MACD Indicator: Formula, Settings, and What Tests Reveal

The activity chart foregrounds the BTCUSDT two-hour 2021–2023 example with no MACD-above-zero entry gate. Its complete chart-data file also retains the 2024–2025 replication: changing signal 3→5 reduced executions from 941 to 781 without a hurdle and increased them from 39 to 135 at 20 basis points. The worked historical indicator chart uses BTCUSDT two-hour candles from 5–11 May 2021; its generic candle labels count from the start of that excerpt, while the downloadable values retain exact UTC timestamps.

For the selected 12/26, 20-basis-point comparison in 2021–2023, the passive control with the same startup and 99% allocation returned −10.95%, compared with −8.75% at signal three and −50.00% at signal five. Repeating the complete Bitcoin two-hour grid at 0.2% cost per execution, across both historical windows, lowered return in 26,827 of 26,832 observed matched pairs; five moved the other way. Execution counts also changed in 6,257 pairs. These controls show sensitivity to the cost and execution model, rather than simply subtracting a larger fee from identical fills. Neither a selected example nor a winning backtest establishes future outperformance.

The main study uses Binance Spot BTCUSDT and ETHUSDT on two-hour and four-hour candles. The core grids were frozen before exploration. We repeated the same settings in 2021–2023 and 2024–2025; these are historical checks, not prospective live validation.

Accepted coverage is 144,768 related evaluations: 107,520 core settings across eight frames, 10,368 focused scaling evaluations across four Bitcoin frames, and 26,880 doubled-cost evaluations across two Bitcoin two-hour frames. There are 144,609 exported traded rows and 159 reconciled zero-trade settings, with no invalid tuples, row errors or duplicate rows. Deliberate equivalent-rule comparisons are included in this evaluation count; it is not a count of independent ideas or trials.

Each run begins with 10,000 USDT cash, holds a long position or cash, requests orders for the next candle’s open, and waits 500 bars before acting. Position size is 99% of equity, leaving a cash reserve. A separate allocation control showed that using every available dollar could delay entries when the next open rose; we therefore excluded the original 100% runs from the main findings and repeated the fixed grids with the reserve. This correction was made for execution consistency, without choosing allocations for returns. Cash earns no interest. The same number of warmup bars covers more elapsed time on the four-hour chart.

The signal rule enters when histogram exceeds a positive hurdle and exits below its negative counterpart. A hurdle of five basis points means 0.05% of that candle’s price. These are explicit state rules: the first eligible bar can trigger an order without a fresh crossing. An optional entry gate additionally requires MACD above zero. Strict equality triggers neither order.

The core grid uses fast EMAs 6–18 by two, slow EMAs 20–50 by two, signal EMAs 3–21 by two, hurdles of 0/1/2.5/5/10/20 basis points, and both entry-gate choices. The exploratory scaling grid uses fast 8/12/16, slow 20/26/40, signal 2–25, the same six hurdles, and original or scaled mode, on both Bitcoin candle sizes and windows. The scaled hurdle multiplies the original hurdle by (signal length − 1) / 8, leaving the nine-bar signal unchanged. For an approximately linear MACD ramp of slope d per bar, the signal EMA trails it by approximately (signal length − 1) / 2 bars after transients. Histogram distance is therefore approximately d × (signal length − 1) / 2. The followup compensates for this length scale; it does not assume real market curves are steady ramps, or promise identical activity after scaling. The scaling followup was motivated by the original exploration and fixed before the original later-window outputs were opened. The reserve-controlled results repeat that design; they are not a newly untouched holdout. All 1,044 observed identical-rule canary pairs (signal nine or zero hurdle) reproduce complete metrics exactly.

The default combined fee/slippage assumption is 0.1% at each execution. Cost controls repeat the same BTC two-hour settings at 0.2%. Zero-cost sensitivity was unavailable through the current interface: entering zero still produced charged-fee results. Those attempts are preserved as excluded diagnostics, not described as frictionless tests. The date inputs are 2021-01-01–2023-12-31 and 2024-01-01–2025-12-31. The final included candle opens at 00:00 UTC on the end date. The platform’s buy-and-hold benchmark uses the first close and last close across that window; its measurement period includes the 500 bars when the strategy stays in cash. Separate recorded passive controls use the same 99% size, 500-bar startup, next-open order and 0.1% cost, then hold the asset. These controls are excluded from main evaluation totals and supply the startup-matched return comparison.

Original compact exports, screenshots and count ledgers are preserved privately. An auditor checks their hashes, exact Cartesian parameter membership, completed counts, capital, candle size, duplicate tuples, errors and repeated-rule agreement. A missing zero-trade row receives no fabricated metric and enters no matched parameter pair. Passive-baseline coverage separates traded rows from reconciled idle-cash settings: with no orders or interest, idle cash has a known 0% return and therefore beats a negative passive return. Related parameter evaluations and deliberate repeats are not independent statistical trials. The published evidence file records completed counts and source checksums; the methods file includes every completed grid and frame.

The worked historical chart is locally calculated indicator data from checksum-verified official Binance candles, with EMA initialization stated in its source file. It contains no reconstructed fills. Eight recorded executions from the original 100% diagnostic smoke were separately reconciled to official next-candle opens and preceding indicator conditions; that sample verifies the sample, not every execution in the study.

The unaltered completed-batch screenshot shows the later Bitcoin core run: 26,880 evaluations across both candle sizes, 26,830 exported traded rows and 50 zero-trade settings, with dates, costs and grid visible.

Download the main signal script, exploratory scaling script, completed evidence, exact methods, and historical-chart provenance.