Adds exponential moving average algorithm (#10273)

* Adds exponential moving average algorithm

* code clean up

* spell correction

* Modifies I/O types of function

* Replaces generator function

* Resolved mypy type error

* readibility of code and documentation

* Update exponential_moving_average.py

---------

Co-authored-by: Christian Clauss <[email protected]>

Author: PoojanSmart

Diff for: financial/exponential_moving_average.py

@@ -0,0 +1,73 @@
+"""
+    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 = }")