Simulation of non-stationary event flow with a nested stationary component

2020 ◽  
Vol 28 (1) ◽  
pp. 35-48
Author(s):  
Ruslan V. Pleshakov
Keyword(s):  
Time Series ◽  
Random Process ◽  
Empirical Distribution ◽  
Price Change ◽  
Random Variable ◽  
Stationary Time Series ◽  
Practical Application ◽  
Nonstationary Flow ◽  
Event Flow ◽  
Stationary Component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

scholarly journals Simulation of non-stationary event flow with a nested stationary component

2020 ◽  
Vol 28 (1) ◽  
pp. 35-48
Author(s):  
Ruslan V. Pleshakov
Keyword(s):  
Time Series ◽  
Random Process ◽  
Empirical Distribution ◽  
Price Change ◽  
Random Variable ◽  
Stationary Time Series ◽  
Practical Application ◽  
Nonstationary Flow ◽  
Event Flow ◽  
Stationary Component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

Simulation of non-stationary event flow with a nested stationary component

2020 ◽  
Vol 28 (1) ◽  
pp. 35-48
Author(s):  
Ruslan V. Pleshakov
Keyword(s):  
Time Series ◽  
Random Process ◽  
Empirical Distribution ◽  
Price Change ◽  
Random Variable ◽  
Stationary Time Series ◽  
Practical Application ◽  
Nonstationary Flow ◽  
Event Flow ◽  
Stationary Component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

scholarly journals The Decomposition Issue of a Time Series in the Forecasting Process

2017 ◽  
Vol 23 (3) ◽  
pp. 43-47 ◽  
Author(s):  
Dariusz Grzesica
Keyword(s):  
Time Series ◽  
Random Process ◽  
Forecast Error ◽  
Random Variable ◽  
Stationary Random Process ◽  
Time Series Modeling ◽  
Seasonal Fluctuations ◽  
Time Series Decomposition ◽  
Building Models

AbstractDecomposition of time series is the estimate and extraction of deterministic part of the series - trend, cyclical and seasonal fluctuations in the hope that the rest of the data, that is, theoretically, a random variable will be stationary random process. During the process of predicting the time series elements affects significantly on the determination of the future values, which are characterized by a low forecast error. Therefore, the purpose of this article is to identify the elements of the time series decomposition and to determine the extent to which they affect the forecasting process. Problems that often appear when you run the forecast and methods of building models and forecasts based on time series will be presented. Observations will be described on the basis of nonparametric time series modeling.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

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