Methods, formulas and interpretation boundaries

State definitions and the common assessment window

The comparison accepts ordered observations containing a date and a reference level. With fast window F, slow window L and lag d, the information row for assessment row t is k=t-d. Lookback change uses sign(level[k]-level[k-L]); level versus mean uses sign(level[k]-mean(level[k-L+1] through level[k])); fast/slow uses sign(mean(last F levels ending k)-mean(last L levels ending k)). Means are arithmetic, with no hidden volatility weights or missing-value substitution.

Every method begins at row L+d, using zero-based indexing, or at a later explicitly stated assessment cutoff. The endpoint comparison needs L+1 observations, while the slow mean needs L. Using the common later start prevents different eligibility windows from distorting a comparison. A difference within 1e-12 times max(1, absolute comparison reference) is neutral. The reference for the first two rules is the permitted current level; for the dual-mean rule it is the slow mean.

Timing, calendar and input checks

Windows and lag count observations, not elapsed days. A lag is a declared information separation in this teaching tool; it is not proof of a publication timestamp, an executable price or a broker fill. The convention does not replace the research-fill policy of Vector Ridge or any other research system. Historical data revisions and contract transitions can remain relevant even when row ordering is correct.

CSV input must contain exactly date and level columns, with ten to two thousand rows and a maximum file size of 128 KiB. Dates must be valid ISO calendar dates, unique and strictly increasing. Levels must be explicit finite numbers between minus one million and plus one million. Zero and negative levels are permitted; logarithmic returns are not calculated. The chosen windows still need enough observations after warmup. Failed imports leave the previous valid reference intact rather than partially replacing it.

Parameter ranges and constructed controls

Fast windows range from two to sixty observations, slow windows from five to ninety, and the fast window must be shorter. Lag ranges from one to five observations. One-way cost ranges from zero to one hundred basis points. The default constructed comparison uses F=10, L=30, d=2 and cost=3. Its 180 weekday-labelled rows produce 148 assessed rows after a common 32-row exclusion.

The four built-in paths are deterministic fixtures: upward drift, a rise followed by reversal, an alternating sequence and a constant-level control. They are not sampled market prices. Weekday labels skip weekends but do not represent an independently checked exchange calendar. Complete constructed inputs are downloadable so a reader can examine the initial rows as well as the assessed portion.

Turnover and the cost denominator

States take the values -1, zero and +1. Starting from zero, turnover sums the absolute difference between each state and its predecessor, then adds the absolute final state to flatten exposure. A direct reversal contributes two units. State changes count entries and transitions during the assessment, while direct reversals count only +1 to -1 or -1 to +1. The terminal flattening is included in turnover, not mislabelled as another directional forecast.

Cost proxy equals unit turnover multiplied by the chosen one-way cost in basis points. This is a fixed reference-exposure calculation. It excludes contract rolls, changing notional exposure, financing, collateral income, market impact and other costs not explicitly represented. It is not account-return drag. Agreement is the proportion of assessed rows on which all three states coincide; it has no future-outcome test and cannot be interpreted as a win rate.

The sizing worksheet

Uncapped exposure equals target annual volatility divided by the entered annual volatility estimate. Selected exposure is the smaller of that ratio and the exposure cap. Target notional is capital times selected exposure. Whole contracts are rounded down from target notional divided by the entered notional per contract. Actual exposure therefore can fall below the selected target. Neither the ratio nor the cap promises a particular realized risk level.

Cost per contract side equals the commission assumption plus slippage ticks times tick value. Scenario cost equals whole contracts times two sides times the entered round trips times cost per side. The round-trip input defines the scenario horizon; the worksheet does not infer an annual trading frequency. Margin equals contracts times the chosen per-contract margin. A long-position adverse-move illustration equals actual notional times the chosen adverse percentage.

Cash interpretation and release evidence

The displayed cash sum adds the margin assumption to that adverse-move illustration. It is not a complete liquidity requirement, a loss limit or a statement of actual exchange margin. If the sum exceeds entered capital, the tool displays the shortfall condition without quietly reducing the position. Portfolio offsets, collateral haircuts, intraday calls and changing requirements need separate analysis.

The dated historical page uses the same directional engine with a fixed 20/60/two-observation protocol and a 2023 cutoff. Its source qualification is narrower than an execution-data certification. Software tests reconcile the arithmetic and the public release; they are not independent samples establishing a profitable strategy. The source inventory and downloadable protocol make the scope and assumptions inspectable.

Source record

1. Simple Statistics: library documentation
2. EIA: Cushing crude-oil futures contract 1 reference history
3. CME Group: continuous price series