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on Econometric Time Series |
| By: | Paulo M.M. Rodrigues; Vivien Less; Philipp Sibbertsen |
| Abstract: | This paper focuses on the estimation and testing of multiple breaks that occur at unknown dates in multivariate long memory time series regression models, allowing for fractional cointegration. A likelihood-ratio based approach for estimating the breaks in the parameters and in the covariance of a system of long memory time series regressions is proposed. The limiting distributions as well as the consistency of the estimators are derived. Furthermore, a testing procedure to determine the unknown number of breaks is introduced which is based on iterative testing on the regression residuals. A Monte Carlo exercise shows the good finite sample properties of our novel approach, and empirical applications on inflation series of France and Germany and on benchmark government bonds of eight euro area countries illustrate theusefulness of the proposed procedures. |
| JEL: | C12 C22 C58 G15 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ptu:wpaper:w202503 |
| By: | Emanuele Bacchiocchi; Toru Kitagawa |
| Abstract: | This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally equivalent under the imposed restrictions. Although the data do not inform us which observationally equivalent point should be selected, the common frequentist practice is to obtain one as a maximum likelihood estimate and perform impulse response analysis accordingly. For Bayesians, the lack of global identification translates to non-vanishing sensitivity of the posterior to the prior, and the multi-modal likelihood gives rise to computational challenges as posterior sampling algorithms can fail to explore all the modes. This paper overcomes these challenges by proposing novel estimation and inference procedures. We characterize a class of identifying restrictions and circumstances that deliver local but non-global identification, and the resulting number of observationally equivalent parameter values. We propose algorithms to exhaustively compute all admissible structural parameters given reduced-form parameters and utilize them to sample from the multi-modal posterior. In addition, viewing the set of observationally equivalent parameter points as the identified set, we develop Bayesian and frequentist procedures for inference on the corresponding set of impulse responses. An empirical example illustrates our proposal. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01441 |
| By: | Markus Bibinger (Faculty of Mathematics and Computer Science, Institute of Mathematics, University of Würzburg); Jun Yu (Faculty of Business Administration, University of Macau); Chen Zhang (Faculty of Business Administration, University of Macau) |
| Abstract: | A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel estimation method for all model parameters, establishing consistency and asymptotic normality of the estimators. Additionally, we develop a time-reversibility test, which is typically not rejected by real volatility data. When the data-generating process is a time-reversible mfBm, we derive optimal forecasting formulae and analyze their properties. A key insight is that an mfBm with different Hurst exponents and non-zero correlations can reduce forecasting errors compared to a one-dimensional model. Consistent with optimal forecasting theory, out-of-sample forecasts using the time-reversible mfBm show improvements over univariate fBm, particularly when the estimated Hurst exponents differ significantly. Empirical results demonstrate that mfBm-based forecasts outperform the (vector) HAR model. |
| Keywords: | Forecasting, Hurst exponent, multivariate fractional Brownian motion, realized volatility, rough volatility |
| JEL: | C12 C58 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202528 |
| By: | Paolo Dai Pra; Paolo Pigato |
| Abstract: | We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [El Euch, Fukasawa, Rosenbaum, The microstructural foundations of leverage effect and rough volatility, Finance and Stochastics, 2018]. We adopt an agent based approach by studying the aggregation of a large number of these point processes, mutually interacting in a mean-field sense. The financial interpretation is that of an asset on which several labeled agents place buy and sell orders following these point processes, influencing the price. The mean-field interaction introduces positive correlations between order volumes coming from different agents that reflect features of real markets such as herd behavior and contagion. When the large scale limit of the aggregated asset price is computed, if parameters are set to a critical value, a singular phenomenon occurs: the aggregated model converges to a stochastic volatility model with leverage effect and faster-than-linear mean reversion of the volatility process. The faster-than-linear mean reversion of the volatility process is supported by econometric evidence, and we have linked it in [Dai Pra, Pigato, Multi-scaling of moments in stochastic volatility models, Stochastic Processes and their Applications, 2015] to the observed multifractal behavior of assets prices and market indices. This seems connected to the Statistical Physics perspective that expects anomalous scaling properties to arise in the critical regime. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.03445 |
| By: | Peter C. B. Phillips (Yale University); Liang Jiang (Fudan University) |
| Abstract: | This paper develops and applies new asymptotic theory for estimation and inference in parametric autoregression with function valued cross section curve time series. The study provides a new approach to dynamic panel regression with high dimensional dependent cross section data. Here we deal with the stationary case and provide a full set of results extending those of standard Euclidean space autoregression, showing how function space curve cross section data raises efficiency and reduces bias in estimation and shortens confidence intervals in inference. Methods are developed for high-dimensional covariance kernel estimation that are useful for inference. The findings reveal that function space models with wide-domain and narrow-domain cross section dependence provide insights on the effects of various forms of cross section dependence in discrete dynamic panel models with fixed and interactive fixed effects. The methodology is applicable to panels of high dimensional wide datasets that are now available in many longitudinal studies. An empirical illustration is provided that sheds light on household Engel curves among ageing seniors in Singapore using the Singapore life panel longitudinal dataset. |
| Date: | 2025–04–19 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2439 |
| By: | Paul Haimerl; Stephan Smeekes; Ines Wilms |
| Abstract: | We introduce a panel data model where coefficients vary both over time and the cross-section. Slope coefficients change smoothly over time and follow a latent group structure, being homogeneous within but heterogeneous across groups. The group structure is identified using a pairwise adaptive group fused-Lasso penalty. The trajectories of time-varying coefficients are estimated via polynomial spline functions. We derive the asymptotic distributions of the penalized and post-selection estimators and show their oracle efficiency. A simulation study demonstrates excellent finite sample properties. An application to the emission intensity of GDP highlights the relevance of addressing cross-sectional heterogeneity and time-variance in empirical settings. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.23165 |