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on Econometric Time Series |
| By: | Harvey, David I; Leybourne, Stephen J; Taylor, AM Robert; Zu, Yang |
| Abstract: | We propose a new class of modified regression-based tests for detecting asset price bubbles designed to be robust to the presence of general forms of both conditional and unconditional heteroskedasticity in the price series. This modification, based on the approach developed in Beare (2018) in the context of conventional unit root testing, is achieved by purging the impact of unconditional heteroskedasticity from the data using a kernel estimate of volatility before the application of the bubble detection methods proposed in Phillips, Shi and Yu (2015) [PSY]. The modified statistic is shown to achieve the same limiting null distribution as the corresponding (heteroskedasticity-uncorrected) statistic from PSY would obtain under homoskedasticity, such that the usual critical values provided in PSY may still be used. Versions of the test based on regressions including either no intercept or a (redundant) intercept are considered. Representations for asymptotic local power against a single bubble model are also derived. Monte Carlo simulation results highlight that neither one of these tests dominates the other across different bubble locations and magnitudes, and across different models of time-varying volatility. Accordingly, we also propose a test based on a union of rejections between the with and without intercept variants of the modified PSY test. The union procedure is shown to perform almost as well as the better of the constituent tests for a given DGP, and also performs very well compared to existing heteroskedasticity-robust tests across a large range of simulation DGPs. |
| Keywords: | Rational bubble; explosive autoregression; time-varying volatility; kernel smoothing; right-tailed unit root testing; union of rejections |
| Date: | 2024–09–13 |
| URL: | https://d.repec.org/n?u=RePEc:esy:uefcwp:39178 |
| By: | Daniel Cunha Oliveira; Yutong Lu; Xi Lin; Mihai Cucuringu; Andre Fujita |
| Abstract: | We introduce a novel framework to financial time series forecasting that leverages causality-inspired models to balance the trade-off between invariance to distributional changes and minimization of prediction errors. To the best of our knowledge, this is the first study to conduct a comprehensive comparative analysis among state-of-the-art causal discovery algorithms, benchmarked against non-causal feature selection techniques, in the application of forecasting asset returns. Empirical evaluations demonstrate the efficacy of our approach in yielding stable and accurate predictions, outperforming baseline models, particularly in tumultuous market conditions. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.09960 |
| By: | Anne Opschoor (Vrije Universiteit Amsterdam); Dewi Peerlings (Vrije Universiteit Amsterdam); Luca Rossini (University of Milan); Andre Lucas (Vrije Universiteit Amsterdam) |
| Abstract: | We introduce the vector-valued t-Riesz distribution for time series models of electricity prices. The t-Riesz distribution extends the well-known Multivariate Student’s t distribution by allowing for tail heterogeneity via a vector of degrees of freedom (DoF) parameters. The closed-form density expression allows for straightforward maximum likelihood estimation. A clustering approach for the DoF parameters is provided to reduce the number of parameters in higher dimensions. We apply the t- Riesz distribution to a 24-dimensional panel of Danish daily electricity prices over the period 2017-2024, considering each hour of the day as a separate coordinate. Results show that multivariate t-Riesz-based density forecasts improve significantly upon the standard Student’s t distribution and the t-copula. Further, the t-Riesz distribution produces superior implied univariate density forecasts during the afternoon for the distribution as a whole and during 8 a.m.- 8 p.m. in its left tail. Moreover, during crisis periods, this effect is even stronger and holds for almost every hour of the day. Finally, portfolio Value-at-Risk forecasts during the central hours of the day improve during crisis periods compared to the classical Student’s t distribution and the t- copula. |
| Keywords: | multivariate distributions, (fat)-tail heterogeneity, (inverse) Riesz distribution, electricity prices |
| JEL: | C1 C22 C53 |
| Date: | 2024–07–19 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240049 |
| By: | Ilze Kalnina; Kokouvi Tewou |
| Abstract: | This paper introduces an econometric framework for analyzing cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Naive estimators of these measures are biased due to the use of the error-laden estimates of idiosyncratic volatilities. We provide bias-corrected estimators and the relevant asymptotic theory. Next, we introduce an idiosyncratic volatility factor model, in which we decompose the variation in idiosyncratic volatilities into two parts: the variation related to the systematic factors such as the market volatility, and the residual variation. Again, naive estimators of the decomposition are biased, and we provide bias-corrected estimators. We also provide the asymptotic theory that allows us to test whether the residual (non-systematic) components of the idiosyncratic volatilities exhibit cross-sectional dependence. We apply our methodology to the S&P 100 index constituents, and document strong cross-sectional dependence in their idiosyncratic volatilities. We consider two different sets of idiosyncratic volatility factors, and find that neither can fully account for the cross-sectional dependence in idiosyncratic volatilities. For each model, we map out the network of dependencies in residual (non-systematic) idiosyncratic volatilities across all stocks. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.13437 |
| By: | Yan-Feng Wu; Xiangyu Yang; Jian-Qiang Hu |
| Abstract: | We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for moments of any order. Consequently, we propose our moment estimators. We then establish a central limit theorem for our estimators and derive the explicit formulas for the asymptotic covariance matrix. Finally, we provide numerical results to validate our method. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.09185 |
| By: | Toru Yano |
| Abstract: | Volatility means the degree of variation of a stock price which is important in finance. Realized Volatility (RV) is an estimator of the volatility calculated using high-frequency observed prices. RV has lately attracted considerable attention of econometrics and mathematical finance. However, it is known that high-frequency data includes observation errors called market microstructure noise (MN). Nagakura and Watanabe[2015] proposed a state space model that resolves RV into true volatility and influence of MN. In this paper, we assume a dependent MN that autocorrelates and correlates with return as reported by Hansen and Lunde[2006] and extends the results of Nagakura and Watanabe[2015] and compare models by simulation and actual data. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.17187 |
| By: | Igor Custodio João (Vrije Universiteit Amsterdam) |
| Abstract: | I refine the test for clustering of Patton and Weller (2022) to allow for cluster switching. In a multivariate panel setting, clustering on time- averages produces consistent estimators of means and group assignments. Once switching is introduced, we lose the consistency. In fact, under switch- ing the time-averaged k-means clustering converges to equal, indistinguishable means. This causes the test for a single cluster to lose power under the alternative of multiple clusters. Power can be regained by clustering the N times T observations independently and carefully subsampling the time dimension. When applied to the empirical setting of Bonhomme and Manresa (2015) of an autoregression of democracy in a panel of countries, we are able to detect clusters in the data under noisier conditions than the original test. |
| JEL: | C12 C33 C38 |
| Date: | 2024–08–22 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240052 |
| By: | Ramon de Punder (University of Amsterdam); Timo Dimitriadis (Heidelberg University); Rutger-Jan Lange (Erasmus University Rotterdam) |
| Abstract: | Score-driven models have been applied in some 400 published articles over the last decade. Much of this literature cites the optimality result in Blasques et al. (2015), which, roughly, states that sufficiently small score-driven updates are unique in locally reducing the Kullback-Leibler (KL) divergence relative to the true density for every observation. This is at odds with other well-known optimality results; the Kalman filter, for example, is optimal in a mean squared error sense, but may move in the wrong direction for atypical observations. We show that score-driven filters are, similarly, not guaranteed to improve the localized KL divergence at every observation. The seemingly stronger result in Blasques et al. (2015) is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, we prove that sufficiently small score-driven updates are unique in reducing the KL divergence relative to the true density in expectation. This positive—albeit weaker— result justifies the continued use of score-driven models and places their information- theoretic properties on solid footing. |
| Keywords: | generalized autoregressive score (GAS), dynamic conditional score (DCS), Kullback Leibler, censoring, scoring rule, divergence |
| JEL: | C10 C22 C58 |
| Date: | 2024–08–06 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240051 |