Mathematics
Time Series Analysis and Autoregressive Models
Quick fact
An autoregressive model of order 1 (AR(1)) can be written as Xt = φ·Xt−1 + εt, where Xt is the value at time t, Xt−1 is the previous value, φ is a coefficient that controls the strength of the memory, and εt is random noise. If φ is between -1 and 1, the series is stable and mean-reverting, making it possible to forecast future values with measurable uncertainty.
Why this is interesting
Stock prices, daily temperatures, and even your heart rate have a hidden property: they can predict their own near future. But how can we turn that intuition into a mathematical model that actually forecasts?