fix: correct EMA window handling

financial/exponential_moving_average.py

@@ -1,11 +1,13 @@
 """
 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
+
+Wikipedia Reference: [https://en.wikipedia.org/wiki/Exponential_smoothing](https://en.wikipedia.org/wiki/Exponential_smoothing)
+
+[https://www.investopedia.com/terms/e/ema.asp#toc-what-is-an-exponential-moving-average-ema](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
+
+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.
 """
 
@@ -17,9 +19,13 @@ def exponential_moving_average(
 ) -> 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)
 
+    >>> tuple(exponential_moving_average(iter([10.0, 20.0, 30.0]), 1))
+    (10.0, 20.0, 30.0)
+
     :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)
@@ -30,9 +36,13 @@ def exponential_moving_average(
     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
@@ -49,14 +59,15 @@ def exponential_moving_average(
     moving_average = 0.0
 
     for i, stock_price in enumerate(stock_prices):
-        if i <= window_size:
+        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
 
 
@@ -68,6 +79,7 @@ def exponential_moving_average(
     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 = }")