One of the main assumptions of the ARIMA family of models is that the input series follows the stationary process structure. This assumption is based on the Wold representation theorem, which states that any stationary process can be represented as a linear combination of white noise. Therefore, before we dive into the ARIMA model components, let's pause and talk about the stationary process. The stationary process, in the context of time series data, describes a stochastic state of the series. Time series data is stationary if the following conditions are taking place:
- The mean and variance of the series do not change over time
- The correlation structure of the series, along with its lags, remains the same over time
In the following examples, we will utilize the arima.sim function from the stats package to simulate a stationary and non-stationary...
