# Time-Varying Parameters as Ridge Regressions

arXiv: https://arxiv.org/abs/2009.00401 · HTML: https://mlsanity.com/paper/2009.00401/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [DMS, AE, DAA: methods and applications of adaptive time series model selection, ensemble, and financial evaluation](https://mlsanity.com/paper/2110.11156/) (2021)

## Abstract (arXiv)

Time-varying parameters (TVPs) models are frequently used in economics to capture structural change. I highlight a rather underutilized fact -- that these are actually ridge regressions. Instantly, this makes computations, tuning, and implementation much easier than in the state-space paradigm. Among other things, solving the equivalent dual ridge problem is computationally very fast even in high dimensions, and the crucial "amount of time variation" is tuned by cross-validation. Evolving volatility is dealt with using a two-step ridge regression. I consider extensions that incorporate sparsity (the algorithm selects which parameters vary and which do not) and reduced-rank restrictions (variation is tied to a factor model). To demonstrate the usefulness of the approach, I use it to study the evolution of monetary policy in Canada using large time-varying local projections. The application requires the estimation of about 4600 TVPs, a task well within the reach of the new method.