Moment method estimation of first-order continuous-time bilinear processes

Bibi, Abdelouahab; Merahi, Fateh

doi:10.1080/03610918.2017.1406507

Cited by 5 publications

(6 citation statements)

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“…In this section, we propose the moment's method (MM) for estimating the unknown parameters, α, μ and γ gathered in vector θ involved in COBL (1,1) Proof. The proof follows essentially the same arguments as in Bibi and Merahi [21].…”

Section: Estimation Issuesmentioning

confidence: 80%

The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

Bibi¹

2023

Time Series Analysis - New Insights

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The models of stochastic subordination, or random time indexing, has been recently applied to model financial returns Xtt≥0 exhibiting some characteristic periods of constant values for instance exchange rate. In reality, sharp and large variations for X(t) do occur. These sharp and large variations are linked to information arrivals and/or represent sudden events and hence we have a model with jumps. For this purpose, by substituting the usual deterministic time t as a subordinator Ttt≥0 in a stochastic process Xtt≥0 we obtain a new process XTtt≥0 whose stochastic time is dominated by the subordinator Ttt≥0. Therefore we propose in this paper an alternative approach based on a combination of the continuous-time bilinear (COBL) process subordinated by a Poisson process (that it is a Levy process) which permits us to introduce further randomness for the phenomena which exhibit either a speeded up or slowed down behavior. So, the main probabilistic properties of such models are studied and the explicit expression of the higher-order moments properties are given. Moreover, moments method (MM) is proposed as an estimation issue of the unknown parameters. Simulation studies confirm the theoretical findings and show that the MM method proposal can effectively reduce both the bias and the mean square error of parameter estimates.

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Section: Estimation Issuesmentioning

confidence: 80%

The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

Bibi¹

2023

Time Series Analysis - New Insights

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“…Beside the above differences, in this paper, the GM M estimator is obtained from AR(1) model after a discretization of SDE (21), and hence the reference by Bibi and Merahi [4] is entirely different from the present.…”

Section: The Major Difference Between Gmm and MM Methodsmentioning

confidence: 99%

“…In order to show the performance of (G) M M , we have reported in each table the root mean squared error (RM SE) (results between brackets). First, from theorem 3, Table (2) and under the condition (13), the fourth-order moments for Model(1) and Model(2) are given by Table (4).…”

Section: Simulation Studymentioning

confidence: 99%

“…Indeed, Kallsen and Muhle-Karbe [12], and Haug et al [8] have proposed an asymptotic inference of moments method (M M ) for a discretized continuous GARCH process. Bibi and Merahi [4] have proposed a M M for estimating the parameters of continuous-time bilinear processes. Chan et al [7] investigated an empirical comparison of GM M for several discretized diffusions processes.…”

Section: Introductionmentioning

confidence: 99%

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GMM Estimation of Continuous-Time Bilinear Processes

Bibi

Merahi

2020

Stat., optim. inf. comput.

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This paper examines the moments properties in frequency domain of the class of first order continuous-timebilinear processes (COBL(1,1) for short) with time-varying (resp. time-invariant) coefficients. So, we used theassociated evolutionary (or time-varying) transfer functions to study the structure of second-order of the process and its powers. In particular, for time-invariant case, an expression of the moments of any order are showed and the continuous-time AR (CAR) representation of COBL(1,1) is given as well as some moments properties of special cases. Based on these results we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM) illustrated by a Monte Carlo study and applied to modelling two foreign exchange rates of Algerian Dinar against U.S-Dollar (USD/DZD) and against the single European currency Euro (EUR/DZD).

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“…A large number of calculations are therefore needed. High-order moment methods 9–11 have proven to be convenient tools to solve these problems that are independent of design points and require neither iteration nor the computation of derivatives. Such methods might be performed efficiently when the performance function can be expressed as an explicit form or analytical form in terms of the basic variables.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic sensitivity analysis for the frame structure of missiles

Yang

Yue

Zhao

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, the high-performance and high-reliability of missiles were achieved under the background of the probabilistic analysis for frame structure of missiles. On the basis of deep investigation of the artificial neural network method and mathematical model of multiorder moment method, artificial neural network based higher order moment approach was proposed for the probabilistic analysis of complex structure. As illustrated in frame structure probabilistic analysis with multiphysics fields based on artificial neural network based higher order moment, the reliability and failure probability of frame structure were studied. Furthermore, it was shown that the radial concentrated force P and the outer radius of the frame R2 are the most important factors, and the inside radius of the frame R1 and the ultimate tensile strength of materials σ b also have an important influence on the frame structure. Through comparison with Monte Carlo simulation, second-order fourth-moment approach and the artificial neural network based first-order second-moment approach, it was demonstrated that artificial neural network based higher order moment reshapes the possibility of complex aero-missile probabilistic analysis and improves computing efficiency while preserving the accuracy. Artificial neural network based higher order moment offers a useful insight for missile reliability design and optimization with multi-discipline. The efforts of this study also enrich the theory and method of mechanical reliability design.

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Moment method estimation of first-order continuous-time bilinear processes

Cited by 5 publications

References 0 publications

The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

GMM Estimation of Continuous-Time Bilinear Processes

Probabilistic sensitivity analysis for the frame structure of missiles

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Moment method estimation of first-order continuous-time bilinear processes

Cited by 5 publications

References 0 publications

The L2 – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

The L2 – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

GMM Estimation of Continuous-Time Bilinear Processes

Probabilistic sensitivity analysis for the frame structure of missiles

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The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series

The L₂ – Structure of Subordinated Solution of Continuous-Time Bilinear Time Series