Autoregressiivse

Autoregressiivse refers to a type of statistical model where past values of a variable are used to predict its future values. The term "autoregression" itself comes from Greek roots meaning "self" and "regression." In an autoregressive model, the current value of a time series is expressed as a linear combination of its previous values, plus a random error term.

For example, an AR(1) model, the simplest form, states that the current value is dependent only on the immediately preceding value. An AR(p) model generalizes this to include the p preceding values. These models are fundamental in time series analysis and are used in various fields such as economics, finance, and climate science to forecast trends and understand temporal dependencies.

The key assumption is that the future behavior of a system is predictable based on its past behavior. The order of the autoregressive model, denoted by 'p', is determined by analyzing the autocorrelation function of the time series data. Higher values of 'p' indicate that more past observations are needed for an accurate prediction. Autoregressive models are often used in conjunction with other time series components, like moving averages (ARMA models) or integrated components (ARIMA models), to create more comprehensive forecasting tools.