最近在学习量化交易，需要自己实现RSI指标，参考了TA-LIB的实现方式。
RSI英文全称：Relative Strength Index
RSI中文名称：相对强弱指数
是衡量价格波动的一个重要指标。

计算公式

UP_AVG = UP_AMOUNT/PERIODS (周期内上涨数量平均)
DOWN_AVG = DOWN_AMOUNT/PERIODS（周期内下跌数量平均）
RS = UP_AVG/DOWN_AVG（相对平均）
RSI  = 100 - 100 / (1 + RS)  （相对强弱指数）

快速计算公式

利用前一个UP_AVG, DOWN_AVG快速计算当前UP_AVG, DOWN_AVG

UP_AVG = (UP_AVG_PREV * (PERIODS - 1) + UP) / PERIODS
DOWN_AVG = (UP_AVG_PREV * (PERIODS - 1) + DOWN) / PERIODS
RS = UP_AVG/DOWN_AVG
RSI  = 100 - 100 / (1 + RS)  

Python代码实现

def RSI(t, periods=10):
    length = len(t)
    rsies = [np.nan]*length
    #数据长度不超过周期，无法计算；
    if length <= periods:
        return rsies
    #用于快速计算；
    up_avg = 0
    down_avg = 0

    #首先计算第一个RSI，用前periods+1个数据，构成periods个价差序列;
    first_t = t[:periods+1]
    for i in range(1, len(first_t)):
        #价格上涨;
        if first_t[i] >= first_t[i-1]:
            up_avg += first_t[i] - first_t[i-1]
        #价格下跌;
        else:
            down_avg += first_t[i-1] - first_t[i]
    up_avg = up_avg / periods
    down_avg = down_avg / periods
    rs = up_avg / down_avg
    rsies[periods] = 100 - 100/(1+rs)

    #后面的将使用快速计算；
    for j in range(periods+1, length):
        up = 0
        down = 0
        if t[j] >= t[j-1]:
            up = t[j] - t[j-1]
            down = 0
        else:
            up = 0
            down = t[j-1] - t[j]
        #类似移动平均的计算公式;
        up_avg = (up_avg*(periods - 1) + up)/periods
        down_avg = (down_avg*(periods - 1) + down)/periods
        rs = up_avg/down_avg
        rsies[j] = 100 - 100/(1+rs)
    return rsies