
on Econometric Time Series 
By:  Rudy Morel; Gaspar Rochette; Roberto Leonarduzzi; JeanPhilippe Bouchaud; St\'ephane Mallat 
Abstract:  We introduce a scattering covariance matrix which provides nonGaussian models of timeseries having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the joint covariance across time and scales of complex wavelet coefficients and their modulus. This covariance is nearly diagonalized by a second wavelet transform, which defines the scattering covariance. We show that this set of moments characterizes a wide range of nonGaussian properties of multiscale processes. This is analyzed for a variety of processes, including fractional Brownian motions, Poisson, multifractal random walks and Hawkes processes. We prove that selfsimilar processes have a scattering covariance matrix which is scale invariant. This property can be estimated numerically and defines a class of widesense selfsimilar processes. We build maximum entropy models conditioned by scattering covariance coefficients, and generate new timeseries with a microcanonical sampling algorithm. Applications are shown for highly nonGaussian financial and turbulence timeseries. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10177&r= 
By:  Julia Nasiadka; Weronika Nitka; Rafa{\l} Weron 
Abstract:  We employ a recently proposed changepoint detection algorithm, the NarrowestOverThreshold (NOT) method, to select subperiods of past observations that are similar to the currently recorded values. Then, contrarily to the traditional time series approach in which the most recent $\tau$ observations are taken as the calibration sample, we estimate autoregressive models only for data in these subperiods. We illustrate our approach using a challenging dataset  dayahead electricity prices in the German EPEX SPOT market  and observe a significant improvement in forecasting accuracy compared to commonly used approaches, including the Autoregressive Hybrid Nearest Neighbors (ARHNN) method. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.00872&r= 
By:  Fang, Qin; Guo, Shaojun; Qiao, Xinghao 
Abstract:  Statistical analysis of highdimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinitedimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional crossspectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional crossspectral stability measure, we develop useful concentration inequalities for estimated cross(auto)covariance matrix functions to accommodate more general subGaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived nonasymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of highdimensional functional/scalar time series. 
Keywords:  crossspectral stability measure; functional linear regression; functional principal component analysis; nonasymptotics; subGaussian functional linear process; sparsity; No. 11771447). 
JEL:  C1 
Date:  2022–01–10 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:114637&r= 
By:  Stefano Bertelli; Gianmarco Vacca; Maria Grazia Zoia 
Abstract:  The paper proposes a new bootstrap approach to the Pesaran, Shin and Smith's bound tests in a conditional equilibrium correction model with the aim to overcome some typical drawbacks of the latter, such as inconclusive inference and distortion in size. The bootstrap tests are worked out under several data generating processes, including degenerate cases. Monte Carlo simulations confirm the better performance of the bootstrap tests with respect to bound ones and to the asymptotic F test on the independent variables of the ARDL model. It is also proved that any inference carried out in misspecified models, such as unconditional ARDLs, may be misleading. Empirical applications highlight the importance of employing the appropriate specification and provide definitive answers to the inconclusive inference of the bound tests when exploring the longterm equilibrium relationship between economic variables. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.04939&r= 
By:  Whitehouse, E. J. (Department of Economics, University of Sheffield, UK); Harvey, D. I. (School of Economics, University of Nottingham); Leybourne, S. J. (School of Economics, University of Nottingham) 
Abstract:  Given the financial and economic damage that can be caused by the collapse of an asset price bubble, it is of critical importance to rapidly detect the onset of a crash once a bubble has been identified. We develop a realtime monitoring procedure for detecting a crash episode in a time series. We adopt an autoregressive framework, with the bubble and crash regimes modelled by explosive and stationary dynamics respectively. The first stage of our approach is to monitor for the presence of a bubble; conditional on having detected a bubble, we monitor for a crash in real time as new data emerges. Our crash detection procedure employs a statistic based on the different signs of the means of the first differences associated with explosive and stationary regimes, and critical values are obtained using a training period, over which no bubble or crash is assumed to occur. Monte Carlo simulations suggest that our recommended procedure has a wellcontrolled false positive rate during a bubble regime, while also allowing very rapid detection of a crash when one occurs. Application to the US housing market demonstrates the efficacy of our procedure in rapidly detecting the house price crash of 2006. 
Keywords:  Realtime monitoring; Bubble; Crash; Explosive autoregression; Stationary autoregression 
JEL:  C12 C22 G01 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:shf:wpaper:2022007&r= 
By:  Mauro Bernardi; Daniele Bianchi; Nicolas Bianco 
Abstract:  We develop a new variational Bayes estimation method for largedimensional sparse multivariate predictive regression models. Our approach allows to elicit orderinginvariant shrinkage priors directly on the regression coefficient matrix rather than a Choleskybased linear transformation, as typically implemented in existing MCMC and variational Bayes approaches. Both a simulation and an empirical study on the crossindustry predictability of equity risk premiums in the US, show that by directly shrinking weak industry interdependencies one can substantially improve both the statistical and economic outofsample performance of multivariate regression models for return predictability. This holds across alternative continuous shrinkage priors, such as the adaptive Bayesian lasso, adaptive normalgamma and the horseshoe. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.12644&r= 
By:  Karsten Reichold; Carsten Jentsch 
Abstract:  Traditional inference in cointegrating regressions requires tuning parameter choices to estimate a longrun variance parameter. Even in case these choices are "optimal", the tests are severely size distorted. We propose a novel selfnormalization approach, which leads to a nuisance parameter free limiting distribution without estimating the longrun variance parameter directly. This makes our selfnormalized test tuning parameter free and considerably less prone to size distortions at the cost of only small power losses. In combination with an asymptotically justified vector autoregressive sieve bootstrap to construct critical values, the selfnormalization approach shows further improvement in small to medium samples when the level of error serial correlation or regressor endogeneity is large. We illustrate the usefulness of the bootstrapassisted selfnormalized test in empirical applications by analyzing the validity of the Fisher effect in Germany and the United States. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.01373&r= 
By:  Florian Bourgey; Stefano De Marco; Peter K. Friz; Paolo Pigato 
Abstract:  Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the smallmaturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, and supporting their calibration power to S&P500 option data. Rough volatility models also generate a local volatility surface, via the socalled Markovian projection of the stochastic volatility. We complement the existing results on the implied volatility by studying the asymptotic behavior of the local volatility surface generated by a class of rough stochastic volatility models, encompassing the rough Bergomi model. Notably, we observe that the celebrated "1/2 skew rule" linking the shortterm atthemoney skew of the implied volatility to the shortterm atthemoney skew of the local volatility, a consequence of the celebrated "harmonic mean formula" of [Berestycki, Busca, and Florent, QF 2002], is replaced by a new rule: the ratio of the atthemoney implied and local volatility skews tends to the constant 1/(H + 3/2) (as opposed to the constant 1/2), where H is the regularity index of the underlying instantaneous volatility process. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.02376&r= 