## Time series analysis concepts

One of the best time series analysis methods is called
**ARIMA** or **Box Jenkins**. **ARIMA** stands for **Autoregressive Integrated Moving Averages**.

Unlike regression models, in which *Yi* is explained by the *k* regressors (*X1*, *X2*, *X3*, ... , *Xk*), the BJ-type time series models allow *Yi* to be explained by past, or lagged, values of *Y* itself and stochastic error terms.

Let's take a small example of the GDP series, as shown in the following diagram:

Let's work with the GDP time series data for the United States given in the diagram. A plot of this time series is given in the undifferenced GDP and first-differenced GDP.

In the level form, GDP is nonstationary, but in the first-differenced form, it is stationary. If a time series is stationary, then it can fit the ARIMA model in a variety of ways. A time series is stationary when mean and variance is constant over time. Let's first understand an
**autoregressive** (**AR**) process:

Let

*Zt*denote the GDP at a given time*t*.This means that we...