Download or read book Mixture Autoregressive Model written by Munhtsetseg Ganbaatar and published by . This book was released on 2002 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Mixture Autoregressive Model Based on Student s T Distribution written by Mika Meitz and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new mixture autoregressive model based on Student's t-distribution is proposed. A key feature of our model is that the conditional t-distributions of the component models are based on autoregressions that have multivariate t-distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component model is a linear function of past observations and the conditional variance is also time varying. Compared to previous mixture autoregressive models our model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. An empirical example employing a realized kernel series constructed from S&P 500 high-frequency intraday data shows that the proposed model performs well in volatility forecasting. Our methodology is implemented in the freely available StMAR Toolbox for MATLAB.
Download or read book Mixture Autoregressive Models with Applications to Heteroskedastic Time Series written by Davide Ravagli and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Gaussian Mixture Autoregressive Model for Univariate Time Series written by Leena Kalliovirta and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gaussian mixture autoregressive model studied in this article belongs to the family of mixture autoregressive models, but it differs from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the definition of the model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. Another major advantage is that, for a pth-order model, explicit expressions of the stationary distributions of dimension p 1 or smaller are known and given by mixtures of Gaussian distributions with constant mixing weights. In contrast, the conditional distribution given the past observations is a Gaussian mixture with time-varying mixing weights that depend on p lagged values of the series in a natural and parsimonious way. Because of the known stationary distribution, exact maximum likelihood estimation is feasible and one can assess the applicability of the model in advance by using a non-parametric estimate of the stationary density. An empirical example with interest rate series illustrates the practical usefulness and flexibility of the model, particularly in allowing for level shifts and temporary changes in variance.
Download or read book Mixture Autoregressive Models written by Vassilios Gkatziolis and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mixture Autoregression with Heavy tailed Conditional Distribution written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: (Uncorrected OCR) Abstract of thesis entitled MIXTURE AUTOREGRESSION WITH HEAVY-TAILED CONDITIONAL DISTRIBUTION submitted by KAM, Po Ling for the degree of Master of Philosophy at the University of Hong Kong in August 2003 In this thesis, we consider two types of the mixture autoregressive model. The first one is Gaussian mixture autoregressive model (GMAR) which is introduced by Wong and Li (2000). The second one is Student t-type MAR (TMAR) model which is a new model proposed by us. For GMAR model, it consists of a mixture K Gaussian autoregressive components. There are several properties which make Gaussian MAR model potentially useful in non-linear time series modelling. Firstly, it can be shown that a mixture of a non-stationary AR component with a stationary AR component can result in an overall stationary process. Secondly, the Gaussian MAR model can capture the shape-changing feature in conditional distribution of the time series. Lastly, the Gaussian MAR model can also capture conditional heteroscedasticity (Engle, 1982) which is a common phenomenon in financial time series. Despite the advantages of Gaussian MAR models, there are some limitations in some real life applications. If densities of some financial time series data are plotted, it can be noticed that the densities tend to be fatter tailed than the normal. Moreover, extreme data are observed more often than those implied by a Gaussian distribution. According to Peel and McLachlan (2000), heavy tails and outliers affect the estimation of means and variances in mixture type models. The applicability of the Gaussian MAR model to financial time series might be questionable. In order to illustrate the problem, we perform several simulation studies to study the estimation of Gaussian MAR model using data generated from heavy tailed distributions. On the other hand, we introduced a new model called Student t-type MAR model. We propose to replace the normal conditional distribution in each component of th.
Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.
Download or read book On Mixture Double Autoregressive Time Series Models written by Zhao Liu and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Mixture Double Autoregressive Time Series Models" by Zhao, Liu, 劉釗, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Conditional heteroscedastic models are one important type of time series models which have been widely investigated and brought out continuously by scholars in time series analysis. Those models play an important role in depicting the characteristics of the real world phenomenon, e.g. the behaviour of _nancial market. This thesis proposes a mixture double autoregressive model by adopting the exibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed by Ling (2004). Probabilistic properties including strict stationarity and higher order moments are derived for this new model and, to make it more exible, a logistic mixture double autoregressive model is further introduced to take into account the time varying mixing proportions. Inference tools including the maximum likelihood estimation, an EM algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model. We notice that the shape changing characteristics of the multimodal conditional distributions is an important feature of this new type of model. The conditional heteroscedasticity of time series is also well depicted. Monte Carlo experiments give further support to these two new models, and the analysis of an empirical example based on our new models as well as other mainstream ones is also reported. DOI: 10.5353/th_b5177350 Subjects: Time-series analysis
Download or read book Mixture Autoregressive Models written by Mary Akinyemi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis extensively studies the class of Mixture autoregressive (MAR) models in terms of its asymptotic properties and applications to financial risk evaluation. We establish geometric ergodicity of the MAR models and by implication absolute regular and strong-mixing properties of the models. In addition, we also show the consistency and asymptotic normality of the maximum likelihood estimators of the MAR models. We compare the estimates of Value at Risk (VaR) and Expected Shortfall (ES) based on the MAR models to estimates based on a number of other methods, for individual stocks, exchange rates and stock indices. We find that the MAR models consistently perform better than the other models. In addition, tail density forecast performance of individual stocks, stock indices and exchange rate, based on some popular GARCH models are compared to tail forecasts based on MAR models with both Gaussian and Student-t innovations. The MAR models mostly outperform the other models. Confirming the claim that MAR models are better suited to capture the kind of data dynamics present in financial data. All the data analysis are implemented in R.The traditional residuals of the MAR model are computed as the difference between the observed values and their conditional means. We show that these residuals form a martingale difference sequence and that the unconditional variance of these residuals is strictly positive and bounded by the expected value of its conditional variance. We compare the class of MAR Models to the class of GARCH models and observed that both the GARCH type models andMAR models can be cast into the framework of random coefficient autoregressive models as well as generalized hidden markov models. We also show that for the MAR(2;1,1) model, the variance-covariance matrix ispositive definite and the same for both the conditional least square and maximum likelihood penalty functions.
Download or read book A Nonlinear Mixture Autoregressive Model for Speaker Verification written by Sundararajan Srinivasan and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we apply a nonlinear mixture autoregressive (MixAR) model to supplant the Gaussian mixture model for speaker verification. MixAR is a statistical model that is a probabilistically weighted combination of components, each of which is an autoregressive filter in addition to a mean. The probabilistic mixing and the datadependent weights are responsible for the nonlinear nature of the model. Our experiments with synthetic as well as real speech data from standard speech corpora show that MixAR model outperforms GMM, especially under unseen noisy conditions. Moreover, MixAR did not require delta features and used 2.5x fewer parameters to achieve comparable or better performance as that of GMM using static as well as delta features. Also, MixAR suffered less from over-fitting issues than GMM when training data was sparse. However, MixAR performance deteriorated more quickly than that of GMM when evaluation data duration was reduced. This could pose limitations on the required minimum amount of evaluation data when using MixAR model for speaker verification.
Download or read book Non Gaussian Autoregressive Type Time Series written by N. Balakrishna and published by Springer Nature. This book was released on 2022-01-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a variety of non-Gaussian autoregressive-type models to analyze time-series data. This book collects and collates most of the available models in the field and provide their probabilistic and inferential properties. This book classifies the stationary time-series models into different groups such as linear stationary models with non-Gaussian innovations, linear stationary models with non-Gaussian marginal distributions, product autoregressive models and minification models. Even though several non-Gaussian time-series models are available in the literature, most of them are focusing on the model structure and the probabilistic properties.
Download or read book StMAR Toolbox written by Mika Meitz and published by . This book was released on 2018 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document provides an overview of the StMAR Toolbox, a MATLAB toolbox specifically designed for simulation, estimation, diagnostic, and forecasting of the Student's t mixture autoregressive (StMAR) model proposed by Meitz, Preve & Saikkonen (2018). The StMAR model is a new type of mixture autoregressive model with observation dependent mixing weights. Its stationary formulation implies that both the conditional and unconditional distributions of its AR component models are Student's t, and that the conditional variances of these models are of ARCH type. The conditional and unconditional distributions of the StMAR model are both mixtures of Student's t distributions. This makes it suitable for modelling time series with excess kurtosis, regime switching, multimodality, persistence, and conditional heteroskedasticity. Potential applications in finance include the modelling and forecasting of return, interest rate, and volatility proxy series, but researchers and practitioners from other fields can also use the toolbox without any modifications. The StMAR Toolbox is free and publicly available software.
Download or read book Modeling the U S Short Term Interest Rate by Mixture Autoregressive Processes written by Markku Lanne and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new kind of mixture autoregressive model with GARCH errors is introduced and applied to the U.S. short-term interest rate. According to the diagnostic tests developed in the article and further informal checks, the model is capable of capturing both of the typical characteristics of the short-term interest rate: volatility persistence and the dependence of volatility on the level of the interest rate. The model also allows for regime switches whose presence has been a third central result emerging from the recent empirical literature on the U.S. short-term interest rate. Realizations generated from the estimated model seem stable and their properties resemble those of the observed series closely. The drift and diffusion functions implied by the new model are in accordance with the results in much of the literature on continuous-time diffusion models for the short-term interest rate, and the term structure implications agree with historically observed patterns.
Download or read book Time Varying Mixing Weights in Mixture Autoregressive Conditional Duration Models written by Giampiero M. Gallo and published by . This book was released on 2006 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial market price formation and exchange activity can be investigated by means of ultra-high frequency data. In this paper we investigate an extension of the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998) by adopting a mixture of distribution approach with time varying weights. Empirical estimation of the Mixture ACD model shows that the limitations of the standard base model and its inadequacy of modelling the behavior in the tail of the distribution are suitably solved by our model.When the weights are made dependent on some market activity data, the model lends itself to some structural interpretation related to price formation and information diffusion in the market.
Download or read book Bayesian Analysis of Change Point Problem in Autoregressive Model written by P. Arumugam and published by . This book was released on 2009 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multinomial Mixture Vector Autoregressive Models written by Yuji Tomita and published by . This book was released on 2003 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Multinomial Logistic Mixture Autoregressive Processes written by Musen Wen and published by . This book was released on 2014 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a brand new class of time series model and analyze its statistical properties and estimation method. We demonstrated that the model is able to successfully model and forecast the high frequency stock prices.
