How Sine and consine transformations help to identify cyclical patterns in the data?

In the below code , the timestamp seconds value is done with sine and cosine transformation to make it more useful. How cosine ans sine transformation is useful ?

df['Day sin'] = np.sin(timestamp_s * (2 * np.pi / day))

df['Day cos'] = np.cos(timestamp_s * (2 * np.pi / day))

df['Year sin'] = np.sin(timestamp_s * (2 * np.pi / year))

df['Year cos'] = np.cos(timestamp_s * (2 * np.pi / year))

Understanding Sine and Cosine Transformation for Time Series

The sine and cosine transformations are used to capture cyclical patterns within your time series data. By converting the timestamp into these trigonometric functions, you're essentially encoding information about the time of day, day of the week, and even year into numerical features.

How it works:

Timestamp Conversion: The timestamp is converted into a numerical representation (e.g., seconds since a specific epoch).

Scaling: The timestamp is scaled to fit within a specific range (e.g., 0 to 2π) for the sine and cosine functions.

Sine and Cosine Transformation: The scaled timestamp is applied to the sine and cosine functions, creating new features.

Why it's useful:

Cyclic Patterns: Many time series exhibit cyclical patterns (e.g., daily, weekly, yearly). Sine and cosine functions naturally capture these patterns.

Feature Engineering: The transformed features can be used as input to machine learning models, improving their ability to learn and predict cyclical trends.

Model Interpretability: The sine and cosine features can provide insights into the importance of different time components for the target variable.

Example:

Day sin and Day cos: Capture the cyclical pattern within a day (e.g., peak traffic during certain hours).

Year sin and Year cos: Capture annual patterns (e.g., seasonal variations).

By incorporating these transformed features into your time series model, you can improve its ability to capture complex patterns and make more accurate predictions.