Autoregressive Model & Stochastic Model - SoojungHong/MachineLearning GitHub Wiki

(reference : https://www.statisticshowto.com/autoregressive-model/)

Autoregressive Model

Time series > Autoregressive Model What is an Autoregressive Model?

An autoregressive (AR) model predicts future behavior based on past behavior. It’s used for forecasting when there is some correlation between values in a time series and the values that precede and succeed them. You only use past data to model the behavior, hence the name autoregressive (the Greek prefix auto– means “self.” ). The process is basically a linear regression of the data in the current series against one or more past values in the same series.

In an AR model, the value of the outcome variable (Y) at some point t in time is — like “regular” linear regression — directly related to the predictor variable (X). Where simple linear regression and AR models differ is that Y is dependent on X and previous values for Y.

The AR process is an example of a stochastic process, which have degrees of uncertainty or randomness built in. The randomness means that you might be able to predict future trends pretty well with past data, but you’re never going to get 100 percent accuracy. Usually, the process gets “close enough” for it to be useful in most scenarios.

AR models are also called conditional models, Markov models, or transition models.

Stochastic Model

https://www.statisticshowto.com/stochastic-model/

A stochastic model represents a situation where uncertainty is present. In other words, it’s a model for a process that has some kind of randomness. The word stochastic comes from the Greek word stokhazesthai meaning to aim or guess. In the real word, uncertainty is a part of everyday life, so a stochastic model could literally represent anything. The opposite is a deterministic model, which predicts outcomes with 100% certainty. Deterministic models always have a set of equations that describe the system inputs and outputs exactly. On the other hand, stochastic models will likely produce different results every time the model is run.

All stochastic models have the following in common:

They reflect all aspects of the problem being studied,
Probabilities are assigned to events within the model,
Those probabilities can can be used to make predictions or supply other relevant information about the process.