scholarly journals Bayesian Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors

2021 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Alexander Dorndorf ◽  
Boris Kargoll ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Time Series ◽  
Nonlinear Models ◽  
Multivariate Time Series ◽  
Functional Model ◽  
Measurement Data ◽  
Model Parameters ◽  
Correlated Noise ◽  
Posterior Density ◽  
Stochastic Properties ◽  
T Distribution

Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usually nonlinear regarding the trend parameters. To deal with these characteristics, a time series model, which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autoregressive (AR) processes the white noise components of which obey independent, scaled t-distributions, was proposed by the authors in previous research papers. In this paper, we extend the aforementioned model to include prior knowledge regarding various model parameters, the information about which is often available in practical situations. We develop an algorithm based on Bayesian inference that provides a robust and reliable estimation of the functional parameters, the coefficients of the AR process and the parameters of the underlying t-distribution. We approximate the resulting posterior density using Markov chain Monte Carlo (MCMC) techniques consisting of a Metropolis-within-Gibbs algorithm.

scholarly journals Transmisión de precios en los mercados regionales de ovino en España

2011 ◽  
Vol 3 (1) ◽  
pp. 71 ◽  
Author(s):  
L. Boshnjaku ◽  
B. Ben-Kaabia ◽  
José M. Gil
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Commodity Markets ◽  
Time Series Models ◽  
The North ◽  
Long Run ◽  
Stochastic Properties ◽  
Price Relationships

The analysis of price relationships in commodity markets provides an approximate idea on markets performance as well as allows the researcher to analyze price responses to unanticipated shocks. The objective of this paper is to explore price relationships in geographical separated markets in the Spanish lamb sector. The methodology used is based on the specification of multivariate time series models which are flexible enough to take into account the stochastic properties of data, the multivariate nature of price relationships and to distinguish between short- and long-run horizons. Results indicate that lamb markets in Spain are strongly related being Zafra the leading market. The influence of Zafra is substantial in the southern markets while in the North, the Lonja del Ebro could be considered as the most representative market.

Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

scholarly journals Multivariate analysis of nonlinearity in sandbar behavior

2008 ◽  
Vol 15 (1) ◽  
pp. 145-158 ◽  
Author(s):  
L. Pape ◽  
B. G. Ruessink
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Nonlinear Models ◽  
Multivariate Time Series ◽  
Series Data ◽  
Small Scale ◽  
Synthetic Datasets ◽  
Long Term Prediction ◽  
Sandbar Migration

Abstract. Alongshore sandbars are often present in the nearshore zones of storm-dominated micro- to mesotidal coasts. Sandbar migration is the result of a large number of small-scale physical processes that are generated by the incoming waves and the interaction between the wave-generated processes and the morphology. The presence of nonlinearity in a sandbar system is an important factor determining its predictability. However, not all nonlinearities in the underlying system are equally expressed in the time-series of sandbar observations. Detecting the presence of nonlinearity in sandbar data is complicated by the dependence of sandbar migration on the external wave forcings. Here, a method for detecting nonlinearity in multivariate time-series data is introduced that can reveal the nonlinear nature of the dependencies between system state and forcing variables. First, this method is applied to four synthetic datasets to demonstrate its ability to qualify nonlinearity for all possible combinations of linear and nonlinear relations between two variables. Next, the method is applied to three sandbar datasets consisting of daily-observed cross-shore sandbar positions and hydrodynamic forcings, spanning between 5 and 9 years. Our analysis reveals the presence of nonlinearity in the time-series of sandbar and wave data, and the relative importance of nonlinearity for each variable. The relation between the results of each sandbar case and patterns in bar behavior are discussed, together with the effects of noise. The small effect of nonlinearity implies that long-term prediction of sandbar positions based on wave forcings might not require sophisticated nonlinear models.

scholarly journals Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

Multivariate Time Series Decomposition into Oscillation Components

2017 ◽  
Vol 29 (8) ◽  
pp. 2055-2075 ◽  
Author(s):  
Takeru Matsuda ◽  
Fumiyasu Komaki
Keyword(s):  
Time Series ◽  
Empirical Bayes ◽  
Multivariate Time Series ◽  
Phase Relationship ◽  
Information Criterion ◽  
Model Parameters ◽  
Phase Dynamics ◽  
Univariate Time Series ◽  
Linear State ◽  
The Given

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

scholarly journals Parallel kd-Tree Based Approach for Computing the Prediction Horizon Using Wolf’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
J. J. Águila ◽  
E. Arias ◽  
M. M. Artigao ◽  
J. J. Miralles
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Measurement Data ◽  
Original System ◽  
Model Parameters ◽  
Maximal Lyapunov Exponent ◽  
Science And Engineering ◽  
Prediction Horizon ◽  
Means Of Measurement

In different fields of science and engineering, a model of a given underlying dynamical system can be obtained by means of measurement data records called time series. This model becomes very important to understand the original system behaviour and to predict the future values of that system. From the model, parameters such as the prediction horizon can be computed to obtain the point where the prediction becomes useless. In this work, a new parallel kd-tree based approach for computing the prediction horizon is presented. The parallel approach uses the maximal Lyapunov exponent, which is computed by Wolf’s method, as an estimator of the prediction horizon.

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