Fourth Moment Structure of Markov Switching Multivariate GARCH Models

2019 ◽  
Author(s):  
Maddalena Cavicchioli
Keyword(s):  
Closed Form ◽  
Moving Average ◽  
Markov Switching ◽  
Computational Cost ◽  
Sufficient Conditions ◽  
Impulse Response Function ◽  
Real Data ◽  
Multivariate Garch ◽  
Fourth Moment ◽  
Spectral Density Matrix

Abstract We derive sufficient conditions for the existence of second and fourth moments of Markov switching multivariate generalized autoregressive conditional heteroscedastic processes in the general vector specification. We provide matrix expressions in closed form for such moments, which are obtained by using a Markov switching vector autoregressive moving-average representation of the initial process. These expressions are shown to be readily programmable in addition of greatly reducing the computational cost. As theoretical applications of the results, we derive the spectral density matrix of the squares and cross products, propose a new definition of multivariate kurtosis measure to recognize heavy-tailed features in financial real data, and provide a matrix expression in closed form of the impulse-response function for the volatility. An empirical example illustrates the results.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

scholarly journals Highway Speed Prediction Using Gated Recurrent Unit Neural Networks

2021 ◽  
Vol 11 (7) ◽  
pp. 3059
Author(s):  
Myeong-Hun Jeong ◽  
Tae-Young Lee ◽  
Seung-Bae Jeon ◽  
Minkyo Youm
Keyword(s):  
Neural Network ◽  
Intelligent Transportation Systems ◽  
Moving Average ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Transportation Systems ◽  
Mobility Data ◽  
Challenges And Opportunities ◽  
Moving Average Model ◽  
Gated Recurrent Unit

Movement analytics and mobility insights play a crucial role in urban planning and transportation management. The plethora of mobility data sources, such as GPS trajectories, poses new challenges and opportunities for understanding and predicting movement patterns. In this study, we predict highway speed using a gated recurrent unit (GRU) neural network. Based on statistical models, previous approaches suffer from the inherited features of traffic data, such as nonlinear problems. The proposed method predicts highway speed based on the GRU method after training on digital tachograph data (DTG). The DTG data were recorded in one month, giving approximately 300 million records. These data included the velocity and locations of vehicles on the highway. Experimental results demonstrate that the GRU-based deep learning approach outperformed the state-of-the-art alternatives, the autoregressive integrated moving average model, and the long short-term neural network (LSTM) model, in terms of prediction accuracy. Further, the computational cost of the GRU model was lower than that of the LSTM. The proposed method can be applied to traffic prediction and intelligent transportation systems.

Multivariate Markov-switching score-driven models: an application to the global crude oil market

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Szabolcs Blazsek ◽  
Alvaro Escribano ◽  
Adrian Licht
Keyword(s):  
Crude Oil ◽  
Moving Average ◽  
Local Level ◽  
Markov Switching ◽  
Impulse Response Functions ◽  
Common Trends ◽  
Vector Autoregressive ◽  
Oil Market ◽  
Long Run ◽  
Special Cases

Abstract A new class of multivariate nonlinear quasi-vector autoregressive (QVAR) models is introduced. It is a Markov switching score-driven model with stochastic seasonality for the multivariate t-distribution (MS-Seasonal-t-QVAR). As an extension, we allow for the possibility of having common-trends and nonlinear co-integration. Score-driven nonlinear updates of local level and seasonality are used, which are robust to outliers within each regime. We show that VAR integrated moving average (VARIMA) type filters are special cases of QVAR filters. Using exclusion, sign, and elasticity identification restrictions in MS-Seasonal-t-QVAR with common-trends, we provide short-run and long-run impulse response functions for the global crude oil market.

scholarly journals Container Throughput Forecasting Using Dynamic Factor Analysis and ARIMAX Model

2017 ◽  
Vol 29 (5) ◽  
pp. 529-542 ◽  
Author(s):  
Marko Intihar ◽  
Tomaž Kramberger ◽  
Dejan Dragan
Keyword(s):  
Factor Analysis ◽  
Goodness Of Fit ◽  
Moving Average ◽  
Real Data ◽  
Information Criteria ◽  
Dynamic Factor Analysis ◽  
Forecasting Model ◽  
Dynamic Factor ◽  
Macroeconomic Indicators ◽  
The Impact

The paper examines the impact of integration of macroeconomic indicators on the accuracy of container throughput time series forecasting model. For this purpose, a Dynamic factor analysis and AutoRegressive Integrated Moving-Average model with eXogenous inputs (ARIMAX) are used. Both methodologies are integrated into a novel four-stage heuristic procedure. Firstly, dynamic factors are extracted from external macroeconomic indicators influencing the observed throughput. Secondly, the family of ARIMAX models of different orders is generated based on the derived factors. In the third stage, the diagnostic and goodness-of-fit testing is applied, which includes statistical criteria such as fit performance, information criteria, and parsimony. Finally, the best model is heuristically selected and tested on the real data of the Port of Koper. The results show that by applying macroeconomic indicators into the forecasting model, more accurate future throughput forecasts can be achieved. The model is also used to produce future forecasts for the next four years indicating a more oscillatory behaviour in (2018-2020). Hence, care must be taken concerning any bigger investment decisions initiated from the management side. It is believed that the proposed model might be a useful reinforcement of the existing forecasting module in the observed port.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

2020 ◽  
pp. 1-22
Author(s):  
Luis E. Nieto-Barajas ◽  
Rodrigo S. Targino
Keyword(s):  
Latent Variables ◽  
Moving Average ◽  
Real Data ◽  
Model Parameters ◽  
Average Process ◽  
Moving Average Process ◽  
Data Set ◽  
Run Off ◽  
Average Form ◽  
Reserve Estimates

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

A Method for Efficient Implementation of a Radial-Based Noise Power Estimator for Weather Radars

2021 ◽  
Author(s):  
Martin Hurtado
Keyword(s):  
Closed Form ◽  
Background Noise ◽  
Computational Cost ◽  
Weather Radar ◽  
Efficient Implementation ◽  
Noise Power ◽  
Free Range ◽  
Weather Radars ◽  
Low Computational Cost

AbstractIn a previous work, a weather radar algorithm with low computational cost has been developed to estimate the background noise power from the data collected at each radial. The algorithm consists of a sequence of steps designed to identify signal-free range volumes which are subsequently used to estimate the noise power. In this paper, we derive compact-closed form expressions to replace the numerical formulations used in the first two steps of the algorithm proposed in the original paper. The goal is to facilitate efficient implementation of the algorithm.

Relative time seislet transform

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V223-V232 ◽  
Author(s):  
Zhicheng Geng ◽  
Xinming Wu ◽  
Sergey Fomel ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Lifting Scheme ◽  
Real Data ◽  
Data Sets ◽  
Relative Time ◽  
New Approach ◽  
New Formulation ◽  
Wavelet Lifting ◽  
Seismic Images

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

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