https://docs.google.com/presentation/d/1kgSCwGau3bhLie7XnFlU1o5HMYaRV1Hj/edit?usp=sharing&ouid=107956359237789538519&rtpof=true&sd=true

1698505795-20231028.png

Definition

(https://deepgenerativemodels.github.io/notes/autoregressive/)

$p(\mathbf{x}) = \prod\limits_{i=1}^{n}p(x_i \vert x_1, x_2, \ldots, x_{i-1}) = \prod\limits_{i=1}^{n} p(x_i \vert \mathbf{x}_{< i } )$

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Predict the next item from the previous items == $p(x_i \vert x_1, x_2, \ldots, x_{i-1})$

AR(p) model

https://en.wikipedia.org/wiki/Autoregressive_model

In statistics, econometrics, and signal processing, an autoregressive model may refer to a more specific type of model, AR model.

AR(p) model is defined as

****${\displaystyle X_{t}=\sum {i=1}^{p}\varphi{i}X_{t-i}+\varepsilon _{t}}$

where $\varphi_i$ are the parameters and $\varepsilon_t$ is white noise.

It can be further generalized to ARMA and ARIMA.

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Time series made easy in Python