SAX Forecaster - MetaTrader 5용 지표

Overview

Almost every tool we build to read a chart stays in the world of numbers. This one leaves it. Symbolic Aggregate approXimation (SAX), introduced by Jessica Lin, Eamonn Keogh and colleagues in 2003, takes a window of price and turns it into a short string of letters, something like bddcbbba. Once a piece of the market is a word, you can do to it everything computer science already knows how to do with text: match it, count it, hash it, search it.

This publication puts that to work on one practical question: the market is doing this now; when has it behaved similarly before, and what followed? The indicator encodes the current window, scans history for past windows of similar shape, reads each match's known future, and draws the resulting distribution of outcomes as a forecast fan cone on the chart with a verdict panel reporting the statistics behind it.

The transform itself has three steps, each there for a reason:

• Z-normalise the window, so what remains is pure shape. A rise on EURUSD and a rise on gold map to the same normalised curve if they rise in the same way.
• Piecewise Aggregate Approximation: chop the normalised window into w equal segments and replace each with its average. A 48-bar window with w = 8 becomes eight numbers, which is dimensionality reduction that smooths noise along the way.
• Discretise: map each segment average to a letter using breakpoints that split the standard normal into equal-probability bands, so every letter is a priori equally likely.

The SAX pipeline: z-normalise the window, average it into cells, then map each cell to a letter using Gaussian breakpoints.

What makes SAX search sound rather than merely fast is MINDIST, a distance between two words that provably lower-bounds the true Euclidean distance between the z-normalised series. Because it can only ever understate the real distance, it can be used to discard candidates with no risk of discarding a true match. That is what licenses the two-stage search here: prune with the cheap word distance, then rank the survivors by true Euclidean distance. The published validation harness confirms the pipeline returns exactly the same matches as brute force while skipping much of the work.

What the Indicator Draws

Two objects, both rebuilt when a new bar closes.

The fan cone projects the analogs' forward distribution into the future from the last closed bar. A solid line traces the median forward move at each step, and dotted lines above and below trace the 25th and 75th percentiles, so the cone widens as agreement between precedents thins out. The per-step distribution is held in ATR units and multiplied by the current ATR to land on the real price axis, which is what lets precedents from calm and violent regimes contribute to the same cone. The cone is drawn only when the verdict is bullish or bearish, so an absence of cone is itself information rather than a rendering failure.

The verdict panel reports the numbers the cone is hiding:

The verdict is deliberately hard to earn. Too few analogs is decided first, then the coin-flip case, and only a sample that clears both conviction bands gets a direction: the median move must exceed the edge threshold in ATR terms, and the up rate must leave the band around 0.5. Fail either and the answer is no edge, whatever the median happens to say.

The forecaster on EURUSD, M30: the fan cone projecting the analogs' median and interquartile band, with the verdict panel reporting the sample behind it.

Key Features

Honesty by construction

• No lookahead. A match's outcome window must end strictly before the query window begins, so nothing from the query's own future can leak into its set of precedents. This is the single guard that separates an analog search from a curve fit.
• ATR-normalised outcomes. Forward moves are expressed in multiples of the ATR that prevailed at match time, so a precedent from a quiet stretch and one from a violent stretch are on comparable footing. This is the compensation for what z-normalisation threw away.
• A verdict that is allowed to say no. The tool withholds a forecast, and suppresses the cone, whenever the sample is too small or the lean is not decisive on both measures.

A real SAX library, not an approximation of one

• Z-normalisation, PAA including the fractional case where the window length does not divide evenly by the word length, Gaussian breakpoints via Acklam's probit, encoding, and a MINDIST that provably lower-bounds the true distance. None of these existed on the platform before.
• Alphabet sizes 2 through 10 are supported, with breakpoints built once at configuration time and cached.
• A flat window is reported as flat rather than silently encoded: with a near-zero standard deviation there is no shape to normalise, and inventing one would produce a meaningless word.
• A brute-force Euclidean metric ships alongside the production pipeline as a switch, so the pruning can be checked against the answer it is supposed to reproduce rather than trusted.

Practical on a live chart

• The search runs once per closed bar, not per tick, and reads history from bar 1 so the forming bar never enters either the query or the precedent set.
• The panel box is sized from the actually rendered text, so nothing clips at any font size or content, and a light and a dark theme are provided so it reads on either chart background.
• Every chart object carries a common prefix and is removed on deinit, leaving no orphans behind.

Recommended Setup

File Structure

One indicator and two headers. The headers are included as <SAX\...>, so they must sit in their own SAX subfolder.

Input Parameters

Research Basis

The implementation follows the original SAX work by Jessica Lin, Eamonn Keogh and colleagues, whose SAX page collects the papers.

SAX is not a crystal ball for price, and this tool will report no edge more often than it reports anything else. Its value lies in the rare, well-supported occasions when many genuine precedents lean the same way, and in the discipline of a tool that refuses to pretend otherwise. The same library invites further work: SAX words as categorical features for a machine-learning model, motif and discord discovery for anomaly detection, or a Markov transition model over the word dictionary.

A companion article derives the transform and the lower bound, walks through the search and its guards, and shows the validation harness passing: Symbolic Aggregate Approximation (SAX) in MQL5: Historical Analog Search and Forecasting.