Relative strength index

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The RSI or relative strength index entails a technical analysis oscillator which indicates
price strength through the comparison of upward or downward movement of the
successive closing prices.

The RSI is popular due to the fact that it is significantly simple to interpret. It was
formulated by J. Welles Wilder and published in the Commodities magazine (now
known as Futures) in June 1978.

The term refers to relative strength in relation to both the general market as a particular
sector. For example, the XYZ value could rise by 2% while the rest of the market
amounts to only 1%. This is sometimes called comparative relative strength to avoid


If the closing balance on a given day is the same as the previous, both U and D are
zero. Average U is computed with the exponential moving average employing N-days
smoothing factor, and likewise for D. The ratio of these averages is the Relative

    RS = {EMA [N] \, of \, U \ over EMA [N] \, of \, D}

This converts to an index RSI (Relative Strength Index) between 0 and 100,

    RSI = 100 - 100 \ times {1 \ over 1 + RS}

And can be expressed as follows, to emphasize how the RSI increases as a proportion
of total movements

    RSI = 100 \ times {EMA [N] \, of \, U \ over (EMA [N] \, of \, U) + (EMA [N] \, of \, D)}


    * Overbought / oversold - when the value of the RSI indicator is closer to "100%" or
"0%", respectively
    * Difference - when the indicator chart form extremes in a direction opposite
direction of price movement
    * Trend in the indicator usually coincides with the trend on the chart until all of the
above events

The EMA in theory uses an infinite amount of data about the past.

    MediaU_ initial {} = {U_2 + U_1 + \ cdots + u_n \ over N}
and then continue from there with the usual EMA formula:

   MediaU_ {today} = \ alpha \ times U_ {today} + (1 - \ alpha) \ times {yesterday}

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