Modelo autoregressivo
An autoregressive model (AR model) is a type of statistical model used for analyzing and prever dados de séries temporais. The core idea of an autoregressive model is to use the relationship between an observation and a number of lagged observations (previous time pontos) para prever valores futuros.
In an autoregressive model, the current value of the time series is expressed as a combinação linear 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
Onde:
- Xt é o valor da série temporal no tempo t.
- c é uma constante.
- φ₁, φ₂, …, φp are the coefficients that represent the relationship between the current value and its lagged values.
- εt é um termo de erro de ruído branco, representando a aleatoriedade nos dados.
A ordem do modelo (p) indica quantos valores passados são usados para prever o valor atual. Por exemplo, um modelo AR(1) usa apenas o valor imediatamente anterior, enquanto um AR(2) usa os dois valores mais recentes.
Autoregressive models are particularly useful in fields such as economics, finance, and ciência ambiental 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.