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on Econometric Time Series |
| By: | Alain Hecq; Ivan Ricardo; Ines Wilms |
| Abstract: | Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement structure. We propose reduced-rank regressions with a tensor structure for the coefficient matrix to provide new insights into co-movements within and between the dimensions of matrix-valued time series. Moreover, we relate the co-movement structures to two commonly used reduced-rank models, namely the serial correlation common feature and the index model. Two empirical applications involving U.S.\ states and economic indicators for the Eurozone and North American countries illustrate how our new tools identify co-movements. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.07973 |
| By: | Tassos Magdalinos; Katerina Petrova |
| Abstract: | A limit theory is developed for the least squares estimator for mildly and purely explosive autoregressions under drifting sequences of parameters with autoregressive roots ρn satisfying ρn → ρ ∈ (—∞, —1] ∪ [1, ∞) and n (|ρn| —1) → ∞. Drifting sequences of innovations and initial conditions are also considered. A standard specification of a short memory linear process for the autoregressive innovations is extended to a triangular array formulation both for the deterministic weights and for the primitive innovations of the linear process, which are allowed to be heteroskedastic L1-mixingales. The paper provides conditions that guarantee the validity of Cauchy limit distribution for the OLS estimator and standard Gaussian limit distribution for the t-statistic under this extended explosive and mildly explosive framework. |
| Keywords: | triangular array; explosive autoregression; linear process; conditional heteroskedasticity; mixingale; Cauchy distribution |
| JEL: | C12 C18 C22 |
| Date: | 2024–08–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:98657 |
| By: | Matteo Barigozzi; Marc Hallin |
| Abstract: | Several fundamental and closely interconnected issues related to factor models are reviewed and discussed: dynamic versus static loadings, rate-strong versus rate-weak factors, the concept of weakly common component recently introduced by Gersing et al. (2023), the irrelevance of cross-sectional ordering and the assumption of cross-sectional exchangeability, and the problem of undetected strong factors. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.10653 |
| By: | Zhaoxing Gao |
| Abstract: | This paper proposes a novel method for sparse latent factor modeling using a new sparse asymptotic Principal Component Analysis (APCA). This approach analyzes the co-movements of large-dimensional panel data systems over time horizons within a general approximate factor model framework. Unlike existing sparse factor modeling approaches based on sparse PCA, which assume sparse loading matrices, our sparse APCA assumes that factor processes are sparse over the time horizon, while the corresponding loading matrices are not necessarily sparse. This development is motivated by the observation that the assumption of sparse loadings may not be appropriate for financial returns, where exposure to market factors is generally universal and non-sparse. We propose a truncated power method to estimate the first sparse factor process and a sequential deflation method for multi-factor cases. Additionally, we develop a data-driven approach to identify the sparsity of risk factors over the time horizon using a novel cross-sectional cross-validation method. Theoretically, we establish that our estimators are consistent under mild conditions. Monte Carlo simulations demonstrate that the proposed method performs well in finite samples. Empirically, we analyze daily stock returns for a balanced panel of S&P 500 stocks from January 2004 to December 2016. Through textual analysis, we examine specific events associated with the identified sparse factors that systematically influence the stock market. Our approach offers a new pathway for economists to study and understand the systematic risks of economic and financial systems over time. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.09738 |
| By: | Fabrizio Lillo; Giorgio Rizzini |
| Abstract: | Modelling how a shock propagates in a temporal network and how the system relaxes back to equilibrium is challenging but important in many applications, such as financial systemic risk. Most studies so far have focused on shocks hitting a link of the network, while often it is the node and its propensity to be connected that are affected by a shock. Using as starting point the configuration model, a specific Exponential Random Graph model, we propose a vector autoregressive (VAR) framework to analytically compute the Impulse Response Function (IRF) of a network metric conditional to a shock on a node. Unlike the standard VAR, the model is a nonlinear function of the shock size and the IRF depends on the state of the network at the shock time. We propose a novel econometric estimation method that combines the Maximum Likelihood Estimation and Kalman filter to estimate the dynamics of the latent parameters and compute the IRF, and we apply the proposed methodology to the dynamical network describing the electronic Market of Interbank Deposit (e-MID). |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.09340 |
| By: | Parley R Yang; Alexander Y Shestopaloff |
| Abstract: | We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across various asset spaces, resulting in portfolios with reduced volatility. Such cointegration relationships persist well over the out-of-sample testing time, providing practical benefits in portfolio construction and optimization. Further studies on drawdown and volatility minimization also highlight the benefits of including cointegrated portfolios as risk management instruments. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.10175 |
| By: | Jos\'e E. Figueroa-L\'opez; Jincheng Pang; Bei Wu |
| Abstract: | For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-side kernels of unbounded support are more accurate, in this paper, an estimator using a general kernel spot volatility estimator as the plug-in is considered. A biased central limit theorem for estimating the integrated functional is established with an optimal convergence rate. Unbiased central limit theorems for estimators with proper de-biasing terms are also obtained both at the optimal convergence regime for the bandwidth and when applying undersmoothing. Our results show that one can significantly reduce the estimator's bias by adopting a general kernel instead of the standard uniform kernel. Our proposed bias-corrected estimators are found to maintain remarkable robustness against bandwidth selection in a variety of sampling frequencies and functions. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.09759 |
| By: | Richard Luger |
| Abstract: | This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within multiple testing procedures, controlling either the traditional familywise error rate, a generalized familywise error rate, or the false discovery proportion. Subsequent shrinkage ensures that the final covariance matrix estimate is positive definite and well-conditioned while preserving the achieved sparsity. Compared to alternative estimators, this new regularization method demonstrates strong performance in simulation experiments and real portfolio optimization. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.09696 |
| By: | Carsten H. Chong; Viktor Todorov |
| Abstract: | We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency asset return data. By showing a feasible CLT for this statistic under the null hypothesis of semimartingale volatility paths, we construct a test with fixed asymptotic size and an asymptotic power equal to one. The test is derived under very general conditions for the data-generating process. In particular, it is robust to jumps with arbitrary activity and to the presence of market microstructure noise. In an application of the test to SPY high-frequency data, we find evidence for rough volatility. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.10659 |
| By: | Òscar Jordà; Alan M. Taylor |
| Abstract: | A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of these interactions can be untangled using local projections. This method’s simplicity makes it a convenient and versatile tool in the empiricist’s kit, one that is generalizable to complex settings. This article reviews the state-of-the art for the practitioner, discusses best practices and possible extensions of local projections methods, along with their limitations. |
| Keywords: | local projections; impulse response; multipliers; bias; inference; instrumental variables; policy evaluation; Kitagawa decomposition; panel data |
| JEL: | C01 C14 C22 C26 C32 C54 |
| Date: | 2024–08–12 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedfwp:98669 |
| By: | Simon Hirsch; Jonathan Berrisch; Florian Ziel |
| Abstract: | Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted towards using probabilistic forecasts, which yields the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity. Against this backdrop, we present a methodology for online estimation of regularized linear distributional models for conditional heteroskedasticity. The proposed algorithm is based on a combination of recent developments for the online estimation of LASSO models and the well-known GAMLSS framework. We provide a case study on day-ahead electricity price forecasting, in which we show the competitive performance of the adaptive estimation combined with strongly reduced computational effort. Our algorithms are implemented in a computationally efficient Python package. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.08750 |