Multivariate linear time series models

1984 ◽  
Vol 16 (3) ◽  
pp. 492-561 ◽  
Author(s):  
E. J. Hannan ◽  
L. Kavalieris
Keyword(s):  
Limit Theorems ◽  
Analysis Of Algorithms ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Real Data ◽  
Rates Of Convergence ◽  
Structure Theory ◽  
Time Series Models ◽  
Transfer Model ◽  
Rational Transfer

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree, n, because of the fact that this space, M(n), can be realised as a kind of high-dimensional algebraic surface of dimension n(2s + m) where s and m are the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determining n and then the appropriate element of M(n). However, the fact that M(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

Multivariate linear time series models

1984 ◽  
Vol 16 (03) ◽  
pp. 492-561 ◽  
Author(s):  
E. J. Hannan ◽  
L. Kavalieris
Keyword(s):  
Limit Theorems ◽  
Analysis Of Algorithms ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Real Data ◽  
Rates Of Convergence ◽  
Structure Theory ◽  
Time Series Models ◽  
Transfer Model ◽  
Rational Transfer

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree,n,because of the fact that this space,M(n), can be realised as a kind of high-dimensional algebraic surface of dimensionn(2s+m) wheresandmare the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determiningnand then the appropriate element ofM(n). However, the fact thatM(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record,T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

scholarly journals Wavelet estimation of functional coefficient regression models

2018 ◽  
Vol 16 (01) ◽  
pp. 1850004
Author(s):  
Michel H. Montoril ◽  
Pedro A. Morettin ◽  
Chang Chiann
Keyword(s):  
Time Series ◽  
Real Data ◽  
Rates Of Convergence ◽  
Nonlinear Time Series ◽  
Local Linear Regression ◽  
Nonparametric Model ◽  
Time Series Models ◽  
Data Set ◽  
Wide Range ◽  
Functional Coefficient

The area of nonlinear time series models has experienced a great development since the 1980s. Although there is a wide range of parametric nonlinear time series models, in general, we do not know if the postulated model is the most appropriated one for a specific data set. This situation highlights the importance of nonparametric models. An interesting nonparametric model to fit nonlinear time series is the well-known functional coefficient regression model. Nonparametric estimations by, e.g., local linear regression and splines, are developed in the literature. In this work, we study the estimation of such a model using wavelets. It is a proposal that takes into account both, classical and warped wavelets. We present the rates of convergence of the proposed estimators and carry out simulation studies to evaluate automatic procedures (among AIC, AICc and BIC) for selecting the coarsest and finest levels to be used during the estimation process. Moreover, we illustrate the methodology with an application to a real data set, where we also calculate multi-step-ahead forecasts and compare the results with other methods known in the literature.

scholarly journals The Hyvärinen scoring rule in Gaussian linear time series models

2021 ◽  
Vol 212 ◽  
pp. 126-140
Author(s):  
Silvia Columbu ◽  
Valentina Mameli ◽  
Monica Musio ◽  
Philip Dawid
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Time Series Models ◽  
Scoring Rule

Linear time series models

2018 ◽  
pp. 57-72
Author(s):  
Erik Lindström ◽  
Henrik Madsen ◽  
Jan Nygaard Nielsen
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Time Series Models

scholarly journals Asymptotic behaviors with convergence rates of distributions of negative-binomial sums

2020 ◽  
Vol 22 (4) ◽  
pp. 415-421
Author(s):  
Tran Loc Hung ◽  
Phan Tri Kien ◽  
Nguyen Tan Nhut
Keyword(s):  
Limit Theorems ◽  
Negative Binomial ◽  
Convergence Rates ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Weak Limit ◽  
Probability Metric ◽  
Weak Limit Theorems ◽  
Distribution Theorem ◽  
Binomial Sums

The negative-binomial sum is an extension of a geometric sum. It has been arisen from the necessity to resolve practical problems in telecommunications, network analysis, stochastic finance and insurance mathematics, etc. Up to the present, the topics related to negative-binomial sums like asymptotic distributions and rates of convergence have been investigated by many mathematicians. However, in a lot of various situations, the results concerned the rates of convergence for negative-binomial sums are still restrictive. The main purpose of this paper is to establish some weak limit theorems for negative-binomial sums of independent, identically distributed (i.i.d.) random variables via Gnedenko's Transfer Theorem originated by Gnedenko and Fahim (1969). Using Zolotarev's probability metric, the rate of convergence in weak limit theorems for negativebinomial sum are established. The received results are the rates of convergence in weak limit theorem for partial sum of i.i.d random variables related to symmetric stable distribution (Theorem 1), and asymptotic distribution together with the convergence rates for negative-binomial sums of i.i.d. random variables concerning to symmetric Linnik laws and Generalized Linnik distribution (Theorem 2 and Theorem 3). Based on the results of this paper, the analogous results for geometric sums of i.i.d. random variables will be concluded as direct consequences. However, the article has just been solved for the case of 1 <a < 2; it is quite hard to estimate in the case of a 2 (0;1) via the Zolotarev's probability metric. Mathematics Subject Classification 2010: 60G50; 60F05; 60E07.

scholarly journals Network Bandwidth Utilization Prediction Based on Observed SNMP Data

2018 ◽  
Vol 13 (1) ◽  
pp. 160-168
Author(s):  
Nandalal Rana ◽  
Krishna P Bhandari ◽  
Surendra Shrestha
Keyword(s):  
Linear Time ◽  
Arima Model ◽  
Real Data ◽  
Service Planning ◽  
Bandwidth Utilization ◽  
Network Nodes ◽  
Network Bandwidth ◽  
Bandwidth Requirement ◽  
Logit Transformation

 Bandwidth requirement prediction is an important part of network design and service planning. The natural way of predicting bandwidth requirement for existing network is to analyze the past trends and apply appropriate mathematical model to predict for the future. For this research, the historical usage data of FWDR network nodes of Nepal Telecom is subject to univariate linear time series ARIMA model after logit transformation to predict future bandwidth requirement. The predicted data is compared to the real data obtained from the same network and the predicted data has been found to be within 10% MAPE. This model reduces the MAPE by 11.71% and 15.42% respectively as compared to the non-logit transformed ARIMA model at 99% CI. The results imply that the logit transformed ARIMA model has better performance compared to non-logit-transformed ARIMA model. For more accurate and longer term predictions, larger dataset can be taken along with season adjustments and consideration of long term variations.Journal of the Institute of Engineering, 2017, 13(1): 160-168

scholarly journals Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

2017 ◽  
Vol 54 (2) ◽  
pp. 569-587 ◽  
Author(s):  
Ollivier Hyrien ◽  
Kosto V. Mitov ◽  
Nikolay M. Yanev
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Cell Populations ◽  
Subcritical Case ◽  
Immigration Process ◽  
Large Numbers

Abstract We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.

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