Non-linear time series and Markov chains

It is shown how Markov chain theory can be exploited to study non-linear time series, the emphasis being on the classification into stationary and non-stationary models. A generalized h-step version of the Tweedie (1975), (1976) criteria is formulated, and applications are given to a number of non-linear models. New results are obtained, and known results are shown to emerge as special cases in both the scalar and vector case. A connection to stability theory is briefly discussed, and it is indicated how the Markov property can be utilized for estimation purposes.

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Generation method for the PV power time series combining the decomposition technique and Markov chain theory

The Journal of Engineering ◽

10.1049/joe.2017.0685 ◽

2017 ◽

Vol 2017 (13) ◽

pp. 2026-2031

Author(s):

Shenzhi Xu ◽

Xiaomeng Ai ◽

Jiakun Fang ◽

Jinyu Wen ◽

Pai Li ◽

...

Keyword(s):

Time Series ◽

Markov Chain ◽

Decomposition Technique ◽

Markov Chain Theory ◽

Chain Theory

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Stochastic fm models and non-linear time series analysis

Advances in Applied Probability ◽

10.2307/1427850 ◽

1997 ◽

Vol 29 (4) ◽

pp. 986-1003

Author(s):

D. Huang

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Linear Models ◽

Linear Time ◽

Transition Kernel ◽

Modulation And Demodulation ◽

Series Analysis ◽

Fm Signals ◽

Non Linear ◽

The Time Domain

An important model in communications is the stochastic FM signal st = A cos , where the message process {mt} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt} is a Gaussian MA (q) sequence. The spectral density of {St} can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St} is asymptotically strictly stationary if {mt} is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt}. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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Stochastic fm models and non-linear time series analysis

Advances in Applied Probability ◽

10.1017/s0001867800047984 ◽

1997 ◽

Vol 29 (04) ◽

pp. 986-1003 ◽

Cited By ~ 1

Author(s):

D. Huang

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Linear Models ◽

Linear Time ◽

Transition Kernel ◽

Modulation And Demodulation ◽

Series Analysis ◽

Fm Signals ◽

Non Linear ◽

The Time Domain

An important model in communications is the stochastic FM signal st = A cos , where the message process {m t} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt } is a Gaussian MA (q) sequence. The spectral density of {St } can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St } is asymptotically strictly stationary if {m t } is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt }. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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Hybrid Time Series Models for Forecasting Maize Production in India

Current Journal of Applied Science and Technology ◽

10.9734/cjast/2021/v40i2331492 ◽

2021 ◽

pp. 49-57

Author(s):

Pramit Pandit ◽

Bishvajit Bakshi ◽

Varun Gangadhar

Keyword(s):

Time Series ◽

Model Building ◽

Linear Models ◽

Linear Time ◽

Arima Model ◽

Hybrid Models ◽

Time Series Models ◽

Real World Data ◽

Maize Production ◽

Non Linear

In spite of the immense success of different linear and non-linear time series models in their respective domains, real-world data are rarely pure linear or non-linear in nature. Hence, a hybrid modelling framework with the capability of handling both linear and non-linear patterns can substantially improve the forecasting accuracy. With this backdrop, an effort has been made in this investigation to evaluate the suitability of hybrid models in compassion to single linear or non-linear models for forecasting maize production in India. Data from 1949-50 to 2016-17 have been utilised for the model building purpose while retaining the data from 2017-18 to 2019-20 for the post-sample accuracy assessment. Outcomes emanated from this investigation clearly reveals that the ARIMA-NLSVR model has outperformed all other candidate models employed in this study. It is noteworthy to mention that both the hybrid models have performed better than their individual counterparts. The superior forecasting ability of both the non-linear models over the linear ARIMA model has also been evident.

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Nonlinear Time Series Analysis with R

10.1093/oso/9780198782933.001.0001 ◽

2018 ◽

Author(s):

Ray Huffaker ◽

Marco Bittelli ◽

Rodolfo Rosa

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Particle Physics ◽

Linear Time ◽

Nonlinear Time Series ◽

Nonlinear Time Series Analysis ◽

Series Analysis ◽

Linear Behavior ◽

Non Linear ◽

Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

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