Add Simple Moving Average (SMA) Calculation (#9300)

* Add Simple Moving Average (SMA) Calculation

This commit adds a Python script for calculating the Simple Moving Average (SMA) of a time series data.

The script also includes a doctest that verifies the correctness of the SMA calculations for a sample dataset.

Usage:
- Run the script with your own time series data and specify the window size for SMA calculations.

* Update financial/simple_moving_average.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update financial/simple_moving_average.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update financial/simple_moving_average.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

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* Update simple_moving_average.py

* Update financial/simple_moving_average.py

* Update simple_moving_average.py

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---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

financial/simple_moving_average.py

@@ -0,0 +1,68 @@
+"""
+The Simple Moving Average (SMA) is a statistical calculation used to analyze data points
+by creating a constantly updated average price over a specific time period.
+In finance, SMA is often used in time series analysis to smooth out price data
+and identify trends.
+
+Reference: https://en.wikipedia.org/wiki/Moving_average
+"""
+from collections.abc import Sequence
+
+
+def simple_moving_average(
+    data: Sequence[float], window_size: int
+) -> list[float | None]:
+    """
+    Calculate the simple moving average (SMA) for some given time series data.
+
+    :param data: A list of numerical data points.
+    :param window_size: An integer representing the size of the SMA window.
+    :return: A list of SMA values with the same length as the input data.
+
+    Examples:
+    >>> sma = simple_moving_average([10, 12, 15, 13, 14, 16, 18, 17, 19, 21], 3)
+    >>> [round(value, 2) if value is not None else None for value in sma]
+    [None, None, 12.33, 13.33, 14.0, 14.33, 16.0, 17.0, 18.0, 19.0]
+    >>> simple_moving_average([10, 12, 15], 5)
+    [None, None, None]
+    >>> simple_moving_average([10, 12, 15, 13, 14, 16, 18, 17, 19, 21], 0)
+    Traceback (most recent call last):
+    ...
+    ValueError: Window size must be a positive integer
+    """
+    if window_size < 1:
+        raise ValueError("Window size must be a positive integer")
+
+    sma: list[float | None] = []
+
+    for i in range(len(data)):
+        if i < window_size - 1:
+            sma.append(None)  # SMA not available for early data points
+        else:
+            window = data[i - window_size + 1 : i + 1]
+            sma_value = sum(window) / window_size
+            sma.append(sma_value)
+    return sma
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example data (replace with your own time series data)
+    data = [10, 12, 15, 13, 14, 16, 18, 17, 19, 21]
+
+    # Specify the window size for the SMA
+    window_size = 3
+
+    # Calculate the Simple Moving Average
+    sma_values = simple_moving_average(data, window_size)
+
+    # Print the SMA values
+    print("Simple Moving Average (SMA) Values:")
+    for i, value in enumerate(sma_values):
+        if value is not None:
+            print(f"Day {i + 1}: {value:.2f}")
+        else:
+            print(f"Day {i + 1}: Not enough data for SMA")