# Posts tagged autoregressive

## The Besag-York-Mollie Model for Spatial Data

- 18 August 2023
- intermediate, tutorial

This notebook uses libraries that are not PyMC dependencies and therefore need to be installed specifically to run this notebook. Open the dropdown below for extra guidance.

## Analysis of An AR(1) Model in PyMC

- 07 January 2023
- , intermediate

Consider the following AR(2) process, initialized in the infinite past: $\( y_t = \rho_0 + \rho_1 y_{t-1} + \rho_2 y_{t-2} + \epsilon_t, \)\( where \)\epsilon_t \overset{iid}{\sim} {\cal N}(0,1)\(. Suppose you'd like to learn about \)\rho\( from a a sample of observations \)Y^T = { y_0, y_1,\ldots, y_T }$.

## Forecasting with Structural AR Timeseries

- 20 October 2022
- intermediate

Bayesian structural timeseries models are an interesting way to learn about the structure inherent in any observed timeseries data. It also gives us the ability to project forward the implied predictive distribution granting us another view on forecasting problems. We can treat the learned characteristics of the timeseries data observed to-date as informative about the structure of the unrealised future state of the same measure.

## Conditional Autoregressive (CAR) Models for Spatial Data

This notebook uses libraries that are not PyMC dependencies and therefore need to be installed specifically to run this notebook. Open the dropdown below for extra guidance.

## About Conditional Autoregressive models in PyMC

- 14 August 2020
- advanced, explanation

This notebook explains the design principles behind the Conditional Autoregressive (CAR) distribution as implemented in PyMC. For a simple tutorial of why and how to use the CAR distribution, see this notebook.