Autóregressískt

Autóregressískt is a term used in statistics and time series analysis to describe a model where a variable's future values are predicted based on its past values. The term "autoregressive" itself comes from the Greek words "auto" meaning "self" and "regression" meaning "to go back." Therefore, an autoregressive model is one that regresses a variable onto itself.

In an autoregressive model of order p, denoted as AR(p), the current value of a time series is expressed as a linear combination of its p preceding values, plus a constant term and a stochastic error term. For example, an AR(1) model has the form $Y_t = c + \phi_1 Y_{t-1} + \epsilon_t$, where $Y_t$ is the value of the time series at time t, $c$ is a constant, $\phi_1$ is a coefficient, $Y_{t-1}$ is the value at the previous time step, and $\epsilon_t$ is an error term. Higher order AR(p) models include more past values in the equation.

These models are fundamental in understanding and forecasting sequential data, such as stock prices, weather patterns, or economic indicators. The assumption is that past behavior is a good predictor of future behavior within the observed series. Autoregressive models are often used in conjunction with other time series components, like moving averages, to form more complex models such as ARIMA (Autoregressive Integrated Moving Average). The order p of the autoregressive component is typically determined through statistical analysis of the autocorrelation function of the time series.