ARIMA Model
ARIMA, which stands for Autoregressive Integrated Moving Average, is a time series forecasting statistical approach. It is a well-known and effective method for modeling and forecasting time-dependent data. ARIMA is made up of three major components: Autoregression (AR), Integration (I), and Moving Average (MA).
Autoregression (AR)
Modeling the link between one observation and numerous lagged observations (prior time steps) is the autoregressive component.
The number of lag observations included in the model is represented by the “p” parameter in ARIMA, abbreviated as AR(p). It represents the amount of time steps in the past that the model utilizes to forecast the current time step.
Integration (I)
To make the time series data steady, the integration component differencing it. Stationarity indicates that a time series’ statistical features, such as mean and variance, stay constant across time.
The I(d) differencing parameter reflects the number of times differencing is conducted to achieve stationarity.
Moving Average (MA)
Modeling the link between an observation and a residual error from a moving average model applied to lagged data is part of the moving average component.
The moving average order is represented by the “q” parameter in ARIMA, written as MA(q). It determines how many lag forecast mistakes are incorporated into the model.
When all of this is considered, the ARIMA model is frequently expressed as ARIMA(p, d, q), where:
- p: The order of the autoregressive component.
- d: The degree of differencing.
- q: The order of the moving average component.
Used randomly generated data to understand the working
The graph depicts a time series dataset and the forecast produced by an ARIMA model. The observed time series data, which is a cumulative total of randomly produced normal values, is shown by the blue line. The figure depicts the underlying trend and volatility in the synthetic data visually. The red line depicts the ARIMA model’s forecast for the following ten steps. The ARIMA model captures patterns and dependencies in the data, creating a prediction that attempts to predict future values based on previous patterns (p=1, d=1, q=1). The graph depicts the use of ARIMA for time series forecasting, showing both the actual data and the model’s anticipated values during the selected forecast period.