Hello Beau,
I believe the Quantopian RSI does not use EMA but uses this formula:
100
RSI = 100 - --------
1 + RS
RS = Average Gain / Average Loss
(See: http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:relative_strength_index_rsi)
The Quantopian closing prices are:
2013-09-11 467.83
2013-09-12 472.69 Gain = 4.86 Loss = 0.00
2013-09-13 464.90 Gain = 0.00 Loss = 7.79
2013-09-16 450.11 Gain = 0.00 Loss = 14.79
Because it's a 3 period RSI:
Average Gain = (4.86 + 0.00 + 0.00/3 = 1.62
Average Loss = (0.00 + 7.79 +14.79)/3 = 7.52666
RS = 1.62/7.52666 = 0.21523
100
RSI = 100 - -------- = 17.71
1 + 0.21523
It seems Yahoo does this as well with their prices being very slightly different to Quantopian. We can check that:
The Yahoo closing prices are:
2013-09-11 467.71
2013-09-12 472.69 Gain = 4.98 Loss = 0.00
2013-09-13 464.90 Gain = 0.00 Loss = 7.79
2013-09-16 450.12 Gain = 0.00 Loss = 14.78
Because it's a 3 period RSI:
Average Gain = (4.98 + 0.00 + 0.00/3 = 1.66
Average Loss = (0.00 + 7.79 +14.78)/3 = 7.52333
RS = 1.66/7.52333 = 0.22064
100
RSI = 100 - -------- = 18.08
1 + 0.22064
The others will be using EMA as in:
RSI = (100 – (100 / (1 + RS)))
RS = 14-day EMA of upday closing gains / 14-day EMA of downday closing losses
(See: http://www.iexplain.org/rsi-how-to-calculate-it/)
EMA has a memory which is as long as all the available data although after 100 days or so it becomes insignificant.
P.