arXiv subjects

Giovanni Ballarin

Publications and source records attributed to Giovanni Ballarin.

8 recordsLinked to original sources

arXiv2025

From Many Models, One: Macroeconomic Forecasting with Reservoir Ensembles

Model combination is a powerful approach for achieving superior performance compared to selecting a single model. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs), which have been shown to achieve state-of-the-art macroeconomic time series forecasting results (Ballarin et al., 2024a). The Hedge and Follow-the-Leader schemes are discussed, and their online learning guarantees are extended to settings with dependent data. In empirical applications, the proposed Ensemble Echo State Networks demonstrate significantly improved predictive performance relative to individual MFESN models.

econ.EM↗

arXiv2025

Multi-Horizon Echo State Network Prediction of Intraday Stock Returns

Stock return prediction is a problem that has received much attention in the finance literature. In recent years, sophisticated machine learning procedures have been shown to perform significantly better than conventional prediction techniques. One downside of these approaches is that they are often numerically expensive to implement, for both training and inference, because of their high complexity. We propose a return prediction framework for intraday returns at multiple horizons based on Echo State Network (ESN) models, wherein a large subset of parameters is drawn at random and never trained. The coefficients that do require training can be fitted by explicitly solving a rolling-window, ridge-regularized least squares problem. Our approach enjoys the flexibility of machine learning methods, has an inherently efficient implementation, and shows strong forecasting performance.

q-fin.CP↗

arXiv2025

Memory Capacity of Nonlinear Recurrent Networks: Is it Informative?

The total memory capacity (MC) of linear recurrent neural networks (RNNs) has been proven to be equal to the rank of the corresponding Kalman controllability matrix, and it is almost surely maximal for connectivity and input weight matrices drawn from regular distributions. This fact questions the usefulness of this metric in distinguishing the performance of linear RNNs in the processing of stochastic signals. This work shows that the MC of random nonlinear RNNs yields arbitrary values within established upper and lower bounds depending exclusively on the scale of the input process. This confirms that the existing definition of MC in linear and nonlinear cases has no practical value.

cs.LG↗

arXiv2023

Impulse Response Analysis of Structural Nonlinear Time Series Models

This paper proposes a semiparametric sieve approach to estimate impulse response functions of nonlinear time series within a general class of structural autoregressive models. We prove that a two-step procedure can flexibly accommodate nonlinear specifications while avoiding the need to choose fixed parametric forms. Sieve impulse responses are proven to be consistent by deriving uniform estimation guarantees, and an iterative algorithm makes it straightforward to compute them in practice. With simulations, we show that the proposed semiparametric approach proves effective against misspecification while suffering only from minor efficiency losses. In a U.S. monetary policy application, the pointwise sieve GDP response associated with an interest rate increase is larger than that of a linear model. Finally, in an analysis of interest rate uncertainty shocks, sieve responses indicate more substantial contractionary effects on production and inflation.

econ.EM↗

arXiv2023

Memory of recurrent networks: Do we compute it right?

Numerical evaluations of the memory capacity (MC) of recurrent neural networks reported in the literature often contradict well-established theoretical bounds. In this paper, we study the case of linear echo state networks, for which the total memory capacity has been proven to be equal to the rank of the corresponding Kalman controllability matrix. We shed light on various reasons for the inaccurate numerical estimations of the memory, and we show that these issues, often overlooked in the recent literature, are of an exclusively numerical nature. More explicitly, we prove that when the Krylov structure of the linear MC is ignored, a gap between the theoretical MC and its empirical counterpart is introduced. As a solution, we develop robust numerical approaches by exploiting a result of MC neutrality with respect to the input mask matrix. Simulations show that the memory curves that are recovered using the proposed methods fully agree with the theory.

cs.LG↗

arXiv2022

Reservoir Computing for Macroeconomic Forecasting with Mixed Frequency Data

Macroeconomic forecasting has recently started embracing techniques that can deal with large-scale datasets and series with unequal release periods. MIxed-DAta Sampling (MIDAS) and Dynamic Factor Models (DFM) are the two main state-of-the-art approaches that allow modeling series with non-homogeneous frequencies. We introduce a new framework called the Multi-Frequency Echo State Network (MFESN) based on a relatively novel machine learning paradigm called reservoir computing. Echo State Networks (ESN) are recurrent neural networks formulated as nonlinear state-space systems with random state coefficients where only the observation map is subject to estimation. MFESNs are considerably more efficient than DFMs and allow for incorporating many series, as opposed to MIDAS models, which are prone to the curse of dimensionality. All methods are compared in extensive multistep forecasting exercises targeting US GDP growth. We find that our MFESN models achieve superior or comparable performance over MIDAS and DFMs at a much lower computational cost.

econ.EM↗

arXiv2021

Ridge Regularized Estimation of VAR Models for Inference

Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a comparison is made with Bayesian ridge-type estimators. The asymptotic distribution and the properties of cross-validation techniques are analyzed. Finally, the estimation of impulse response functions is evaluated with Monte Carlo simulations and ridge regression is compared with a number of similar and competing methods.

stat.ME↗

arXiv2021

On the Limiting Distribution of Sieve VAR($\infty$) Estimators in Small Samples

When a finite order vector autoregressive model is fitted to VAR($\infty$) data the asymptotic distribution of statistics obtained via smooth functions of least-squares estimates requires care. Lütkepohl and Poskitt (1991) provide a closed-form expression for the limiting distribution of (structural) impulse responses for sieve VAR models based on the Delta method. Yet, numerical simulations have shown that confidence intervals built in such way appear overly conservative. In this note I argue that these results stem naturally from the limit arguments used in Lütkepohl and Poskitt (1991), that they manifest when sieve inference is improperly applied, and that they can be "remedied" by either using bootstrap resampling or, simply, by using standard (non-sieve) asymptotics.

stat.ME↗