ARFIMA

ARFIMA, or Autoregressive Fractionally Integrated Moving Average, is a statistical model used for time series analysis. It is an extension of the ARIMA (Autoregressive Integrated Moving Average) model, which is widely used for forecasting and analyzing time series data. The ARFIMA model incorporates fractional differencing, allowing it to handle time series data with long memory or long-range dependence. This means that the model can capture the persistence of certain patterns over time, which is not possible with traditional ARIMA models.

The ARFIMA model is defined by three parameters: p, d, and q. The parameter p represents the order of the autoregressive part, d is the fractional differencing parameter, and q is the order of the moving average part. The fractional differencing parameter d can take non-integer values, which allows the model to capture the long memory property of the time series.

ARFIMA models are particularly useful in fields such as finance, economics, and environmental science, where time series data often exhibit long-range dependence. They provide a more accurate representation of the underlying data and can lead to better forecasts compared to traditional ARIMA models. However, the estimation of ARFIMA models can be more complex and computationally intensive due to the fractional differencing parameter.