## How to detect seasonality on time series data?

Detecting seasonality in time series data involves examining patterns that repeat at regular intervals. There are several methods to identify seasonality in time series data:

### Visual Inspection:

Plot the time series data and observe if there are recurring patterns at regular intervals. Seasonal patterns may appear as peaks and troughs that repeat over time. A line plot or a heatmap can help visualize these patterns.

### Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF):

Use ACF and PACF plots to identify the correlation structure in the data. Peaks in the ACF plot at multiples of a certain lag may indicate seasonality. PACF helps to identify the direct relationship between the current observation and its lagged values.

### Periodogram Analysis:

Calculate the periodogram of the time series, which is a frequency-domain plot of the data’s spectral density. Peaks in the periodogram at specific frequencies may indicate the presence of seasonality.

### Moving Averages:

Apply moving average smoothing to the time series data and observe if there are recurring patterns. Seasonality may become more apparent after smoothing, making it easier to identify.

### Seasonal Subseries Plot:

Create seasonal subseries plots by aggregating data within each season and plotting the subseries separately. This visual representation can highlight seasonal patterns more clearly.

### Box Plots:

Use box plots to compare the distribution of data across different seasons. If there is a consistent pattern in the distribution, it may indicate seasonality.

### Decomposition Techniques:

Apply decomposition methods like Seasonal-Trend decomposition using LOESS (STL) or Seasonal Decomposition of Time Series (STL). These methods separate the time series into its components (trend, seasonality, and residual), making it easier to identify and analyze seasonality.

### Statistical Tests:

Perform statistical tests such as the Augmented Dickey-Fuller (ADF) test for stationarity. If the time series is non-stationary, it may suggest the presence of seasonality.

### Fourier Transform:

Apply Fourier transform to analyze the frequency components of the time series. Peaks at specific frequencies may indicate the presence of seasonality.

### Time Series Decomposition using SARIMA Models:

Seasonal Autoregressive Integrated Moving Average (SARIMA) models explicitly incorporate seasonality. Fitting a SARIMA model to the data and analyzing the residuals can help identify and understand the seasonal patterns.

### Conclusion:

It’s often useful to combine multiple methods for a comprehensive analysis. Additionally, considering domain knowledge and the context of the data can enhance the accuracy of seasonality detection. Once seasonality is identified, it can be incorporated into forecasting models or further analyzed to understand its impact on the time series data.