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74 lines
2.6 KiB
Python
74 lines
2.6 KiB
Python
"""
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Calculate the exponential moving average (EMA) on the series of stock prices.
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Wikipedia Reference: https://en.wikipedia.org/wiki/Exponential_smoothing
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https://www.investopedia.com/terms/e/ema.asp#toc-what-is-an-exponential
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-moving-average-ema
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Exponential moving average is used in finance to analyze changes stock prices.
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EMA is used in conjunction with Simple moving average (SMA), EMA reacts to the
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changes in the value quicker than SMA, which is one of the advantages of using EMA.
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"""
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from collections.abc import Iterator
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def exponential_moving_average(
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stock_prices: Iterator[float], window_size: int
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) -> Iterator[float]:
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"""
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Yields exponential moving averages of the given stock prices.
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>>> tuple(exponential_moving_average(iter([2, 5, 3, 8.2, 6, 9, 10]), 3))
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(2, 3.5, 3.25, 5.725, 5.8625, 7.43125, 8.715625)
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:param stock_prices: A stream of stock prices
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:param window_size: The number of stock prices that will trigger a new calculation
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of the exponential average (window_size > 0)
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:return: Yields a sequence of exponential moving averages
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Formula:
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st = alpha * xt + (1 - alpha) * st_prev
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Where,
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st : Exponential moving average at timestamp t
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xt : stock price in from the stock prices at timestamp t
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st_prev : Exponential moving average at timestamp t-1
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alpha : 2/(1 + window_size) - smoothing factor
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Exponential moving average (EMA) is a rule of thumb technique for
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smoothing time series data using an exponential window function.
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"""
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if window_size <= 0:
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raise ValueError("window_size must be > 0")
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# Calculating smoothing factor
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alpha = 2 / (1 + window_size)
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# Exponential average at timestamp t
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moving_average = 0.0
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for i, stock_price in enumerate(stock_prices):
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if i <= window_size:
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# Assigning simple moving average till the window_size for the first time
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# is reached
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moving_average = (moving_average + stock_price) * 0.5 if i else stock_price
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else:
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# Calculating exponential moving average based on current timestamp data
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# point and previous exponential average value
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moving_average = (alpha * stock_price) + ((1 - alpha) * moving_average)
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yield moving_average
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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stock_prices = [2.0, 5, 3, 8.2, 6, 9, 10]
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window_size = 3
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result = tuple(exponential_moving_average(iter(stock_prices), window_size))
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print(f"{stock_prices = }")
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print(f"{window_size = }")
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print(f"{result = }")
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