The AR process

The AR process defines the current value of the series, Y_t, as a linear combination of the previous p lags of the series, and can be formalized with the following equation:

Following are the terms used in the preceding equation:

• AR(p) is the notation for an AR process with p-order
• c represents a constant (or drift)
• p defines the number of lags to regress against Y_t

• is the coefficient of the i lag of the series (here, must be between -1 and 1, otherwise, the series would be trending up or down and therefore cannot be stationary over time)
• Y_t-i is the i lag of the series
• ∈_t represents the error term, which is white noise

An AR process can be used on time series data if, and only if, the series is stationary. Therefore, before applying an AR process on a series, you will have to verify that the series is stationary. Otherwise, you will have to apply some...