## Introduction to Moving Averages

Do you ever wonder how statisticians and data analysts extract patterns and trends from time-series data? Well, wonder no more! It’s called a moving average, a powerful tool that can help identify short-term fluctuations amidst longer-term trends.

A moving average is a type of statistical analysis that is primarily used with time-series data. It smooths out variations in the data, allowing for clearer identification of patterns and trends.

Moving averages are commonly used in technical analysis to determine potential areas of support and resistance in stock prices and other financial data.

## Example Dataset and Calculation Methods

To understand moving averages, let’s take a look at a simple example dataset. Say we have sales data for a small business spanning six months.

- Month 1 : 20
- Month 2 : 22
- Month 3 : 26
- Month 4 : 24
- Month 5 : 23
- Month 6 : 27

To calculate the simple moving average for this dataset, we need to determine the sum of the sales for a given period and divide by the number of periods. For example, to calculate the simple moving average sales for the first two months, we’d add 20 + 22 and divide by two, resulting in a moving average of 21.

However, this calculation method has a significant drawback. As new data becomes available, the moving average must be updated. This means we must recalculate the moving average every time a new datapoint is added, causing multiple calculations and making it inconvenient to work with larger datasets. Calculation Method 1: Using cumsum()

Fortunately, there is a more efficient way to calculate moving averages, namely using the cumsum() function of pandas.

### Implementation of Moving Average Function using cumsum()

```
import pandas as pd
import numpy as np
def moving_average(x, w):
return np.convolve(x, np.ones(w), 'valid') / w
data = [20, 22, 26, 24, 23, 27]
N = 4
cumulative_sum = np.cumsum(np.insert(data, 0, 0))
ma = (cumulative_sum[N:] - cumulative_sum[:-N]) / float(N)
```

In this code, we use the NumPy library to calculate the moving average. First, we use np.insert() to insert a zero in the beginning of the data series as a placeholder.

We then call the np.cumsum() function to calculate the cumulative sum of the data series. This step generates a new series where each value is the sum of all previous values in the original series.

We then use the np.convolve() function to compute the rolling sum of the data series, followed by division by the window size to generate the moving average.

### Interpretation of Output

By implementing the moving average function using the cumsum() method, we can easily calculate the moving average of a time-series dataset without the need for multiple calculations or recalculations. For example, when we apply the function for a 4-period MA on the sales data provided earlier, we get the following results:

- Month 4 : 23
- Month 5 : 23.25
- Month 6 : 25

The moving average for the first 3 months cannot be calculated as we need at least 4 periods of data to calculate a 4-period moving average.

## Conclusion

In conclusion, the moving average is a powerful tool used in data analysis and technical analysis to identify patterns and trends. Although the simple moving average requires multiple calculations, the cumsum() method efficiently calculates rolling averages and provides accurate results as new data is added. Use it as a starting point for your data-driven analysis and better insights.

## Calculation Method 2: Using pandas

In addition to the cumsum() method, pandas offer a built-in function for calculating moving averages called rolling(). This method is intuitive and straightforward, making it a go-to method for many data analysts.

### Implementation of Moving Average Function using pandas

```
import pandas as pd
import numpy as np
# Read the dataset
df = pd.read_csv('sales_data.csv')
# Calculate the moving average using rolling() and mean()
df['MA'] = df['Sales'].rolling(window=4).mean()
```

In this example, we first read-in a dataset called ‘sales_data.csv’ and create a pandas DataFrame called df. Next, we use the rolling() method with a window size of 4 to calculate the rolling window statistics for the Sales column.

We then call the mean() method to calculate the moving average for each window and store the results in a new column called ‘MA’.

### Comparison with Method 1

Although the cumsum() method is efficient and effective in handling large datasets, the rolling() method offers more flexibility in calculating rolling statistics. One of the key advantages of the rolling() method is that it provides options for customizing the size of the rolling window.

In the example above, we set the window size as 4. However, depending on the specific dataset and analysis goals, we can modify the size of the window as needed. This flexibility in choosing the window size allows for better control over the results and longer or shorter-term patterns.

Another advantage of the rolling() function is that it can handle missing data with greater ease than the cumsum() method. When the cumsum() method encounters a missing datapoint, it generates an error. However, the rolling() method can fill in missing data points with estimated values, making it a more robust approach for working with incomplete time-series data.

### Flexibility in Choosing Number of Previous Time Periods

The rolling() method also offers flexibility in selecting the number of previous time periods to use when calculating the moving average. We can pass an argument called min_periods to the rolling() function to specify the minimum number of periods required to calculate the rolling window statistics.

This approach allows us to generate accurate moving averages with no missing values, even when the dataset has a different number of periods. For instance, to require a minimum of 2 periods to generate the moving average, we can use the following code:

```
df['MA'] = df['Sales'].rolling(window=4, min_periods=2).mean()
```

This code calculates the moving average for every rolling window of size four but with at least two non-missing values. This ensures that the rolling() method always returns a result and maintains the integrity of the time-series data.

## Conclusion

In conclusion, both the cumsum() and the pandas rolling() methods offer effective ways to calculate moving averages for time-series data. The cumsum() method is efficient and capable of handling large datasets, while the rolling() method provides more flexibility and can handle missing data with superior ease.

This flexibility would be particularly useful for data analyses with different window sizes and missing data. Whichever method we choose, the moving average remains a powerful tool for identifying trends and patterns in time-series data.

In conclusion, moving averages are essential tools for identifying patterns and trends in time-series data, making them a crucial component of any data analysis. This article introduced two methods for calculating moving averages – the cumsum() function and the pandas rolling() method.

Although the cumsum() method is efficient, the rolling() method provides more flexibility in selecting the number of previous time periods and can handle missing data with greater ease. Whichever method we choose, the key takeaway is that moving averages remain a powerful tool for identifying trends and patterns in time-series data.

Choose the method that best suits your data to generate accurate and reliable insights for data-driven decision-making.