Autoregression
An autoregression is a time series model that typically uses the previous values of the same series as an explanatory factor for the regression in order to predict the next value. Let's say that we have measured and kept track of a metric over time, called yt, which is measured at time t when this value is regressed on previous values from that same time series. For example, yt on yt-1:
As shown in the preceding equation, the previous value yt-1 has become the predictor here and yt is the response value that is to be predicted. Also, εt is normally distributed with a mean of zero and variance of 1. The order of the autoregression model is defined by the number of previous values that are being used by the model to determine the next value. Therefore, the preceding equation is a first-order autoregression, or AR(1). If we have to generalize it, a kth order autoregression, written as AR(k), is a multiple linear regression in which the value of the series at any time (t) is a...
