Python/financial/exponential_moving_average.py

"""
    Calculate the exponential moving average (EMA) on the series of stock prices.
    Wikipedia Reference: https://en.wikipedia.org/wiki/Exponential_smoothing
    https://www.investopedia.com/terms/e/ema.asp#toc-what-is-an-exponential
    -moving-average-ema

    Exponential moving average is used in finance to analyze changes stock prices.
    EMA is used in conjunction with Simple moving average (SMA), EMA reacts to the
    changes in the value quicker than SMA, which is one of the advantages of using EMA.
"""

from collections.abc import Iterator


def exponential_moving_average(
    stock_prices: Iterator[float], window_size: int
) -> Iterator[float]:
    """
    Yields exponential moving averages of the given stock prices.
    >>> tuple(exponential_moving_average(iter([2, 5, 3, 8.2, 6, 9, 10]), 3))
    (2, 3.5, 3.25, 5.725, 5.8625, 7.43125, 8.715625)

    :param stock_prices: A stream of stock prices
    :param window_size: The number of stock prices that will trigger a new calculation
                        of the exponential average (window_size > 0)
    :return: Yields a sequence of exponential moving averages

    Formula:

    st = alpha * xt + (1 - alpha) * st_prev

    Where,
    st : Exponential moving average at timestamp t
    xt : stock price in from the stock prices at timestamp t
    st_prev : Exponential moving average at timestamp t-1
    alpha : 2/(1 + window_size) - smoothing factor

    Exponential moving average (EMA) is a rule of thumb technique for
    smoothing time series data using an exponential window function.
    """

    if window_size <= 0:
        raise ValueError("window_size must be > 0")

    # Calculating smoothing factor
    alpha = 2 / (1 + window_size)

    # Exponential average at timestamp t
    moving_average = 0.0

    for i, stock_price in enumerate(stock_prices):
        if i <= window_size:
            # Assigning simple moving average till the window_size for the first time
            # is reached
            moving_average = (moving_average + stock_price) * 0.5 if i else stock_price
        else:
            # Calculating exponential moving average based on current timestamp data
            # point and previous exponential average value
            moving_average = (alpha * stock_price) + ((1 - alpha) * moving_average)
        yield moving_average


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    stock_prices = [2.0, 5, 3, 8.2, 6, 9, 10]
    window_size = 3
    result = tuple(exponential_moving_average(iter(stock_prices), window_size))
    print(f"{stock_prices = }")
    print(f"{window_size = }")
    print(f"{result = }")