State space with lasso Is it possible to incorporate lasso variable selection in the high dimensional state space model. If yes, is there any code or package available in R
 A: Thanks for your question!
There are 2 packages in R (to my knowledge) that allow you to use LASSO variable selection.
Package 1: glmnet
Package 2: lars
How to use it?


*

*glmnet function


General: glmnet(x, y, family=c("gaussian","binomial","poisson","multinomial","cox","mgaussian"),
    weights, offset=NULL, alpha = 1, nlambda = 100,
    lambda.min.ratio = ifelse(nobs))
Your case: x is an input matrix, y is a response, alpha = 1 means it is using LASSO method. If you set alpha = 0 it will use Ridge Regularization method.


*lars function


General: lars(x, y, type = c("lasso", "lar", "forward.stagewise", "stepwise"),  trace = FALSE, normalize = TRUE, intercept = TRUE, Gram, eps = .Machine$double.eps, max.steps, use.Gram = TRUE)

Your case: lars(x, y, type = lasso) where x is a matrix of predictors, and y is a response.
A: I give Maybe an over simplified example of a state space model:
You could for example model the transition probabilities
$$p(s’|s)=N(\beta s, \sigma^2)$$
However, when fitting this model, you could potentially put a lasso norm on $\beta$ if $s$ is high dimensional.
So you have some objective with least squares and a penalty.
A: Your best bet is using Bayesian lasso. Check out belmonte koop 2015 or bitto 2019. Park and Casella  wrote the first Bayesian lasso paper. You'd do it with a Gibbs sampler or some other MCMC process.
