arXiv subjects

Graciela González-Farías

Publications and source records attributed to Graciela González-Farías.

4 recordsLinked to original sources

arXiv2025

Over the Stability Space of a Multivariate Time Series

This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space, aimed at capturing stationary components in settings where traditional assumptions may not hold. Based on the dimensionality reduction techniques of Partial Least Squares and Principal Component Analysis, we proposed two non-parametric procedures for estimating such a space and a targeted selection of components that prioritise stationarity. We compare these alternatives with the parametric Johansen procedure when possible. Through simulations and real-data applications, we evaluated the performance of these methodologies across various scenarios, including high-dimensional configurations where regularisation techniques are explored, considering a sparse version of the Principal Component Analysis.

stat.ME↗

arXiv2022

Nonparametric Estimation of Functional Dynamic Factor Model

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for functional data. In this paper, we study functional factor models for time-dependent functional data. We propose nonparametric estimators under stationary and nonstationary processes. We obtain estimators that consider the time-dependence property. Specifically, we use the information contained in the covariances at different lags. We show that the proposed estimators are consistent. Through Monte Carlo simulations, we find that our methodology outperforms estimators based on functional principal components. We also apply our methodology to monthly yield curves. In general, the suitable integration of time-dependent information improves the estimation of the latent factors.

stat.ME↗

arXiv2021

A nowcasting approach to generate timely estimates of Mexican economic activity: An application to the period of COVID-19

In this paper, we present a new approach based on dynamic factor models (DFMs) to perform nowcasts for the percentage annual variation of the Mexican Global Economic Activity Indicator (IGAE in Spanish). The procedure consists of the following steps: i) build a timely and correlated database by using economic and financial time series and real-time variables such as social mobility and significant topics extracted by Google Trends; ii) estimate the common factors using the two-step methodology of Doz et al. (2011); iii) use the common factors in univariate time-series models for test data; and iv) according to the best results obtained in the previous step, combine the statistically equal better nowcasts (Diebold-Mariano test) to generate the current nowcasts. We obtain timely and accurate nowcasts for the IGAE, including those for the current phase of drastic drops in the economy related to COVID-19 sanitary measures. Additionally, the approach allows us to disentangle the key variables in the DFM by estimating the confidence interval for both the factor loadings and the factor estimates. This approach can be used in official statistics to obtain preliminary estimates for IGAE up to 50 days before the official results.

stat.AP↗

arXiv2019

Determining the number of factors in a forecast model by a random matrix test: cryptocurrencies

We determine the number of statistically significant factors in a forecast model using a random matrices test. The applied forecast model is of the type of Reduced Rank Regression (RRR), in particular, we chose a flavor which can be seen as the Canonical Correlation Analysis (CCA). As empirical data, we use cryptocurrencies at hour frequency, where the variable selection was made by a criterion from information theory. The results are consistent with the usual visual inspection, with the advantage that the subjective element is avoided. Furthermore, the computational cost is minimal compared to the cross-validation approach.

q-fin.ST↗