自己回帰モデル
An autoregressive model (AR model) is a type of statistical model used for analyzing and 時系列データの分析と予測に使用されます。. The core idea of an autoregressive model is to use the relationship between an observation and a number of lagged observations (previous time 未来の値を予測するためのポイントです。
In an autoregressive model, the current value of the time series is expressed as a 線形結合 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
ここで：
- Xt は時刻tにおける時系列の値です。
- c は定数です。
- φ₁, φ₂, …, φp are the coefficients that represent the relationship between the current value and its lagged values.
- εt はホワイトノイズ誤差項であり、データのランダム性を表します。
モデルの次数（p）は、現在の値を予測するために使用される過去の値の数を示します。例えば、AR(1)モデルは直前の値のみを使用し、AR(2)は最も最近の2つの値を使用します。
Autoregressive models are particularly useful in fields such as economics, finance, and 環境科学 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.