RSI: Wilder’s Smoothing Makes the Value Depend on How Much History You Feed It — One Platform Uses 250 Bars to Contain It

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]

Source 1 states the dependency abstractly. A charting platform's own documentation states what it does about it, which is the more useful fact. StockCharts describes the same smoothing — the first averages are plain ones, “The first calculations for average gain and average loss are simple 14-period averages”, and thereafter “Average Gain = [(previous Average Gain) x 13 + current Gain] / 14.” — and notes that “Taking the prior value plus the current value is a smoothing technique similar to calculating an exponential moving average.”^[2]

Then the consequence, stated as an operating decision: “This also means RSI values become more accurate as the calculation period extends.” “SharpCharts uses at least 250 data points before the starting date of any chart (assuming that much data exists) when calculating its RSI values.” And the reproducibility warning that follows from it — “A formula will need at least 250 data points to replicate our RSI numbers.”^[2]

The size of the effect is described, not quantified: “Because of this smoothing, RSI values may differ based on the total calculation period.” “250 periods will allow for more smoothing than 30 periods, which will slightly affect RSI values.” “StockCharts.com goes back 250 days whenever possible.” “Slightly” is the platform's own word; neither source gives a numeric difference for a named instrument.^[2]

This is one vendor describing its own implementation, not an industry standard. 250 is StockCharts' choice. Another platform may use a different history length, and that is precisely why two charts of the same instrument can disagree.^[2]

The endpoints are defined rather than computed: “When the Average Gain equals zero, RSI is zero.” “RSI is 100 when the Average Loss equals zero.” and in the degenerate case “If the Average Loss equals zero, a “divide by zero” situation occurs for RS, and RSI is set to 100 by definition.”^[2]

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]

Source 2 attributes a different set of ranges to a different author. It reports that in Constance Brown's *Technical Analysis for the Trading Professional*, “Brown identifies a bull market range and a bear market for RSI.” — “RSI tends to fluctuate between 40 and 90 in a bull market (uptrend) with the 40–50 zones acting as support.” while “RSI tends to fluctuate between 10 and 60 in a bear market (downtrend) with the 50-60 zone acting as resistance.”^[2]

The two sources do not agree on the numbers, and they credit different people. Source 1 reports Cardwell with 40–80 in uptrends and 60–20 in downtrends; source 2 reports Brown with 40–90 and 10–60. This page does not resolve which is right — it records that the bands are author-specific, and source 2 itself adds that “These ranges may vary depending on RSI parameters, strength of trend and volatility of the underlying security.”^[1][2]

Source 2 also states the defaults are adjustable in both directions: “The default look-back period for RSI is 14, but you can lower it to increase sensitivity or raise it to decrease sensitivity.” and “The traditional overbought and oversold levels can be adjusted to better fit the security or analytical requirements.”^[2]

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]

Source 2 describes Cardwell's construction by name. “Andrew Cardwell developed positive and negative reversals for RSI, which are the opposite of bearish and bullish divergences.” “Cardwell considered bearish divergences to be bull market phenomena.” “A positive reversal forms when RSI forges a lower low, and the security forms a higher low.”^[2]

And it warns against the signal in the situation where it appears most — “it must be noted that divergences are misleading in a strong trend”, because “A strong uptrend can show numerous bearish divergences before a top materializes.”^[2]

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]

Source 2 carries no backtest at all, and qualifies the conventional reading instead: “overbought and oversold readings for RSI work best when prices move sideways within a range”, and “Momentum oscillators can become overbought (oversold) and remain so in a strong up (down) trend.” Its closing advice is that “RSI should be used in conjunction with other tools and indicators to confirm signals and avoid potential false alarms.”^[2]

This page now rests on two sources: an encyclopedia article and one charting platform's own documentation. Wilder's 1978 book was not consulted, though both sources name it — source 2 adds that “This book also includes the Parabolic SAR, Average True Range, and the Directional Movement Concept (ADX).”^[1][2]

Not established: the numeric RSI difference for a given instrument between two history lengths (both sources describe the effect; neither measures it); what history length any platform other than StockCharts uses; whether any of the interpretive schemes above is profitable. No backtest figures of this page's own appear anywhere on it.^[1][2]

Vendor limitation, stated plainly: source 2 is StockCharts describing StockCharts. Its 250-bar rule is that platform's implementation choice, not an industry standard, and this page does not claim otherwise.^[2]

Retrieved 2026-09-28. Source 2 HTTP 200, read in full (206 lines); 30 quotations from it were each searched for in the fetched text before publication.^[1][2]