Adds exponential moving average algorithm

Author: PoojanSmart

Diff for: financial/exponential_moving_average.py

@@ -0,0 +1,67 @@
+"""
+    Calculates exponential moving average (EMA) on the series of numbers
+    Wikipedia Reference: https://en.wikipedia.org/wiki/Exponential_smoothing
+    Reference: https://www.investopedia.com/terms/e/ema.asp#toc-what-is-an-exponential-moving-average-ema
+
+    Exponential moving average is used in financial field to analyze changes stock prices.
+    EMA is used in conjuction 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.
+"""
+
+import numpy as np
+
+def exponential_moving_average(series : list[float], window_size : int) -> list [float]:
+    '''
+        :param series: Array of numbers (Time series data)
+        :param window_size: Window size for calculating average (window_size > 0)
+        :return: Resulting array of exponentially averaged numbers
+
+        Formula: 
+
+        st = alpha * xt + (1 - alpha) * st_prev
+        alpha = 2/(1 + window_size) - smoothing factor
+
+        Exponential moving average (EMA) is a rule of thumb technique for
+        smoothing time series data using the exponential window function.
+    '''
+
+    if (window_size <= 0):
+        raise ValueError("window_size must be > 0")
+    elif (window_size >= len(series)):
+        raise ValueError("window_size must be < length of series")
+
+    # Resultent array
+    exp_averaged_arr : list[float] = []
+
+    # Calculating smoothing factor
+    alpha = 2 / (1 + window_size)
+
+    # Exponential average at timestamp t
+    st = series[0]
+
+    for t in range(len(series)):
+        if t <= window_size:
+            # Assigning simple moving average till the window_size for the first time
+            # is reached
+            st = (st + series[t]) * 0.5
+            exp_averaged_arr.append(st)
+        else:
+            # Calculating exponential moving average based on current timestamp data
+            # point and previous exponential average value
+            st = (alpha * series[t]) + ((1 - alpha) * st)
+            exp_averaged_arr.append(st)
+    
+    return exp_averaged_arr
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    test_series = [2,5,3,8.2,6,9,10]
+    test_window_size = 3
+    result = exponential_moving_average(test_series, test_window_size)
+    print("Test series: ", test_series)
+    print("Window size: ", test_window_size)
+    print("Result: ", result)
+