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on Econometric Time Series |
| By: | Dimitris Korobilis |
| Abstract: | A comprehensive methodology for inference in vector autoregressions (VARs) using sign and other structural restrictions is developed. The reduced-form VAR disturbances are driven by a few common factors and structural identification restrictions can be incorporated in their loadings in the form of parametric restrictions. A Gibbs sampler is derived that allows for reduced-form parameters and structural restrictions to be sampled efficiently in one step. A key benefit of the proposed approach is that it allows for treating parameter estimation and structural inference as a joint problem. An additional benefit is that the methodology can scale to large VARs with multiple shocks, and it can be extended to accommodate non-linearities, asymmetries, and numerous other interesting empirical features. The excellent properties of the new algorithm for inference are explored using synthetic data experiments, and by revisiting the role of financial factors in economic fluctuations using identification based on sign restrictions. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.06892&r= |
| By: | Simone Tonini; Francesca Chiaromonte; Alessandro Giovannelli |
| Abstract: | This paper characterizes the impact of serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation of covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious cross-correlations caused by serial dependence. In this respect, we study analytically the density of sample cross-correlations in the simplest case of two orthogonal Gaussian AR(1) processes. Simulations show that our results can be extended to the general case of weakly cross-correlated non Gaussian AR processes of any autoregressive order. To improve the estimation performance of PRs in a time series regime, we propose an approach based on applying PRs to the residuals of ARMA models fit on the observed time series. We show that under mild assumptions the proposed approach allows us both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is numerically evaluated through simulations. To assess the effectiveness of the forecasting strategy, we provide the results of an empirical application to monthly macroeconomic data relative to the Euro Area economy. |
| Keywords: | Serial dependence; spurious correlation; minimum eigenvalue; penalized regressions; estimation accuracy. |
| Date: | 2022–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2022/21&r= |
| By: | Chiranjit Dutta; Nalini Ravishanker; Sumanta Basu |
| Abstract: | In this paper we describe fast Bayesian statistical analysis of vector positive-valued time series, with application to interesting financial data streams. We discuss a flexible level correlated model (LCM) framework for building hierarchical models for vector positive-valued time series. The LCM allows us to combine marginal gamma distributions for the positive-valued component responses, while accounting for association among the components at a latent level. We use integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling via the \texttt{R-INLA} package, building custom functions to handle this setup. We use the proposed method to model interdependencies between realized volatility measures from several stock indexes. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.05374&r= |
| By: | Christian Bongiorno; Damien Challet |
| Abstract: | Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.10173&r= |
| By: | Chang, Jinyuan; Cheng, Guanghui; Yao, Qiwei |
| Abstract: | We propose a new unit-root test for a stationary null hypothesis H0 against a unit-root alternative H1. Our approach is nonparametric as H0 assumes only that the process concerned is I(0), without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for an I(0) process, but diverges to infinity for a process with unit roots. Therefore, the new test rejects H0 for large values of the sample autocovariance function. To address the technical question of how large is large, we split the sample and establish an appropriate normal approximation for the null distribution of the test statistic. The substantial discriminative power of the new test statistic is due to the fact that it takes finite values under H0 and diverges to infinity under H1. This property allows one to truncate the critical values of the test so that it has asymptotic power 1; it also alleviates the loss of power due to the sample-splitting. The test is implemented in R. |
| Keywords: | autocovariance; integrated processes; normal approximation; power-one test; sample-splitting; EP/V007556/1; OUP deal |
| JEL: | C1 |
| Date: | 2022–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:114620&r= |
| By: | Weronika Ormaniec; Marcin Pitera; Sajad Safarveisi; Thorsten Schmidt |
| Abstract: | Estimating value-at-risk on time series data with possibly heteroscedastic dynamics is a highly challenging task. Typically, we face a small data problem in combination with a high degree of non-linearity, causing difficulties for both classical and machine-learning estimation algorithms. In this paper, we propose a novel value-at-risk estimator using a long short-term memory (LSTM) neural network and compare its performance to benchmark GARCH estimators. Our results indicate that even for a relatively short time series, the LSTM could be used to refine or monitor risk estimation processes and correctly identify the underlying risk dynamics in a non-parametric fashion. We evaluate the estimator on both simulated and market data with a focus on heteroscedasticity, finding that LSTM exhibits a similar performance to GARCH estimators on simulated data, whereas on real market data it is more sensitive towards increasing or decreasing volatility and outperforms all existing estimators of value-at-risk in terms of exception rate and mean quantile score. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.10539&r= |