ljyflores / bayes-for-markov-switching

Python implementation of Markov Switching Model using Bayesian inference (Gibbs Sampling) by Lim et al (2020)

bayes-for-markov-switching

TLDR: We provide a Python implementation of the original R code for fitting a Markov Switching Model using Bayesian inference (Gibbs Sampling) by Lim et al (2020). We explore such methods of estimation as Bayesian methods have been found to be more flexible and efficient that standard MLE approaches (Ghysels, 1998), (Harris, 2014).

This repository can be used to fit the following model using Bayesian inference:

$$ y_t = \mu_{S_t} + \sum_{i=1}^{k} \phi_{S_t}^i (y_{t-i}-\mu_{S_t-i}) + e_t, \quad e_t \sim N(0,\sigma_{S_t}^2) $$

$$ \mu_{S_t} = \sum_{i=1}^l \mu_i S_{it} \quad \text{(Mean of State $i$)}, \quad \sigma_{S_t}^2 = \sum_{i=1}^l \sigma_i^2 S_{it} \quad \text{(Variance of State $i$)} $$

$$ S_{it} = I[S_t=i] \quad \text{(Indicator Variable)}, \quad p_{i,j} = P[S_t=j|S_{t-1}=i] \quad \sum_{j=1}^l p_{i,j}=1 \quad \text{(Transition Probabilities)} $$

The main.ipynb notebook provides an example of applying this to FED return data.

Check out the writeup explaining the algorithm here!

In case this repository was helpful, please consider citing the main authors:

@article{10.1371/journal.pcbi.1007839,
    doi = {10.1371/journal.pcbi.1007839},
    author = {Lim, Jue Tao AND Dickens, Borame Sue AND Haoyang, Sun AND Ching, Ng Lee AND Cook, Alex R.},
    journal = {PLOS Computational Biology},
    publisher = {Public Library of Science},
    title = {Inference on dengue epidemics with Bayesian regime switching models},
    year = {2020},
    month = {05},
    volume = {16},
    url = {https://doi.org/10.1371/journal.pcbi.1007839},
    pages = {1-15},
    number = {5},
}