ARIMA Modelling

ARIMA modelling or Autoregressive Integrated Moving Average is a time series analysis and forecasting method, the ARIMA model is a combination of autoregression, differencing and moving average which are used in the modelling of time series. Let’s break it down and discuss the different components one by one:

• Autoregressive (AR) Component: The autoregressive component involves modeling the relationship between an observation and several lagged observations (previously observed points). This component gives us the idea that the current value of the time series is related to the previous values of the series. The term “autoregressive” signifies that the model uses the relationship of the variable with its own past values. The AR component is denoted by p which can be expressed as:

Where:

• is the value of time series on time t.
• c is a constant value.
• are autoregressive coefficients.
• is error at time t.

• Integrated(I) Component: Integrated component makes the time series stationary by differencing; it means that the statistical properties of the time series do not change over time. It helps in stabilizing the mean and removing trends from the time series. Differencing is denoted by d, and represents first order differencing. We can further increase the order of differencing through , etc.
  

• Moving Average (MA) Component: This component represents the effect of past error terms on the current value of the time series. The moving average component can be represented as q, which is also known as the order of moving average. The moving average process can also be represented as:

Where:

• is the value of time series at time t.
• c is a constant.
• are the noise terms or the error terms.
• are the moving average constants.

ARIMA(p,d,q):

ARIMA model combines all the AR, I, MA components in it. ARIMA modelling combines all the components mentioned above and its general form is given by:

The general ARIMA forecasting process involves selecting appropriate values for p, d, and q, estimating the model parameters, and using the model to make predictions. The Box-Jenkins methodology is often used for identifying and fitting ARIMA models to time series data.

Let’s discuss the box-jenkins method in detail now.

Time series data records data points with respect to time intervals. The analysis of such dataset is important to recognize patterns and making predictions as well as providing informative insights. Box-Jenkins model is a forecasting method that is used to forecasts time series data for a specific period of time.

In this article we will be taking a dive into the Box-Jenkins method for ARIMA modelling as it helps us analyze and forecast time series data.

Let us first discuss an overview about what is an ARIMA model so that we can get a sound understanding about the process.