What is an Auto Regressive Model

Autoregressive Model (AR)

An autoregressive (AR) model is a statistical model used to predict future values of a variable based on its past values. In simpler terms, it assumes that the current value of a time series is dependent on its previous values.

Key Characteristics:

Time Series Data: Specifically designed for time-series data, where the order of observations is crucial.

Linear Regression: Mathematically, it's a linear regression model where the predictors are past values of the same variable.

Order (p): The number of past values used to predict the current value is called the order of the model (denoted as AR(p)).

Mathematical Representation:

An AR(p) model can be expressed as:

Yt = c + φ1Yt-1 + φ2Yt-2 + ... + φpYt-p + εt

Yt is the value of the variable at time t

c is a constant

φ1, φ2, ..., φp are the coefficients for the past p values

Yt-1, Yt-2, ..., Yt-p are the previous p values of the variable

εt is the error term (white noise)

AR models are widely used in various fields, including:

Economics: Predicting stock prices, GDP growth, inflation rates

Finance: Forecasting asset returns, risk management

Meteorology: Predicting weather patterns

Signal processing: Analyzing time-series signals

Limitations:

AR models are best suited for stationary time series (where the statistical properties remain constant over time). Non-stationary data might require differencing or other transformations before applying AR models.

The order of the model (p) needs to be determined carefully using techniques like AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion)

In essence, AR models provide a powerful tool for understanding and forecasting time-series data by leveraging the information contained in past observations.

references:

https://www.analyticsvidhya.com/blog/2021/10/a-comprehensive-guide-to-time-series-analysis/