same instrument can look different without either being wrong. A timeframe selects how observations are grouped. Comparing the underlying series teaches you to explain the difference rather than choosing whichever picture supports a preferred story. No bucket width is intrinsically superior or predictive.
Explanation
A chart timeframe is a bucket duration, not the duration for which a person should hold a position. It must be accompanied by a boundary convention, time origin, price basis and coverage statement. A four-minute bucket starting at t0 differs from one starting at t1 even when both are four minutes wide.
To combine aligned, complete child candles, take the open of the first child, the maximum child high, minimum child low and close of the last child. Sum volumes only when the child windows do not overlap, quantities share units and the same eligible executions are counted once. Do not average closes to derive the larger candle's close. Do not add the high prices: extrema are not additive.
Increasing bucket width removes local detail. Decreasing width exposes more endpoints and local excursions but does not repair missing prints or add evidence of causality. The last event in a bucket is its close, regardless of whether that event is representative of the whole interval. A single wide candle cannot show when its extrema happened.
Comparisons require the same instrument and feed, compatible eligibility rules and aligned cutoffs. One chart might use trades while another uses a mark or midpoint. A supposed contradiction may then be a different measurement. Comparing an unfinished short bucket to a completed long bucket also changes the information available at the decision cutoff.
The primary candle documentation gives examples of supported granularities and incomplete intervals. Our four/eight-minute convention is an original offline teaching rule, not an assertion that a particular API offers those granularities. No API requests or current prices are needed here.
Source-to-claim scope
- Aggregation uses first open, extrema and last close over matched buckets [S04-CANDLES].
- Candle summaries describe endpoints and extremes, not all intermediate paths [S04-CHARTS].
The fixture's arithmetic, bucket alignment, strict swing rule, matching/trigger assumptions, journal convention and rubric are explicitly supplied teaching conventions where applicable; these references do not authenticate fictional values or endorse a venue. US securities and futures sources support bounded vocabulary and limitations, not a claim that their rules apply universally to crypto.
Key terms
- Bucket width: length of each aggregation interval.
- Alignment: the origin and boundaries of those intervals.
- Cutoff: latest included event time, important for avoiding future leakage.
- Endpoint change: close minus open, different from every movement inside.
- Nested aggregation: combining complete, aligned smaller buckets.
Historical example
Data status: ILLUSTRATIVE / FICTIONAL. Prices CU/FU, quantities FU; t0–t7 are synthetic minute offsets. The following eight prints are the complete input for [t0,t8).
| Offset | Price | Quantity |
|---|---|---|
| t0 | 100 | 1 |
| t1 | 104 | 2 |
| t2 | 98 | 1 |
| t3 | 102 | 2 |
| t4 | 103 | 1 |
| t5 | 99 | 3 |
| t6 | 105 | 1 |
| t7 | 101 | 1 |
| Window | Open | High | Low | Close | Volume |
|---|---|---|---|---|---|
| [t0,t4) | 100 | 104 | 98 | 102 | 6 |
| [t4,t8) | 103 | 105 | 99 | 101 | 6 |
| [t0,t8) | 100 | 105 | 98 | 101 | 12 |
The first small candle has endpoint change+2, the second−2, and the large candle+1. Adding +2 and−2 gives 0, not+1, because the between-bucket transition 102→103 is omitted from the two body changes. The wide candle is not the average of the small bodies. All three summaries are consistent with the input.
A shifted four-minute window [t1,t5) includes t1,t2,t3,t4: O104,H104,L98,C103,V6. That same width now has endpoint change−1. To complete the shifted neighboring windows, data before t0 and after t7 would be needed. Do not compare their absent edges as though all aligned windows were available.
What the evidence proves
| State | Claim and locator | Limit |
|---|---|---|
| OBSERVED | The eight fixture prints and their quantities | Only this fictional series |
| INFERRED | The three aggregates above and shifted [t1,t5) | Defined reduction and boundary rules |
| UNKNOWN | Any event after t7, or outside the provided series | No extrapolation |
| INSUFFICIENT EVIDENCE | Four-minute or eight-minute representation predicts better outcomes | No prospective performance evidence |
The dataset supports a representation comparison, not a timeframe recommendation. A wider positive body and narrower negative body can both be correct. Neither proves stronger “demand,” a safer entry or an impending reversal.
Common mistakes
Averaging child closes; counting t4 twice; treating body changes as complete returns; choosing a boundary after seeing the outcome; comparing trade and mark-price feeds without disclosure; and using completed future candles to explain what was known earlier all distort the comparison.
Practical exercise
Inputs: FIX-P04-02 only. Tasks: reproduce both four-minute rows, derive the eight-minute row from those rows, calculate the shifted [t1,t5) row, and explain the +2−2 versus+1 difference. At a cutoff immediately after t3, identify which complete buckets can be reported.
Show worked correction
Expected reasoning: Use one print list, explicit membership and non-overlapping windows. Separate a complete prefix from future observations.
Complete correction: First row (100,104,98,102,V6); second (103,105,99,101,V6). Combined: first open 100, max high 105, min low 98, last close 101, V12. Shifted row (104,104,98,103,V6). The cross-boundary price change is+1 and explains the missing part of the body-change sum. Immediately after t3 the first four-minute bucket's supplied prints are known, but bucket closure is established only when the t4 boundary is reached with the stated completeness assumption. The second bucket and full eight-minute candle are unavailable at that cutoff. You may report a provisional prefix (O100,H104,L98,C102,V6) with its cutoff; do not present future t6=105 as an earlier known high. Both bucket durations answer different summarization questions; neither earns predictive priority.
Checklist
State width, origin, interval inclusion and cutoff; use one input series; preserve endpoints and extrema; sum compatible non-overlapping volume; flag missing edges; and avoid timeframe rankings unsupported by prospective evidence.
Summary
Aggregation can change the visual narrative without changing the raw observations. Resolve apparent contradictions by reconstructing inputs and alignment. Chart scale is a descriptive choice, not a guarantee about future prices.
Visual specifications
P04-L02-V01 — annotated candlestick
Educational question: How does the same series change when the bucket width changes?
Dataset: FIX-P04-02; ILLUSTRATIVE; observedAt=null. Mechanism sources: S04-CANDLES, S04-CHARTS. Use one price axis and one aligned time axis for eight prints, two four-minute candles and one eight-minute candle. Label the t4 boundary, first/last inclusion, H105 L98 and volumes 6+6=12. Add a shifted-window inset with explicit missing-edge warning.
Caption: Fictional aggregations change representation while retaining the same included prints.
Alt text: Two four-minute candles summarize an up then down endpoint change; the eight-minute candle closes one unit above its open.
Layout: 390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending. RTL: RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored. Style: Dark navy with cyan, electric blue and violet; readable contrast and labels independent of color; official ZECOIN branding only. Deterministic chart/SVG/HTML; no fabricated market screenshot.
Status: SPECIFICATION_ONLY; version 1; needs_review. No rendered asset or runtime integration is claimed.
P04-L02-V02 — evidence panel
Educational question: Which conclusions follow from these inputs, and which remain unsupported?
Dataset: FIX-P04-02; ILLUSTRATIVE; observedAt=null. Mechanism sources: S04-CANDLES, S04-CHARTS. Bind four labelled rows OBSERVED / INFERRED / UNKNOWN / INSUFFICIENT EVIDENCE to this lesson's evidence table and record locators. Include one calculation or classification and its assumptions. Display missing data and execution limits explicitly; no financial call or forecast badges.
Caption: Illustrative evidence states under the stated data and execution assumptions.
Alt text: A four-state table distinguishes supplied fictional records, conditional calculations, missing information and unsupported claims.
Layout: 390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending. RTL: RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored. Style: Dark navy with cyan, electric blue and violet; readable contrast and labels independent of color; official ZECOIN branding only. Deterministic chart/SVG/HTML; no fabricated market screenshot.
Status: SPECIFICATION_ONLY; version 1; needs_review. No rendered asset or runtime integration is claimed.
Tools
NONE. Use the embedded fixture, paper or an offline worksheet. No paid access, live market feed, real funds, wallet connection, account creation, signatures or trades are needed. No production tool capability is added or asserted.
Sources & claim boundaries
- S04-CANDLES — Coinbase product candles: https://docs.cdp.coinbase.com/api-reference/exchange-api/rest-api/products/get-product-candles Supports: First/last/extreme trade prices, time buckets and missing intervals; no market observations imported. Checked 2026-09-30; primary page inspected.
- S04-CHARTS — CME chart types: https://www.cmegroup.com/education/courses/technical-analysis/chart-types-candlestick-line-bar Supports: OHLC body and wick conventions only; predictive interpretations are not adopted. Checked 2026-09-30; primary page inspected.
These references support mechanism definitions only. All fixture values, paths, tickets, capital, fills and calculations are original ILLUSTRATIVE / FICTIONAL teaching material, not source-observed prices, a historical performance series or a recommendation for a current market. Documentation examples and official venue names do not endorse a platform. Dataset FIX-P04-02 is bounded to the embedded records and assumptions; observedAt=null because no real-world observation was collected. Future source review and editorial acceptance remain pending: reviewStatus=needs_review, lastReviewedAt=null.
Next lesson
P04-L03 — Volume. Continue within this program's learning sequence.
Visual specifications
P04-L02-V01
How does the same series change when the bucket width changes?
Fictional aggregations change representation while retaining the same included prints.
Use one price axis and one aligned time axis for eight prints, two four-minute candles and one eight-minute candle. Label the t4 boundary, first/last inclusion, H105 L98 and volumes 6+6=12. Add a shifted-window inset with explicit missing-edge warning.
Two four-minute candles summarize an up then down endpoint change; the eight-minute candle closes one unit above its open.
390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending.
RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored.
FIX-P04-02
P04-L02-V02
Which conclusions follow from these inputs, and which remain unsupported?
Illustrative evidence states under the stated data and execution assumptions.
Bind four labelled rows OBSERVED / INFERRED / UNKNOWN / INSUFFICIENT EVIDENCE to this lesson's evidence table and record locators. Include one calculation or classification and its assumptions. Display missing data and execution limits explicitly; no financial call or forecast badges.
A four-state table distinguishes supplied fictional records, conditional calculations, missing information and unsupported claims.
390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending.
RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored.
FIX-P04-02
Sources & claim boundaries
S04-CANDLES · primary_official_documentation_or_education
Coinbase product candles
- Supported claim
- First/last/extreme trade prices, time buckets and missing intervals; no market observations imported.
- Verification boundary
- Primary page inspected. Original synthetic data and results below are not observations of this source's markets.
- Checked at
- 2026-09-30
https://docs.cdp.coinbase.com/api-reference/exchange-api/rest-api/products/get-product-candles
S04-CHARTS · primary_official_documentation_or_education
CME chart types
- Supported claim
- OHLC body and wick conventions only; predictive interpretations are not adopted.
- Verification boundary
- Primary page inspected. Original synthetic data and results below are not observations of this source's markets.
- Checked at
- 2026-09-30
https://www.cmegroup.com/education/courses/technical-analysis/chart-types-candlestick-line-bar
Dataset provenance
id: FIX-P04-02
dataStatus: ILLUSTRATIVE
observedAt: null
source: Original frozen teaching fixture fully embedded in this lesson
scope: Eight synthetic minute-offset trade prints aggregated into four-minute and eight-minute windows.
identifiers: Fictional instrument FU and quote unit CU; training markers, not usable asset IDs or accounts.
timeBasis: Synthetic offsets or T markers only; no actual market timestamps or current/historical market collection.