yannmclatchie / projpred-arma

Kullback-Leibler Projections for Automatic Order Identification of Bayesian ARMA Models

Kullback-Leibler Projections for Automatic Order Identification of Bayesian ARMA Models

This repository implements Algorithm 1 of the paper Bayesian order identification of ARMA models with projection predictive inference by McLatchie et al. (2022).

Algorithm

Inputs: Time series data ${y_t}$, reference model $P^\ast$, reference model $Q^\ast$, projpred model selection heuristic parameters alpha and pct

1. Perform Ljung-Box test for stationarity to data ${y_t}$ and print warning message if failed
2. Fit a linear reference model (AR) to these data observations ${y_t}$ with BRMS and lag parameter $P^\ast$
3. Apply the model selection heuristic to this reference AR model to get some restricted AR lag value $P^\perp$
4. Fit a linear restricted model (AR) to ${y_t}$ with BRMS and this new restricted lag parameter $P^\perp$
5. Extract the residuals from this AR restricted model, denote these residuals ${\epsilon_t}$
6. Fit a linear reference model (MA) to these residuals ${\epsilon_t}$ with BRMS and lag parameter $Q^\ast$
7. Apply the model selection heuristic to this reference MA model to get some restricted MA lag value $Q^\perp$

Returns: The restricted lag values $P^\perp$ and $Q^\perp$

Development

This algorithm requires a custom search heuristic, detailed in Figure 1 by McLatchie et al. (2022), which is available in a personal fork of projpred available for download through

devtools::install_github("yannmclatchie/projpred@time_series)