Autocorrelation, Stationarity, and Why Your Equity Curve Matters

What the Statistical Properties of an Equity Curve Reveal About Whether an Edge Is Real

Most traders look at an equity curve and ask one question: is it going up?

That is the right instinct. But it is not a sufficient test.

An equity curve can go up because a framework has a real edge. It can also go up because of one good streak that masked everything else. Or because the testing period happened to contain the exact conditions the framework was tuned to. Or because the trades are correlated in a way that inflates the apparent consistency.

The shape of the curve tells you something. The statistical properties of the curve tell you everything.

I needed to understand whether the Algorithmic framework's equity curve reflected a genuine, persistent edge — or something that would evaporate under scrutiny. That required a set of tests most retail traders have never encountered.

What "stationarity" means and why it matters

This is a concept borrowed from time series econometrics. It sounds technical. The intuition is simple.

A stationary series is one whose statistical properties — mean, variance, autocorrelation — do not change over time. A non-stationary series is one where those properties drift or trend.

Here is the key insight for trading: you want your equity curve to be non-stationary. And you want your returns to be stationary.

That sounds contradictory. It is not.

A non-stationary equity curve means it trends. It goes somewhere. Specifically, it goes up. A flat equity curve — one that wanders around the same level — is stationary. That is not what you want.

Stationary returns mean the framework generates consistent results over time. The per-trade or per-session outcomes are drawn from the same distribution, not from a distribution that shifts. A framework with non-stationary returns is one where the edge appeared in one period and disappeared in another. That is a framework that worked once, not a framework that works.

The textbook signature of a real edge is exactly this combination: a trending equity curve with stationary returns. Consistent income, compounding over time.

I tested this directly.

The Augmented Dickey-Fuller test

The ADF test is the standard tool for testing stationarity in time series data. It poses a simple null hypothesis: the series has a unit root (meaning it is non-stationary). If the p-value is low, you reject the null and conclude the series is stationary.

I ran two ADF tests on the Algorithmic framework's 18-year results.

Equity curve ADF p-value: 1.0. The test failed to reject non-stationarity. The equity curve is trending. It goes up with statistical certainty. This is exactly what you want.

Returns ADF p-value: 0.0. The test rejected non-stationarity decisively. The returns are stationary. The distribution of outcomes is stable over time. The framework generates the same kind of results in 2008 as it does in 2025.

This is the textbook pattern. A trending equity curve built on stationary returns. Not a lucky streak. Not a one-regime artifact. A stable process that compounds.

Most trading strategies never get tested this way. The ones that do often fail the returns test — they show an edge in one period and decay in another. The ADF test catches that immediately.

Autocorrelation: are your trades independent?

Here is a problem most backtests ignore entirely.

Standard statistical tests — confidence intervals, t-tests, significance thresholds — assume that each observation is independent of the others. When you calculate a confidence interval around a win rate, you are implicitly assuming that trade 47 has no relationship to trade 48.

That assumption is often wrong.

If you take two trades in the same session, the same market conditions affect both. A trending morning session that produces one winning long is likely to produce another winning long ten minutes later. Those are not independent events. They are correlated.

Autocorrelation measures this. It quantifies the degree to which consecutive observations in a time series are related to each other.

I ran a full autocorrelation analysis at two levels of granularity.

Signal-level autocorrelation (ACF): +0.34. Trades within the same session are positively correlated. This makes intuitive sense. If the market is respecting levels cleanly in the first hour, it tends to continue doing so throughout the session. One good trade increases the probability that the next trade in the same session is also good.

Session-level autocorrelation: +0.02. Effectively zero. Sessions are independent. A profitable Monday tells you nothing about Tuesday. A losing Wednesday tells you nothing about Thursday.

This is an important distinction. The within-session correlation is expected and structurally explainable. The between-session independence confirms there is no serial dependency driving the results. No momentum effect. No clustering of good weeks or bad weeks beyond what randomness would produce.

Why autocorrelation changes everything about confidence intervals

Here is where this gets practical.

If trades are correlated within sessions, then treating each trade as an independent sample will overstate your confidence. Your confidence intervals will be too narrow. Your statistical significance will be inflated. You will believe your edge is more certain than it actually is.

This is how strategies pass naive significance tests and still fail in live trading. The math looked correct, but the independence assumption was violated.

I addressed this directly. The Algorithmic framework's bootstrap analysis uses session-level resampling, not trade-level resampling. Instead of shuffling individual trades, it shuffles entire sessions. This preserves the within-session correlation structure and produces honest confidence intervals.

The result: the standard error from the session-level bootstrap is 1.4 times wider than the naive trade-level estimate. The conservative test is harder to pass. The framework passes it anyway.

I also ran the Ljung-Box test and the Runs test as part of the autocorrelation suite. Both confirmed the same picture. Minor clustering within sessions, accounted for by the bootstrap methodology. No problematic serial dependence at the session level.

This is the kind of adjustment that separates real quantitative analysis from curve fitting with statistics pasted on top.

Equity curve regression: R-squared above 0.90

After stationarity and autocorrelation, there is a simpler question worth asking: how closely does the equity curve track a straight line?

This is what linear regression against the equity curve measures. The R-squared value tells you how much of the curve's variance is explained by a simple linear trend.

An R-squared of 1.0 would mean the equity curve is a perfect straight line. No drawdowns, no deviation. That does not exist in real trading. An R-squared near 0 would mean the curve is wandering randomly — no trend, just noise.

The Algorithmic framework's equity curve R-squared is above 0.90 — remarkably high.

That means the vast majority of the equity curve's behavior is explained by a straight line trending upward. The remaining 8% is drawdowns and variance. They exist. They are real. But they are noise around a strong, persistent trend — not the dominant pattern.

Over 18 years, that trend produced consistent equity growth across all 18 years on a single MES contract, after all friction costs (commissions and slippage included).

The R-squared matters because it distinguishes between two very different kinds of profitable strategies. A strategy can produce a high total return by having a few massive winning periods that offset long stretches of nothing. That strategy might show a positive equity curve in aggregate, but the R-squared will be low because the line is not smooth. The money came from concentration, not consistency.

An R-squared above 0.90 says the Algorithmic framework's returns are spread evenly across the entire 18-year period. The equity accumulates steadily. The drawdowns are contained. The trend is the signal, not the outliers.

What fake strategies look like under these tests

This entire battery of tests exists because most strategies fail them.

A strategy that was curve-fit to recent data will show non-stationary returns. The ADF test catches it. The edge was a one-period artifact, and the returns distribution shifts when conditions change.

A strategy with correlated trades that uses naive statistics will show tight confidence intervals that are actually meaningless. The autocorrelation analysis catches it. The bootstrap adjustment reveals how much of the apparent certainty was an illusion.

A strategy that relies on one good streak will show a low R-squared. The regression catches it. The equity curve looks profitable in aggregate but the money came from one period, and the rest of the history is flat or negative.

These are not hypothetical failure modes. They are the norm. Most published strategies — especially in the retail space — would fail one or more of these tests. Many would fail all three.

The Algorithmic framework passes each one. Not because I designed the tests to be easy. The session-level bootstrap is the harder version. The ADF test is a standard tool with no parameters to tune. The R-squared is a single number with no room for interpretation.

I ran the hard tests because easy tests are worthless.

How this connects to everything else

This post is part of a broader series on the statistical validation behind the Algorithmic framework. The equity curve analysis does not exist in isolation.

The Monte Carlo simulation tests whether the results could have occurred by chance. The Sharpe ratio and risk-adjusted return analysis measures how much return the framework generates per unit of risk. The market regime testing confirms the edge persists across every volatility environment.

Each post examines a different dimension of the same question: is this real?

The stationarity tests confirm the edge is stable over time. The autocorrelation analysis confirms the statistical methodology is honest. The R-squared confirms the equity curve reflects consistent compounding, not concentrated luck.

The transaction cost analysis confirms the edge survives real-world friction. Together, they describe a framework that has been tested the way institutional strategies are tested — not the way retail indicators are marketed.

Try the framework

The Algorithmic Suite is available on TradingView for ES, NQ, and YM index futures.

Every test described in this post was run on the same framework you get access to. No separate version. No institutional-only features. The same indicators, the same levels, the same logic.

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Algorithmic is charting software for decision support on TradingView. It is not financial advice. Trading involves risk. Outcomes depend on your rules, risk management, and execution. Past performance does not guarantee future results.