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on Econometric Time Series |
| By: | Robin Braun; George Kapetanios; Massimiliano Marcellino |
| Abstract: | This paper studies the estimation and inference of time-varying impulse response functions in structural vector autoregressions (SVARs) identified with external instruments. Building on kernel estimators that allow for nonparametric time variation, we derive the asymptotic distributions of the relevant quantities. Our estimators are simple and computationally trivial and allow for potentially weak instruments. Simulations suggest satisfactory empirical coverage even in relatively small samples as long as the underlying parameter instabilities are sufficiently smooth. We illustrate the methods by studying the time-varying effects of global oil supply news shocks on US industrial production. |
| Keywords: | Time-varying parameters; Nonparametric estimation; Structural VAR; External instruments; Weak instruments; Oil supply news shocks; Impulse response analysis |
| JEL: | C14 C32 C53 C55 |
| Date: | 2025–01–06 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-04 |
| By: | Gianluca Cubadda |
| Abstract: | The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI], originally proposed by reinsel1983some , and their applications to economic and financial time series. MAI has recently gained momentum because it can be seen as a link between two popular but distinct multivariate time series approaches: vector autoregressive modeling [VAR] and the dynamic factor model [DFM]. Indeed, on the one hand, the MAI is a VAR model with a peculiar reduced-rank structure; on the other hand, it allows for identification of common components and common shocks in a similar way as the DFM. The focus is on recent developments of the MAI, which include extending the original model with individual autoregressive structures, stochastic volatility, time-varying parameters, high-dimensionality, and cointegration. In addition, new insights on previous contributions and a novel model are also provided. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.11278 |
| By: | Pierluigi Vallarino (Erasmus University Rotterdam and Tinbergen Institute) |
| Abstract: | This paper introduces the family of Dynamic Kernel models. These models study the predictive density function of a time series through a weighted average of kernel densities possessing a dynamic bandwidth. A general specification is presented and several particular models are studied in details. We propose an M-estimator for model parameters and derive its asymptotic properties under a misspecified setting. A consistent density estimator also introduced. Monte Carlo results show that the new models effectively track the time-varying distribution of several data generating processes. Dynamic Kernel models outperform extant kernel-based approaches in tracking the predictive distribution of GDP growth. |
| JEL: | C14 C51 C53 |
| Date: | 2024–12–31 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240082 |
| By: | Kexin Zhang (City University of Hong Kong); Simon Trimborn (University of Amsterdam and Tinbergen Institute) |
| Abstract: | When a company releases earnings results or makes announcements, a dominant sectoral wide lead-lag effect from the stock on the entire system may occur. To improve the estimation of a system experiencing dominant system-wide lead-lag effects from one or a few asset in the presence of short time series, we introduce a model for Large-scale Influencer Structures in Vector AutoRegressions (LISAR). To investigate its performance when little observations are available, we compare the LISAR model against competing models on synthetic data, showing that LISAR outperforms in forecasting accuracy and structural detection even for different strength of system persistence and when the model is misspecified. On high-frequency data for the constituents of the S&P100, separated by sectors, we find the LISAR model to significantly outperform or perform equally good for up to 91% of the time series under consideration in terms of forecasting accuracy. We show in this study, that in the presence of influencer structures within a sector, the LISAR model, compared to alternative models, provides higher accuracy, better forecasting results, and improves the understanding of market movements and sectoral structures. |
| Date: | 2024–12–20 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240080 |
| By: | Jad Beyhum |
| Abstract: | This article investigates factor-augmented sparse MIDAS (Mixed Data Sampling) regressions for high-dimensional time series data, which may be observed at different frequencies. Our novel approach integrates sparse and dense dimensionality reduction techniques. We derive the convergence rate of our estimator under misspecification, τ -mixing dependence, and polynomial tails. Our method’s finite sample performance is assessed via Monte Carlo simulations. We apply the methodology to nowcasting U.S. GDP growth and demonstrate that it outperforms both sparse regression and standard factor-augmented regression during the COVID-19 pandemic. To ensure the robustness of these results, we also implement factor-augmented sparse logistic regression, which further confirms the superior accuracy of our nowcast probabilities during recessions. These findings indicate that recessions are influenced by both idiosyncratic (sparse) and common (dense) shocks. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ete:ceswps:757474 |
| By: | Beatrice Foroni; Luca Merlo; Lea Petrella |
| Abstract: | In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and accommodate stylized facts embedded in financial time series, we rely upon the generalized hyperbolic family of distributions with time-dependent parameters evolving according to a latent Markov chain. We exploit its location-scale mixture representation to build a penalized EM algorithm for estimating the state-specific sparse precision matrices by means of an $L_1$ penalty. The proposed approach leads to regime-specific conditional correlation graphs that allow us to identify different degrees of network connectivity of returns over time. The methodology's effectiveness is validated through simulation exercises under different scenarios. In the empirical analysis we apply our model to daily returns of a large set of market indexes, cryptocurrencies and commodity futures over the period 2017-2023. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.03668 |
| By: | Giuseppe Buccheri; Fulvio Corsi; Emilija Dzuverovic |
| Abstract: | We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild restrictions. This result has no analogue in parameter-driven models, as it exploits the different structure of the score-driven factor dynamics. Consequently, score-driven models offer a clear advantage in terms of economic interpretability compared to parameter-driven factor models, which are identifiable only up to orthogonal transformations. Our restrictions are order-invariant and can be generalized to scoredriven factor models with dynamic loadings and nonlinear factor models. We test extensively the identification strategy using simulated and real data. The empirical analysis on financial and macroeconomic data reveals a substantial increase of log-likelihood ratios and significantly improved out-of-sample forecast performance when switching from the classical restrictions adopted in the literature to our more flexible specifications. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.01367 |
| By: | Matias Quiroz; Laleh Tafakori; Hans Manner |
| Abstract: | We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the models' rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.10791 |
| By: | Dobrislav Dobrev; Pawel J. Szerszen |
| Abstract: | Replacing faulty measurements with missing values can suppress outlier-induced distortions in state-space inference. We therefore put forward two complementary methods for enhanced outlier-robust filtering and forecasting: supervised missing data substitution (MD) upon exceeding a Huber threshold, and unsupervised missing data substitution via exogenous randomization (RMDX).Our supervised method, MD, is designed to improve performance of existing Huber-based linear filters known to lose optimality when outliers of the same sign are clustered in time rather than arriving independently. The unsupervised method, RMDX, further aims to suppress smaller outliers whose size may fall below the Huber detection threshold. To this end, RMDX averages filtered or forecasted targets based on measurement series with randomly induced subsets of missing data at an exogenously set randomization rate. This gives rise to regularization and bias-variance trade-off as a function of the missing data randomization rate, which can be set optimally using standard cross-validation techniques.We validate through Monte Carlo simulations that both methods for missing data substitution can significantly improve robust filtering, especially when combined together. As further empirical validation, we document consistently attractive performance in linear models for forecasting inflation trends prone to clustering of measurement outliers. |
| Keywords: | Kalman filter; Outliers; Huberization; Missing data; Randomization |
| JEL: | C15 C22 C53 E37 |
| Date: | 2025–01–03 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-01 |
| By: | Sylvia Kaufmann (Study Center Gerzensee); Markus Pape (Ruhr-University Bochum) |
| Abstract: | We use the geometric representation of factor models to represent the factor loading structure by sets corresponding to unit-specific non-zero loadings. We formulate global and local, rotational identification conditions based on set conditions. We propose two algorithms to efficiently evaluate Sato (1992)’s counting rule. We demonstrate the efficiency and the performance of the algorithms by a simulation study. An application to exchange rate returns illustrates the approach. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2406r |
| By: | Miguel C. Herculano; Santiago Montoya-Bland\'on |
| Abstract: | We develop a probabilistic variant of Partial Least Squares (PLS) we call Probabilistic Targeted Factor Analysis (PTFA), which can be used to extract common factors in predictors that are useful to predict a set of predetermined target variables. Along with the technique, we provide an efficient expectation-maximization (EM) algorithm to learn the parameters and forecast the targets of interest. We develop a number of extensions to missing-at-random data, stochastic volatility, and mixed-frequency data for real-time forecasting. In a simulation exercise, we show that PTFA outperforms PLS at recovering the common underlying factors affecting both features and target variables delivering better in-sample fit, and providing valid forecasts under contamination such as measurement error or outliers. Finally, we provide two applications in Economics and Finance where PTFA performs competitively compared with PLS and Principal Component Analysis (PCA) at out-of-sample forecasting. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.06688 |
| By: | Xinghong Fu; Masanori Hirano; Kentaro Imajo |
| Abstract: | Large models have shown unprecedented capabilities in natural language processing, image generation, and most recently, time series forecasting. This leads us to ask the question: treating market prices as a time series, can large models be used to predict the market? In this paper, we answer this by evaluating the performance of the latest time series foundation model TimesFM on price prediction. We find that due to the irregular nature of price data, directly applying TimesFM gives unsatisfactory results and propose to fine-tune TimeFM on financial data for the task of price prediction. This is done by continual pre-training of the latest time series foundation model TimesFM on price data containing 100 million time points, spanning a range of financial instruments spanning hourly and daily granularities. The fine-tuned model demonstrates higher price prediction accuracy than the baseline model. We conduct mock trading for our model in various financial markets and show that it outperforms various benchmarks in terms of returns, sharpe ratio, max drawdown and trading cost. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.09880 |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Daanish Padha (University of California, Riverside) |
| Abstract: | We extend the Three-Pass Regression Filter (3PRF) in two key dimensions: (1) accommodating weak factors and, (2) allowing for a correlation between the target variable and the predictors, even after adjusting for common factors, driven by correlations in the idiosyncratic components of the covariates and the prediction target. Our theoretical contribution is to establish the consistency of 3PRF under these flexible assumptions, showing that relevant factors can be consistently estimated even when they are weak, albeit at slower rates. Stronger relevant factors improve 3PRF convergence to the infeasible best forecast, while weaker relevant factors dampen it. Conversely, stronger irrelevant factors hinder the rate of convergence, whereas weaker irrelevant factors enhance it. We compare 3PRF with Principal Component Regression (PCR), highlighting scenarios where 3PRF performs better. Methodologically, we extend 3PRF by integrating a LASSO step to develop the 3PRF LASSO estimator, which effectively captures the target's dependency on the predictors' idiosyncratic components. We derive the rate at which the average prediction error from this step converges to zero, accounting for generated regressor effects. Simulation results confirm that 3PRF performs well under these broad assumptions, with the LASSO step delivering a substantial gain. In an empirical application using the FRED-QD dataset, 3PRF LASSO delivers reliable forecasts of key macroeconomic variables across multiple horizons. |
| Keywords: | Weak Factors; Forecasting; high dimension; supervision; three pass regression filter; LASSO. |
| JEL: | C18 C22 C53 C55 E27 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:ucr:wpaper:202502 |
| By: | Sung Hoon Choi; Donggyu Kim |
| Abstract: | In this paper, we develop a novel method for predicting future large volatility matrices based on high-dimensional factor-based It\^o processes. Several studies have proposed volatility matrix prediction methods using parametric models to account for volatility dynamics. However, these methods often impose restrictions, such as constant eigenvectors over time. To generalize the factor structure, we construct a cubic (order-3 tensor) form of an integrated volatility matrix process, which can be decomposed into low-rank tensor and idiosyncratic tensor components. To predict conditional expected large volatility matrices, we introduce the Projected Tensor Principal Orthogonal componEnt Thresholding (PT-POET) procedure and establish its asymptotic properties. Finally, the advantages of PT-POET are also verified by a simulation study and illustrated by applying minimum variance portfolio allocation using high-frequency trading data. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.04293 |
| By: | Andrea Bucci; Michele Palma; Chao Zhang |
| Abstract: | Traditional methods employed in matrix volatility forecasting often overlook the inherent Riemannian manifold structure of symmetric positive definite matrices, treating them as elements of Euclidean space, which can lead to suboptimal predictive performance. Moreover, they often struggle to handle high-dimensional matrices. In this paper, we propose a novel approach for forecasting realized covariance matrices of asset returns using a Riemannian-geometry-aware deep learning framework. In this way, we account for the geometric properties of the covariance matrices, including possible non-linear dynamics and efficient handling of high-dimensionality. Moreover, building upon a Fr\'echet sample mean of realized covariance matrices, we are able to extend the HAR model to the matrix-variate. We demonstrate the efficacy of our approach using daily realized covariance matrices for the 50 most capitalized companies in the S&P 500 index, showing that our method outperforms traditional approaches in terms of predictive accuracy. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.09517 |
| By: | Pål Boug; Håvard Hungnes (Statistics Norway); Takamitsu Kurita |
| Abstract: | This paper examines the forecast accuracy of cointegrated vector autoregressive models when confronted with extreme observations at the end of the sample period. It focuses on comparing two outlier correction methods, additive outliers and innovational outliers, within a forecasting framework for macroeconomic variables. Drawing on data from the COVID-19 pandemic, the study empirically demonstrates that cointegrated vector autoregressive models incorporating additive outlier corrections outperform both those with innovational outlier corrections and no outlier corrections in forecasting post-pandemic household consumption. Theoretical analysis and Monte Carlo simulations further support these findings, showing that additive outlier adjustments are particularly effective when macroeconomic variables rapidly return to their initial trajectories following short-lived extreme observations, as in the case of pandemics. These results carry important implications for macroeconomic forecasting, emphasising the usefulness of additive outlier corrections in enhancing forecasts after periods of transient extreme observations. |
| Keywords: | Extreme observations; additive outliers; innovational outliers; cointegrated vector autoregressive models; forecasting |
| JEL: | C32 C53 E21 E27 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:ssb:dispap:1018 |
| By: | Sylvia Kaufmann (Study Center Gerzensee); Markus Pape (Ruhr-University Bochum) |
| Abstract: | Factor modelling extracts common information from a high-dimensional data set into few common components, where the latent factors usually explain a large share of data variation. Exploratory factor estimation induces sparsity into the loading matrix to associate units or series with those factors most strongly loading on them, eventually determining factor interpretation. The authors motivate geometrically under which circumstances it may be necessary to consider the existence of multiple sparse factor loading matrices with similar degrees of sparsity for a given data set. They propose two MCMC approaches for Bayesian inference and corresponding post-processing algorithms to uncover multiple sparse representations of the factor loading matrix. They investigate both approaches in a simulation study. Applying the methods to data on U.S. sectoral inflation and country-specific gross domestic product growth series, they retrieve multiple sparse factor representations for each data set. Both approaches prove useful to discriminate between pervasive and weaker factors. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2304r |
| By: | Mikkel Bennedsen; Eric Hillebrand; Morten {\O}rregaard Nielsen |
| Abstract: | The Global Carbon Budget, maintained by the Global Carbon Project, summarizes Earth's global carbon cycle through four annual time series beginning in 1959: atmospheric CO$_2$ concentrations, anthropogenic CO$_2$ emissions, and CO$_2$ uptake by land and ocean. We analyze these four time series as a multivariate (cointegrated) system. Statistical tests show that the four time series are cointegrated with rank three and identify anthropogenic CO$_2$ emissions as the single stochastic trend driving the nonstationary dynamics of the system. The three cointegrated relations correspond to the physical relations that the sinks are linearly related to atmospheric concentrations and that the change in concentrations equals emissions minus the combined uptake by land and ocean. Furthermore, likelihood ratio tests show that a parametrically restricted error-correction model that embodies these physical relations and accounts for the El-Ni\~no/Southern Oscillation cannot be rejected on the data. Finally, projections based on this model, using Shared Socioeconomic Pathways scenarios, yield results consistent with established climate science. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.09226 |