如何计算 Python 中的指数移动平均线

Question

I've been trying to calculate the Exponential Moving Average (EMA) for stock prices. I have the following methods:

def ema(self, prices, period):
    if len(prices) < period:
        return 'Not enough data to calculate EMA'

    return self.ema_helper(prices, period, (2 / (period + 1)), len(prices))


def ema_helper(self, prices, N, k, length):
    if len(prices) == length-N:
        return prices[0]
    
    return prices[0] * k + self.ema_helper(prices[1:], N, k, length) * (1 - k)

I'm going off of this formula:

EMA = Price(t) × k + EMA(y) × (1 − k)

where:
t = today
y = yesterday
N = number of days in EMA
k = 2 ÷ (N + 1)

Why is it not calculating the EMA?

This is the dataset I'm using: (from the latest price 22.27 to the oldest price 22.17 )

[22.27, 22.19, 22.08, 22.17, 22.18, 22.13, 22.23, 22.43, 22.24, 22.29, 22.15, 22.39, 22.38, 22.61, 23.36, 24.05, 23.75, 23.83, 23.95, 23.63, 23.82, 23.87, 23.65, 23.19, 23.1, 23.33, 22.68, 23.1, 22.4, 22.17]

The period is the number of days in EMA. I am assuming a 10 day EMA .

Answer 1

Your EMA uses the result from yesterday so this needs to be kept. Maybe rather use a list like so (this can certainly be cleaned and improved upon, I just changed the ema_helper):

def ema_helper(prices, N, k, length):
    if len(prices) == length-N:
        return prices[0]
    res_ema = [p for p in prices[:N]] # this keeps the ema
    for t in range(N, length):
        res_ema.append(prices[t] * k + res_ema[t-1] * (1 - k))
    return res_ema

This produces

[22.27, 22.19, 22.08, 22.17, 22.18, 22.13, 22.23, 22.43, 22.24, 22.29, 22.264545454545452, 22.287355371900823, 22.304199849737035, 22.359799877057576, 22.541654444865287, 22.815899091253414, 22.98573562011643, 23.139238234640715, 23.286649464706038, 23.349076834759483, 23.434699228439577, 23.513844823268744, 23.538600309947153, 23.475218435411307, 23.406996901700158, 23.3929974650274, 23.263361562295145, 23.233659460059663, 23.082085012776083, 22.916251374089523]

for your dataset. (I assume you have taken it from Moving Averages ), the values correspond.

If you just need the last value you can also use (no need for a list here):

def ema_helper(prices, N, k, length):
    if len(prices) == length-N:
        return prices[0]
    res_ema = prices[N-1]
    for t in range(N, length):
        res_ema = (prices[t] * k + res_ema * (1 - k))
    return res_ema

which gives 22.916251374089523 (or just take the last list item res_ema[-1] ).