RSI: Wilder's Smoothing Makes the Value Depend on Where Your Data Starts

The RSI has a quirk that surprises people comparing charts, and it has a name. Averages of up and down moves use **"an n-period smoothed or modified moving average (SMMA or MMA), which is the exponentially smoothed moving average with alpha = 1/n"**. Because that average has no fixed window, every value carries some weight from every earlier bar.^[1]

★**The consequence is that the number depends on how much history you fed it.** Cutler found that **"since Wilder used a smoothed moving average to calculate RSI, the value of Wilder's RSI depended upon where in the data file his calculations started. Cutler termed this Data Length Dependency."** ★**So the same instrument, the same 14-period setting and the same closing prices can yield different RSI values on two platforms** if one loaded more history than the other.^[1]

There is a variant without the problem. **Cutler's RSI uses a simple moving average of U and D instead of the exponential one**, is **"not data length dependent"**, and **"returns consistent results regardless of the length of, or the starting point within a data file."** The article notes it **"generally comes out slightly different from the normal Wilder RSI, but the two are similar, since SMA and SMMA are also similar."** ★**Neither is wrong; they are different definitions, and a comparison should say which one it used.**^[1]

★**How far back the dependency reaches follows from the formula above.** With alpha = 1/n, the weight carried by a bar k periods back is (1 - 1/n)^k. ★**For the standard n = 14 that is about 0.108 at k = 30, 0.0117 at k = 60, and 0.000137 at k = 120** — halving roughly every 9.4 periods and falling below 0.1% after about 93. ★**These figures are arithmetic from the stated smoothing constant, not a measurement reported by the source.** ★★**And they bound the weight of old data, not the difference in the RSI value.** A small weight multiplied by a large price move can still shift the result, so ★**a decayed weight does not by itself make the two calculations agree.** ★**How much the values actually differ for a given instrument and history length is not established here** — it depends on what happened in those early bars, which the decay constant says nothing about.^[1]

For each period the change is split in two. **An up period sets U to the rise and D to zero; a down period sets U to zero and D to the fall; an unchanged close sets both to zero.** ★**Both U and D are non-negative** — the sign is carried by which bucket the move lands in, not by the number itself. RS is then the ratio of the averaged U to the averaged D, and the index is scaled into 0-100.^[1]

The indicator was **developed by J. Welles Wilder and published in a 1978 book, New Concepts in Technical Trading Systems, and in Commodities magazine in the June 1978 issue.** **Wilder recommended a smoothing period of 14.** It is **"classified as a momentum oscillator, measuring the velocity and magnitude of price movements."** ★**The article also warns it "should not be confused with relative strength"** — a different concept comparing one asset against another.^[1]

The familiar lines are conventions. The RSI is **"most typically used on a 14-day timeframe… with high and low levels marked at 70 and 30, respectively"**, and **"short or longer timeframes are used for alternately shorter or longer outlooks."** ★**The source lists alternatives in the same breath:** **"high and low levels - 80 and 20, or 90 and 10 - occur less frequently but indicate stronger momentum."**^[1]

A further reading shifts the levels by trend. **Andrew Cardwell is reported to hold that uptrends generally trade between RSI 40 and 80 while downtrends trade between 60 and 20**, with a **"range shift"** when trend direction changes. ★**This page flags the sourcing:** the Wikipedia section carrying Cardwell's interpretations is **tagged as citing no sources, a tag dated June 2014.** ★**It is reported here as an attributed reading, not as an established result.**^[1]

**Wilder "believed that divergence between RSI and price action is a very strong indication that a market turning point is imminent."** Specifically, **bearish divergence is price making a new high while RSI makes a lower high**, and **bullish divergence is price making a new low while RSI makes a higher low.** He also treated **"failure swings" above and below 50** as reversal indications, and took **50 as the centre line, often seen as both support and resistance.**^[1]

★**Cardwell's reading inverts the conclusion.** He is reported to note that bearish divergence **"1) only occurs in uptrends, and 2) mostly only leads to a brief correction instead of a reversal in trend"**, and therefore that **"bearish divergence is a sign confirming an uptrend"**, with bullish divergence confirming a downtrend. ★**Same pattern, opposite inference** — one treats it as a reversal warning, the other as trend confirmation. ★**This page does not adjudicate between them**, and notes again that the Cardwell material sits in the unsourced section.^[1]

The article carries a test result rather than a claim of effectiveness. **Marek and Sediva (2017)** tested RSI **"with recommended parameters and its day-to-day optimization"** against other strategies, **"randomised in time and companies (e.g., Apple, Exxon Mobil, IBM, Microsoft)"**, and found that RSI **"can still produce good results; however, in longer time it is usually overcome by the simple buy-and-hold strategy."**^[1]

★**This page carries no backtest figures of its own and makes no judgement about whether the indicator works.** The conventional reading — **"buy when the security or currency is oversold and sell when it is overbought"** — is recorded as the convention. ★**Whether acting on it produces a profit is not addressed here.**^[1]

★**This page rests on one institution — a single Wikipedia article — with no independent cross-check.** ★**Wilder's 1978 book was not consulted**, nor was the Marek and Sediva paper; both are reported as the article summarises them. ★**Investopedia, a usual second reference for this topic, returned HTTP 402 on 2026-09-23 and could not be read.**^[1]

★**Not established:** the resulting difference in RSI values for a given instrument and history length (the weight decay above bounds the cause, not the effect), which platforms implement Wilder smoothing versus a simple average, how the first RSI value is seeded, and whether 14 periods outperforms other settings. ★**Two sections of the source article carry "does not cite any sources" tags** (June 2014 and February 2023), and material from them is marked as such above. **As of 2026-09-23.**^[1]