Search results for "autoregressive model"
showing 10 items of 120 documents
A PHASE TRANSITION FOR LARGE VALUES OF BIFURCATING AUTOREGRESSIVE MODELS
2019
We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$ . The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive pr…
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Dynamic copula models for the spark spread
2011
We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.
Digital generation of multivariate wind field processes
2001
Abstract A very efficient procedure for the generation of multivariate wind velocity stochastic processes by wave superposition as well as autoregressive time series is proposed in this paper. The procedure starts by decomposing the wind velocity field into a summation of fully coherent independent vector processes using the frequency dependent eigenvectors of the Power Spectral Density matrix. It is shown that the application of the method allows to show some very interesting physical properties that allow to reduce drastically the computational effort. Moreover, using a standard finite element procedure for approximating the frequency dependent eigenvectors, the generation procedure requi…
Stochastic analysis of motorcycle dynamics
2011
Off-road and racing motorcycles require a particular setup of the suspensions to improve the comfort and the safety of the rider, maintaining a continuous contact between the road and the motorcycle (by means of the tires). Further, because of the ground roughness, in the case of offroad motorcycle, suspensions usually experience extreme and erratic excursions (suspension stroke) in performing their function. In this regard, the adoption of nonlinear devices can, perhaps, limit both the acceleration experienced by the sprung mass and the excursions of the suspensions. This leads to the consideration of asymmetric nonlinearly-behaving suspensions. This option, however, induces the difficulty…
An identifiable model to assess frequency-domain Granger causality in the presence of significant instantaneous interactions
2010
We present a new approach for the investigation of Granger causality in the frequency domain by means of the partial directed coherence (PDC). The approach is based on the utilization of an extended multivariate autoregressive (MVAR) model, including instantaneous effects in addition to the lagged effects traditionally studied, to fit the observed multiple time series prior to PDC computation. Model identification is performed combining standard MVAR coefficient estimation with a recent technique for instantaneous causal modeling based on independent component analysis. The approach is first validated on simulated MVAR processes showing that, in the presence of instantaneous effects, only t…
A method for the time-varying nonlinear prediction of complex nonstationary biomedical signals
2009
A method to perform time-varying (TV) nonlinear prediction of biomedical signals in the presence of nonstationarity is presented in this paper. The method is based on identification of TV autoregressive models through expansion of the TV coefficients onto a set of basis functions and on k -nearest neighbor local linear approximation to perform nonlinear prediction. The approach provides reasonable nonlinear prediction even for TV deterministic chaotic signals, which has been a daunting task to date. Moreover, the method is used in conjunction with a TV surrogate method to provide statistical validation that the presence of nonlinearity is not due to nonstationarity itself. The approach is t…
Trend Following with Momentum Versus Moving Average: A Tale of Differences
2018
Despite the ever-growing interest in trend following and a series of publications in academic journals, there is still a great shortage of theoretical results on the properties of trend following rules. Our paper fills this gap by comparing and contrasting the two most popular trend following rules, the Momentum (MOM) and Moving Average (MA) rules, from a theoretical perspective. Our approach is based on the return-based formulation of trading rules and modelling the price trends by an autoregressive return process. We provide theoretical results on the similarity between various trend following rules and the forecast accuracy of trading rules. Our results show that the similarity between t…
Investigation of vehicle crash modeling techniques: theory and application
2013
Published version of an article in the journal: The International Journal of Advanced Manufacturing Technology. Also available from the publisher at: http://dx.doi.org/10.1007/s00170-013-5320-3 Creating a mathematical model of a vehicle crash is a task which involves considerations and analysis of different areas which need to be addressed because of the mathematical complexity of a crash event representation. Therefore, to simplify the analysis and enhance the modeling process, in this work, a brief overview of different vehicle crash modeling methodologies is proposed. The acceleration of a colliding vehicle is measured in its center of gravity—this crash pulse contains detailed informati…
A Spatial Difference-in-Differences Estimator to Evaluate the Effect of Change in Public Mass Transit Systems on House Prices
2014
Evaluating the impact of public mass transit systems on real-estate values is an important application of the hedonic price model (HPM). Recently, a mathematical transformation of this approach has been proposed to account for the potential omission of latent spatial variables that may overestimate the impact of accessibility to mass transit systems on values. The development of a Difference-in-Differences (DID) estimator, based on the repeat-sales approach, is a move in the right direction. However, such an estimator neglects the possibility that specification of the price equation may follow a spatial autoregressive process with respect to the dependent variable. The objective of this pap…