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on Econometric Time Series |
| By: | Sylvia Fr\"uhwirth-Schnatter; Peter Knaus |
| Abstract: | In this chapter, we review variance selection for time-varying parameter (TVP) models for univariate and multivariate time series within a Bayesian framework. We show how both continuous as well as discrete spike-and-slab shrinkage priors can be transferred from variable selection for regression models to variance selection for TVP models by using a non-centered parametrization. We discuss efficient MCMC estimation and provide an application to US inflation modeling. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.12147&r= |
| By: | Niccol\`o Ajroldi; Jacopo Diquigiovanni; Matteo Fontana; Simone Vantini |
| Abstract: | Conformal Prediction (CP) is a versatile nonparametric framework used to quantify uncertainty in prediction problems. In this work, we provide an extension of such method to the case of time series of functions defined on a bivariate domain, by proposing for the first time a distribution-free technique which can be applied to time-evolving surfaces. In order to obtain meaningful and efficient prediction regions, CP must be coupled with an accurate forecasting algorithm, for this reason, we extend the theory of autoregressive processes in Hilbert space in order to allow for functions with a bivariate domain. Given the novelty of the subject, we present estimation techniques for the Functional Autoregressive model (FAR). A simulation study is implemented, in order to investigate how different point predictors affect the resulting prediction bands. Finally, we explore benefits and limits of the proposed approach on a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea in the last twenty years. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.13656&r= |
| By: | Rodrigo Alfaro; Mathias Drehmann |
| Abstract: | We show that the trend of the one-sided HP filter can be asymptotically approx-imated by the Holt-Winters (HW) filter. The later is an elegant, moving average representation and facilitates the computation of trends tremendously. We confirm the accuracy of this approximation empirically by comparing the one-sided HP filter with the HW filter for generating credit-to-GDP gaps. We find negligible differences, most of them concentrated at the beginning of the sample. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:1033&r= |
| By: | Beatrice Franzolini; Alexandros Beskos; Maria De Iorio; Warrick Poklewski Koziell; Karolina Grzeszkiewicz |
| Abstract: | Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US industry stock portfolios, over a time horizon that covers the COVID-19 pandemic. The selected stocks give a comprehensive picture of the US stock market. To this end, we develop a Bayesian multivariate stochastic volatility model based on a time-varying sequence of graphs capturing the evolution of the dependence structure. The model builds on the Gaussian graphical models and the random change points literature. In particular, we treat the number, the position of change points, and the graphs as object of posterior inference, allowing for sparsity in graph recovery and change point detection. The high dimension of the parameter space poses complex computational challenges. However, the model admits a hidden Markov model formulation. This leads to the development of an efficient computational strategy, based on a combination of sequential Monte-Carlo and Markov chain Monte-Carlo techniques. Model and computational development are widely applicable, beyond the scope of the application of interest in this work. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.00952&r= |
| By: | Gianluca Cubadda; Alain Hecq; Elisa Voisin |
| Abstract: | This paper proposes methods to investigate whether the bubble patterns observed in individual series are common to various series. We detect the non-linear dynamics using the recent mixed causal and noncausal models. Both a likelihood ratio test and information criteria are investigated, the former having better performances in our Monte Carlo simulations. Implementing our approach on three commodity prices we do not find evidence of commonalities although some series look very similar. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.11557&r= |
| By: | Stefanos Bennett; Jase Clarkson |
| Abstract: | Time series prediction is often complicated by distribution shift which demands adaptive models to accommodate time-varying distributions. We frame time series prediction under distribution shift as a weighted empirical risk minimisation problem. The weighting of previous observations in the empirical risk is determined by a forgetting mechanism which controls the trade-off between the relevancy and effective sample size that is used for the estimation of the predictive model. In contrast to previous work, we propose a gradient-based learning method for the parameters of the forgetting mechanism. This speeds up optimisation and therefore allows more expressive forgetting mechanisms. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.11486&r= |
| By: | Ilias Chronopoulos; Katerina Chrysikou; George Kapetanios |
| Abstract: | In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their distribution. While the Lasso estimator performs poorly under such circumstances, we estimate via GLS Lasso the parameters of interest and extend the asymptotic properties of the Lasso under more general conditions. Our theoretical results indicate that the non-asymptotic bounds for stationary dependent processes are sharper, while the rate of Lasso under general conditions appears slower as $T,p\to \infty$. Further we employ the debiased Lasso to perform inference uniformly on the parameters of interest. Monte Carlo results support the proposed estimator, as it has significant efficiency gains over traditional methods. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.07055&r= |
| By: | Marcin W\k{a}torek; Jaros{\l}aw Kwapie\'n; Stanis{\l}aw Dro\.zd\.z |
| Abstract: | Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a subject of systematic study. In order to fill this gap, we analyse detrended correlations of the price returns, the average number of trades in time unit, and the traded volume based on high-frequency data representing two major cryptocurrencies: bitcoin and ether. We apply the multifractal detrended cross-correlation analysis, which is considered the most reliable method for identifying nonlinear correlations in time series. We find that all the quantities considered in our study show an unambiguous multifractal structure from both the univariate (auto-correlation) and bivariate (cross-correlation) perspectives. We looked at the bitcoin--ether cross-correlations in simultaneously recorded signals, as well as in time-lagged signals, in which a time series for one of the cryptocurrencies is shifted with respect to the other. Such a shift suppresses the cross-correlations partially for short time scales, but does not remove them completely. We did not observe any qualitative asymmetry in the results for the two choices of a leading asset. The cross-correlations for the simultaneous and lagged time series became the same in magnitude for the sufficiently long scales. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.01445&r= |