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 @@
 ) -> 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 @@
     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 +59,19 @@
     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
+            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)
+            moving_average = (alpha * stock_price) + (
+                (1 - alpha) * moving_average
+            )
+
         yield moving_average
 
 
@@ -68,6 +83,7 @@
     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 = }")
+    print(f"{result = }")