First-Passage Time Properties of Correlated Time Series with Scale-Invariant Behavior and with Crossovers in the Scaling

Discrete time-series models are commonly used to represent economic and physical data. In decision making and system control, the first-passage time and level-crossing probabilities of these processes against certain threshold levels are important quantities. In this paper, we apply an integral-equation approach together with the state-space representations of time-series models to evaluate level-crossing probabilities for the AR(p) and ARMA(1,1) models and the mean first passage time for AR(p) processes. We also extend Novikov's martingale approach to ARMA(p,q) processes. Numerical schemes are used to solve the integral equations for specific examples.

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Comparison of Jump-Diffusion Parameters Using Passage Times Estimation

Journal of Applied Mathematics ◽

10.1155/2014/975418 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

K. Khaldi ◽

K. Djeddour ◽

S. Meddahi

Keyword(s):

Time Series ◽

First Passage Time ◽

Jump Diffusion ◽

Passage Time ◽

Share Price ◽

First Passage ◽

Diffusion Parameters ◽

Stochastic Jump ◽

Moments Method ◽

Passage Times

The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time generalized for all passage times (PT method), in order to estimate the parameters of stochastic jump-diffusion process. (2) It compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the PT method and those obtained by the moments method applied to the MJD model.

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Level-crossing probabilities and first-passage times for linear processes

Advances in Applied Probability ◽

10.1017/s0001867800013641 ◽

2004 ◽

Vol 36 (02) ◽

pp. 643-666 ◽

Cited By ~ 1

Author(s):

Gopal K. Basak ◽

Kwok-Wah Remus Ho

Keyword(s):

Time Series ◽

First Passage Time ◽

Passage Time ◽

Time Series Models ◽

System Control ◽

Level Crossing ◽

First Passage ◽

Linear Processes ◽

Integral Equation Approach ◽

Crossing Probabilities

Discrete time-series models are commonly used to represent economic and physical data. In decision making and system control, the first-passage time and level-crossing probabilities of these processes against certain threshold levels are important quantities. In this paper, we apply an integral-equation approach together with the state-space representations of time-series models to evaluate level-crossing probabilities for the AR(p) and ARMA(1,1) models and the mean first passage time for AR(p) processes. We also extend Novikov's martingale approach to ARMA(p,q) processes. Numerical schemes are used to solve the integral equations for specific examples.

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Phase transitions in the first-passage time of scale-invariant correlated processes

Physical Review E ◽

10.1103/physreve.85.011139 ◽

2012 ◽

Vol 85 (1) ◽

Cited By ~ 23

Author(s):

Concepción Carretero-Campos ◽

Pedro Bernaola-Galván ◽

Plamen Ch. Ivanov ◽

Pedro Carpena

Keyword(s):

Phase Transitions ◽

First Passage Time ◽

Passage Time ◽

Scale Invariant ◽

First Passage

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First passage time for the state of exact chemical equilibrium

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19800777 ◽

1980 ◽

Vol 45 (3) ◽

pp. 777-782 ◽

Cited By ~ 1

Author(s):

Milan Šolc

Keyword(s):

Chemical Equilibrium ◽

First Passage Time ◽

Passage Time ◽

The State ◽

Recurrence Time ◽

First Passage ◽

First Order ◽

The Mean ◽

Passage Times ◽

Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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