A note on self-similarity for discrete time series

The purpose of this paper is to study the self-similar properties of discrete-time long memory processes. We apply our results to specific processes such as GARMA processes and GIGARCH processes, heteroscedastic models and the processes with switches and jumps.Covariance stationary, Long memory processes, short memory processes, self-similar, asymptotically second-order self-similar, autocorrelation function.

Testing unit roots and long range dependence of foreign exchange

Foreign exchange rate plays an important role in international finance. This paper examines unit roots and the long range dependence of 23 foreign exchange rates using Robinson's (1994) test, which is one of the most efficient tests when testing fractional orders of seasonal/cyclical long memory processes. Monte Carlo simulations are carried out to explore the accuracy of the test before implementing the empirical applications.Long memory processes ; test ; Monte Carlo Simulations ; unit roots ; exchange rate

Wavelet Method for Locally Stationary Seasonal Long Memory Processes

Long memory processes have been extensively studied over the past decades. When dealing with the financial and economic data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity can exist inside financial data sets. To take into account this kind of phenomena, we propose a new class of stochastic process : the locally stationary k-factor Gegenbauer process. We describe a procedure of estimating consistently the time-varying parameters by applying the discrete wavelet packet transform (DWPT). The robustness of the algorithm is investigated through simulation study. An application based on the error correction term of fractional cointegration analysis of the Nikkei Stock Average 225 index is proposed.Discrete wavelet packet transform ; Gegenbauer process ; Nikkei Stock Average 225 index ; non-stationarity ; ordinary least square estimation

Testing fractional order of long memory processes : a Monte Carlo study

Testing the fractionally integrated order of seasonal and non-seasonal unit roots is quite important for the economic and financial time series modelling. In this paper, Robinson test (1994) is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes.Long memory processes, test, Monte Carlo simulations.

Testing Fractional Order of Long Memory Processes: A Monte Carlo Study

Testing the fractionally integrated order of seasonal and nonseasonal unit roots is quite important for the economic and financial time series modeling. In this article, the widely used Robinson's (1994) test is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes.Long memory processes – test – Monte Carlo simulations

A note on self-similarity for discrete time series

URL des Documents de travail :http://ces.univ-paris1.fr/cesdp/CESFramDP2007.htmClassification JEL : C02, C32, C40, C60.Documents de travail du Centre d'Economie de la Sorbonne 2007.55 - ISSN : 1955-611XThe purpose of this paper is to study the self-similar properties of discrete-time long memory processes. We apply our results to specific processes such as GARMA processes and GIGARCH processes, heteroscedastic models and the processes with switches and jumps.On démontre dans ce papier que les processus longue mémoire à temps discret sont self-similaires. Le comportement de self similarité de processus hétéroscédastiques est aussi étudié

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet, which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet by predicting five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a "plug-and-play" mode.Comment: 30 pages, 17 figure

Two-dimensional Massless Dirac Fermions in Antiferromagnetic AFe2As2 (A = Ba, Sr)

We report infrared studies of AFe$_{2}$As$_{2}$ (A = Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a $\sqrt{B}$ dependence of the LL transition energies, the zero-energy intercepts at B = 0 T under the linear extrapolations of the transition energies and the energy ratio ($\sim$ 2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in antiferromagnetic BaFe$_{2}$As$_{2}$. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction $k_{z}$ indicate that massless Dirac fermions in BaFe$_{2}$As$_{2}$ are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe$_{2}$As$_{2}$ by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.Comment: Magneto-infrared study, Landau level spectroscopy, DFT+DMFT calculation