Seasonal Autoregressive Integrated Moving Average (SARIMA)

A statistical time series model called Seasonal Autoregressive Integrated Moving Average (SARIMA) is used to predict future values of a time series based on historical observations. It is a special kind of ARIMA (Autoregressive Integrated Moving Average) model created to take seasonality in time series data into account.

According to the example given below, seasonality is the recurring pattern in a time series of data that happens at regular intervals, such as weekly, monthly, or annually. It is vital to include this data in the statistical model in order to successfully anticipate seasonality in time series data. SARIMA does this by fusing the ideas of moving averages and autoregression with seasonal considerations.

The moving average (MA), the difference component (I), and the autoregression (AR) component make up the fundamental three parts of a SARIMA model. The I component reflects the discrepancy between the observed and predicted values of the time series, whereas the AR component models the connection between past and future values of the time series. The random error or noise in the time series is modelled by the MA component. To explain the recurring patterns in the time series data, SARIMA combines these elements with seasonal influences.

Three hyperparameters, denoted by p, d, and q, are used to specify SARIMA models. The parameters p, d, and q specify the order of the moving average component, differencing, and autoregression components, respectively. Moreover, P and Q are the two seasonal hyperparameters included in SARIMA models. These hyperparameters, which stand for the moving average component and seasonal autoregression order, respectively.

The hyperparameters p, d, q, P, and Q must be set to their ideal values in order to fit a SARIMA model. Combining trial-and-error with statistical methods like maximum likelihood estimate or AIC can be used to accomplish this (Akaike Information Criterion). The SARIMA model may be fitted to the time series data and used for forecasting when the hyperparameters have been chosen.

The ability of SARIMA models to detect seasonality in time series data is one of its key features. For predicting future values of time series data with repeated patterns, such as sales data or weather data, this is especially helpful. SARIMA models are accessible to a broad spectrum of users due to their ease of implementation and interpretation. It modifies the seasonality which is employed in terms of predicting for the following several years.