Modelo Autoregresivo
An autoregressive model (AR model) is a type of statistical model used for analyzing and pronosticar datos de series temporales. The core idea of an autoregressive model is to use the relationship between an observation and a number of lagged observations (previous time puntos) para predecir valores futuros.
In an autoregressive model, the current value of the time series is expressed as a combinación lineal of its previous values, plus a stochastic (random) error term. The general form of an autoregressive model of order p, denoted as AR(p), can be described by the equation:
Xt = c + φ₁ Xt-1 + φ₂ Xt-2 + … + φp Xt-p + εt
Donde:
- Xt es el valor de la serie temporal en el tiempo t.
- c es una constante.
- φ₁, φ₂, …, φp are the coefficients that represent the relationship between the current value and its lagged values.
- εt es un término de error de ruido blanco, que representa la aleatoriedad en los datos.
El orden del modelo (p) indica cuántos valores pasados se utilizan para predecir el valor actual. Por ejemplo, un modelo AR(1) usa solo el valor pasado inmediato, mientras que un AR(2) usa los dos valores más recientes.
Autoregressive models are particularly useful in fields such as economics, finance, and ciencias ambientales for tasks like stock price forecasting, economic indicators analysis, and climate data prediction. However, they assume that the underlying relationships are linear and stationary, meaning that the statistical properties of the time series do not change over time.