Time-Varying Parameters as Ridge Regressions

Time-varying parameters (TVPs) models are frequently used in economics to model structural change. I show that they are in fact 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. The application requires the estimation of about 4600 TVPs, a task well within the reach of the new method

Maximally Machine-Learnable Portfolios

When it comes to stock returns, any form of predictability can bolster risk-adjusted profitability. We develop a collaborative machine learning algorithm that optimizes portfolio weights so that the resulting synthetic security is maximally predictable. Precisely, we introduce MACE, a multivariate extension of Alternating Conditional Expectations that achieves the aforementioned goal by wielding a Random Forest on one side of the equation, and a constrained Ridge Regression on the other. There are two key improvements with respect to Lo and MacKinlay's original maximally predictable portfolio approach. First, it accommodates for any (nonlinear) forecasting algorithm and predictor set. Second, it handles large portfolios. We conduct exercises at the daily and monthly frequency and report significant increases in predictability and profitability using very little conditioning information. Interestingly, predictability is found in bad as well as good times, and MACE successfully navigates the debacle of 2022

Machine Learning Econometrics

Much of econometrics is based on a tight probabilistic approach to empirical modeling that dates back to Haavelmo (1944). This thesis explores a modern algorithmic view, and by doing so, finds solutions to classic problems while developing new avenues. In the first chapter, Kalman-filter based computations of random walk coefficients are replaced by a closed-form solution only second to least squares in the pantheon of simplicity. In the second chapter, random walk “drifting” coefficients are themselves dismissed. Rather, evolving coefficients are modeled and forecasted with a powerful machine learning algorithm. Conveniently, this generalization of time-varying parameters provides statistical efficiency and interpretability, which off-the-shelf machine learning algorithms cannot easily offer. The third chapter is about the to the fundamental problem of detecting at which point a learner stops learning and starts imitating. It answers “why can’t Random Forest overfit?” The phenomenon is shown to be a surprising byproduct of randomized “greedy” algorithms – often deployed in the face of computational adversity. Then, the insights are utilized to develop new high-performing non-overfitting algorithms

Assessing and Comparing Fixed-Target Forecasts of Arctic Sea Ice: Glide Charts for Feature-Engineered Linear Regression and Machine Learning Models

We use "glide charts" (plots of sequences of root mean squared forecast errors as the target date is approached) to evaluate and compare fixed-target forecasts of Arctic sea ice. We first use them to evaluate the simple feature-engineered linear regression (FELR) forecasts of Diebold and Goebel (2021), and to compare FELR forecasts to naive pure-trend benchmark forecasts. Then we introduce a much more sophisticated feature-engineered machine learning (FEML) model, and we use glide charts to evaluate FEML forecasts and compare them to a FELR benchmark. Our substantive results include the frequent appearance of predictability thresholds, which differ across months, meaning that accuracy initially fails to improve as the target date is approached but then increases progressively once a threshold lead time is crossed. Also, we find that FEML can improve appreciably over FELR when forecasting "turning point" months in the annual cycle at horizons of one to three months ahead

Predicting September Arctic Sea Ice: A Multi-Model Seasonal Skill Comparison

Abstract This study quantifies the state-of-the-art in the rapidly growing field of seasonal Arctic sea ice prediction. A novel multi-model dataset of retrospective seasonal predictions of September Arctic sea ice is created and analyzed, consisting of community contributions from 17 statistical models and 17 dynamical models. Prediction skill is compared over the period 2001–2020 for predictions of Pan-Arctic sea ice extent (SIE), regional SIE, and local sea ice concentration (SIC) initialized on June 1, July 1, August 1, and September 1. This diverse set of statistical and dynamical models can individually predict linearly detrended Pan-Arctic SIE anomalies with skill, and a multi-model median prediction has correlation coefficients of 0.79, 0.86, 0.92, and 0.99 at these respective initialization times. Regional SIE predictions have similar skill to Pan-Arctic predictions in the Alaskan and Siberian regions, whereas regional skill is lower in the Canadian, Atlantic, and Central Arctic sectors. The skill of dynamical and statistical models is generally comparable for Pan-Arctic SIE, whereas dynamical models outperform their statistical counterparts for regional and local predictions. The prediction systems are found to provide the most value added relative to basic reference forecasts in the extreme SIE years of 1996, 2007, and 2012. SIE prediction errors do not show clear trends over time, suggesting that there has been minimal change in inherent sea ice predictability over the satellite era. Overall, this study demonstrates that there are bright prospects for skillful operational predictions of September sea ice at least three months in advance.</jats:p