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Simple Moving Average | Stationary Models
Time Series Analysis

Course Content

Time Series Analysis

## Time Series Analysis

1. Time Series: Let's Start

2. Time Series Processing

3. Time Series Visualization

# Simple Moving Average

Mathematically, the simple moving average model is represented as follows:

In this equation, the prediction SMA consists of variables, where `k` is the window size (how many past values we will take to calculate the next value), and `p` is the value taken.

How does this model work? In fact, the simple moving average at each prediction moment calculates the average of several past values - the resulting number is the next prediction. You can imagine a graph on the path of which a window of size `n` moves (you can take 2 values, you can take 3, etc.). The smaller the window, the smoother the predictions. Let's demonstrate it below:

In the first image, the window size for which the average value is calculated is 8, while on the second graph, `n` = 3. The smaller the window, the fewer peaks it can capture.

Python allows you to implement this model like this:

`rolling()` - a function used to calculate the moving average.

The simple moving average is one of the simplest models, so it is enough to use the `pandas` library to implement it.

Make predictions for dataset `pr_air_quality.csv` with window size 5.

1. Convert the `"date.utc"` column to `datetime` type.
2. Calculate moving averages using moving windows with the size of `5`.
3. Compare the results on a plot: visualize the first 50 values of the `"value"` column of the `df` within the first call of the `.plot()` function and the first 50 values of the `pred` within the second call.
4. Display the legend and the plot.

Everything was clear?

Section 4. Chapter 2

# Simple Moving Average

Mathematically, the simple moving average model is represented as follows:

In this equation, the prediction SMA consists of variables, where `k` is the window size (how many past values we will take to calculate the next value), and `p` is the value taken.

How does this model work? In fact, the simple moving average at each prediction moment calculates the average of several past values - the resulting number is the next prediction. You can imagine a graph on the path of which a window of size `n` moves (you can take 2 values, you can take 3, etc.). The smaller the window, the smoother the predictions. Let's demonstrate it below:

In the first image, the window size for which the average value is calculated is 8, while on the second graph, `n` = 3. The smaller the window, the fewer peaks it can capture.

Python allows you to implement this model like this:

`rolling()` - a function used to calculate the moving average.

The simple moving average is one of the simplest models, so it is enough to use the `pandas` library to implement it.

Make predictions for dataset `pr_air_quality.csv` with window size 5.
1. Convert the `"date.utc"` column to `datetime` type.
2. Calculate moving averages using moving windows with the size of `5`.
3. Compare the results on a plot: visualize the first 50 values of the `"value"` column of the `df` within the first call of the `.plot()` function and the first 50 values of the `pred` within the second call.