
on Econometric Time Series 
By:  Joshua C. C. Chan; Gary Koop; Xuewen Yu 
Abstract:  Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way the variables are ordered due to the use of a Cholesky decomposition for the error covariance matrix. We show that the order invariance problem in existing approaches is likely to become more serious in large VARs. We propose the use of a specification which avoids the use of this Cholesky decomposition. We show that the presence of multivariate stochastic volatility allows for identification of the proposed model and prove that it is invariant to ordering. We develop a Markov Chain Monte Carlo algorithm which allows for Bayesian estimation and prediction. In exercises involving artificial and real macroeconomic data, we demonstrate that the choice of variable ordering can have nonnegligible effects on empirical results. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our orderinvariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, nonorder invariant, approach. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.07225&r= 
By:  Clements, Adam (Queensland University of Technology, Australia); Hurn, Stan (Queensland University of Technology, Australia); Volkov, Vladimir (Tasmanian School of Business & Economics, University of Tasmania) 
Abstract:  Forecasting intraday trading volume is an important problem in economics and finance. One influential approach to achieving this objective is the nonlinear Component Multiplicative Error Model (CMEM) that captures time series dependence and intraday periodicity in volume. While the model is well suited to dealing with a nonnegative time series, it is relatively cumbersome to implement. This paper proposes a system of linear equations, that is estimated using ordinary least squares, and provides at least as good a forecasting performance as that of the CMEM. This linear specification can easily be applied to model any time series that exhibits diurnal behaviour. 
Keywords:  Volume, forecasting, highfrequency data, CMEM, diurnal 
JEL:  C22 G00 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:tas:wpaper:38716&r= 
By:  Xingwei Hu 
Abstract:  In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the causeeffect relations within the data. Regression analysis, however, is generally for correlation relation, and very few researches have focused on variance analysis for causality discovery. We first set up an equilibrium for the causeeffect relations using a fictitious vector autoregressive model. In the equilibrium, longrun relations are identified from noise, and spurious ones are negligibly close to zero. The solution, called causality distribution, measures the relative strength causing the movement of all series or specific affected ones. If a group of exogenous data affects the others but not vice versa, then, in theory, the causality distribution for other variables is necessarily zero. The hypothesis test of zero causality is the rule to decide a variable is endogenous or not. Our new approach has high accuracy in identifying the true causeeffect relations among the data in the simulation studies. We also apply the approach to estimating the causal factors' contribution to climate change. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.07465&r= 
By:  Luxuan Yang; Ting Gao; Yubin Lu; Jinqiao Duan; Tao Liu 
Abstract:  With the fast development of modern deep learning techniques, the study of dynamic systems and neural networks is increasingly benefiting each other in a lot of different ways. Since uncertainties often arise in real world observations, SDEs (stochastic differential equations) come to play an important role. To be more specific, in this paper, we use a collection of SDEs equipped with neural networks to predict longterm trend of noisy time series which has big jump properties and high probability distribution shift. Our contributions are, first, we use the phase space reconstruction method to extract intrinsic dimension of the time series data so as to determine the input structure for our forecasting model. Second, we explore SDEs driven by $\alpha$stable L\'evy motion to model the time series data and solve the problem through neural network approximation. Third, we construct the attention mechanism to achieve multitime step prediction. Finally, we illustrate our method by applying it to stock marketing time series prediction and show the results outperform several baseline deep learning models. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.13164&r= 
By:  Christian Bongiorno; Damien Challet; Gr\'egoire Loeper 
Abstract:  We propose a datadriven way to clean covariance matrices in strongly nonstationary systems. Our method rests on longterm averaging of optimal eigenvalues obtained from temporally contiguous covariance matrices, which encodes the average influence of the future on present eigenvalues. This zeroth order approximation outperforms optimal methods designed for stationary systems. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.13109&r= 