Download or read book On the Three Step Non Gaussian Quasi Maximum Likelihood Estimation of Heavy Tailed Double Autoregressive Models written by Dong Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note considers a three-step non-Gaussian quasi-maximum likelihood estimation (TS-NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy-tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy-tailed.
Download or read book Non Stationarity and Quasi Maximum Likelihood Estimation on a Double Autoregressive Model written by Min Chen and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Dependence in Econometrics written by Van-Nam Huynh and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: In economics, many quantities are related to each other. Such economic relations are often much more complex than relations in science and engineering, where some quantities are independence and the relation between others can be well approximated by linear functions. As a result of this complexity, when we apply traditional statistical techniques - developed for science and engineering - to process economic data, the inadequate treatment of dependence leads to misleading models and erroneous predictions. Some economists even blamed such inadequate treatment of dependence for the 2008 financial crisis. To make economic models more adequate, we need more accurate techniques for describing dependence. Such techniques are currently being developed. This book contains description of state-of-the-art techniques for modeling dependence and economic applications of these techniques. Most of these research developments are centered around the notion of a copula - a general way of describing dependence in probability theory and statistics. To be even more adequate, many papers go beyond traditional copula techniques and take into account, e.g., the dynamical (changing) character of the dependence in economics.
Download or read book MIXTURE AUTOREGRESSION W HEAVY written by Po-Ling Kam and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mixture Autoregression With Heavy-tailed Conditional Distribution" by Po-ling, Kam, 甘寶玲, 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: 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 compo- nents. 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 iin 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 com- ponent of the Gaussian MAR model by the Student t distribution. There is a parameter called degree of freedom which can be used to adjust the degree of heavy-tailness of the conditional distributions according to our need. As the de- gree of freedom in a Student t distribution approaches infinity, the distribution approaches normal. Hence, the Gaussian MAR model is a limiting case of the proposed Student t-type MAR model. The parameter estimation of TMAR model can be carried out via the EM al- gorithm (Dempster et al., 1977). The standard errors of the parameter estimates can be computed by the Missing Information Principle (Louis, 1982). For model selection, corrected Bayesian information criteria (BIC ) is adopted. Several simulation studies are preformed to illustrate the importance of correct choice of model when the true data generating process is a Student t-type MAR model. iiWe compare the performance of Gaussian and Student t-type MAR model by some simulation studies and real life examples. Several financial time series are employed to illustrate the usefulness of the Student t-type MAR model. (460 words) iii DOI: 10.5353/th_b2961492 Subjects: Autoregression (Statistics) Distribution (Probability theory) Time-series analysis Gaussian processes Finance - Statistical methods
Download or read book Simple and Efficient Estimation of Parameters of Non Gaussian Autoregressive Processes written by Steven M. Kay and published by . This book was released on 1986 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new technique for the estimation of autoregressive filter parameters of a non-Gaussian autoregressive process is proposed. The probability density function of the driving noise is assumed to be known. The new technique is a two-stage procedure motivated by maximum likelihood estimation. It is computationally much simpler than the maximum likelihood estimator and does not suffer from convergence problems. Computer simulations indicate that unlike the least squares or linear prediction estimators, the proposed estimator is nearly efficient, even for moderately sized data records. By a slight modification the proposed estimator can also be used in the case when the parameters of the driving noise probability density function are not known. Keywords: Parameter estimation; Autoregressive processes; Non Gaussian processes; Maximum likelihood estimator; Weighted least squares; Efficiency robustness.
Download or read book Pseudo variance Quasi maximum Likelihood Estimation of Semiparametric Time Series Models written by Mirko Armillotta and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.
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 Unified Interval Estimation for Random Coefficient Autoregressive Models written by Jonathan B. Hill and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The consistency of the quasi-maximum likelihood estimator for random coefficient autoregressive models requires that the coefficient be a non-degenerate random variable. In this article, we propose empirical likelihood methods based on weighted-score equations to construct a confidence interval for the coefficient. We do not need to distinguish whether the coefficient is random or deterministic and whether the process is stationary or non-stationary, and we present two classes of equations depending on whether a constant trend is included in the model. A simulation study confirms the good finite-sample behaviour of our resulting empirical likelihood-based confidence intervals. We also apply our methods to study US macroeconomic data.
Download or read book Efficient Estimation of Parameters for Non Gaussian Autoregressive Processes written by Debasis Sengupta and published by . This book was released on 1986 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of estimating the parameters of a non-Gaussian autoregressive process is addressed. Departure of the driving noise from Gaussianity is shown to have the potential of improving the accuracy of the estimation of the parameters. While the standard linear prediction techniques are computationally efficient, they show a substantial loss of efficiency when applied to non-Gaussian processes. A maximum likelihood estimator is proposed for more precise estimation of the parameters of these processes coupled with a realistic non-Gaussian model for the driving noise. The performance is compared to that of the linear prediction estimator and as expected the maximum likelihood estimator displays a marked improvement.
Download or read book Autoregressive Model Inference in Finite Samples written by Hans Einar Wensink and published by . This book was released on 1996 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non asymptotic Analysis of Learning Long range Autoregressive Generalized Linear Models for Discrete High dimensional Data written by Parthe Pandit and published by . This book was released on 2021 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fitting multivariate autoregressive (AR) models is fundamental for analysis of time-series data in a wide range of applications in science, engineering, econometrics, signal processing, and data-science. This dissertation considers the problem of learning a $p$-lag multivariate AR generalized linear model (GLM). In this model, the state of the time-series at each time step, conditioned on the history, is drawn from an exponential family distribution with the mean parameter depending on a linear combination of the last $p$ states. The problem is to learn the linear connectivity tensor from a single observed trajectory of the time-series. We provide non-asymptotic error bounds on the regularized Maximum Likelihood estimator in high dimensions. We focus on the sparse tensor setting, which arises in applications where there exists a limited number of direct connections between variables. For such problems, $\ell_1$-regularized maximum likelihood estimation (or M-estimation more generally) is often straightforward to apply and works well in practice. The M-estimator can be posed as a convex optimization problem and hence can also be solved efficiently. However, the statistical analysis of such methods is difficult due to the feedback in the state dynamics and the presence of a non-linear link function, especially when the underlying process is non-Gaussian. Our main result in Chapter 3 provides a bound on the mean-squared error of the estimated connectivity tensor as a function of the sparsity and the number of samples, for a class of discrete multivariate AR($p$) GLMs, in the high-dimensional regime. Importantly, the bound indicates that, with sufficient sparsity, consistent estimation in cases where the number of samples is significantly less than the total number of free parameters. Towards proving the main result, we present a general framework to establish the Restricted Strong Convexity (RSC) property for time-averaged loss functions often seen in time-series analysis. We also derive new concentration inequalities of functions of discrete non-Markovian random variables. These intermediate results may be of independent interest to the reader.
Download or read book Quasi maximum Likelihood Estimation of Periodic Autoregressive Conditionally Heteroscedastic Time Series written by Florian Ziel and published by . This book was released on 2013 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Maximum Likelihood Estimation of Spatial Autoregressive Models with Normal But Heteroskedastic Disturbances written by Takahisa Yokoi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Likelihood functions of spatial autoregressive models with normal but heteroskedastic disturbances have been already derived [Anselin (1988, ch.6)]. But there is no implementation for maximum likelihood estimation of these likelihood functions in general (heteroskedastic disturbances) cases. This is the reason why less efficient IV-based methods, 'robust 2-SLS' estimation for example, must be applied when disturbance terms may be heteroskedastic. In this paper, we develop a new computer program for maximum likelihood estimation and confirm the efficiency of our estimator in heteroskedastic disturbance cases using Monte Carlo simulations.
Download or read book Efficiency IV Estimation for Autoregressive Models with Conditional Heterogeneity written by Guido M. Kuersteiner and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyzes autoregressive time series models where the errors are assumed to be martingale difference sequences that satisfy an additional symmetry condition on their fourth order moments. Under these conditions Quasi Maximum Likelihood estimators of the autoregressive parameters are no longer efficient in the GMM sense. The main result of the paper is the construction of efficient semiparametric instrumental variables estimators for the autoregressive parameters. The optimal instruments are linear functions of the innovation sequence. It is shown that a frequency domain approximation of the optimal instruments leads to an estimator which only depends on the data periodogram and an unknown linear filter. Semiparametric methods to estimate the optimal filter are proposed. The procedure is equivalent to GMM estimators where lagged observations are used as instruments. Due to the additional symmetry assumption on the fourth moments the number of instruments is allowed to grow at the same rate as the sample. No lag truncation parameters are needed to implement the estimator which makes it particularly appealing from an applied point of view.
Download or read book Maximum Likelihood Estimation for Nearly Non Stationary Stable Autoregressive Processes written by Rong-Mao Zhang and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Likelihood Estimation of the Autoregressive Coefficients and Moving Average Covariances of Vector Autoregressive Moving Average Models written by Fereydoon Ahrabi and published by . This book was released on 1979 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to derive asymptotically efficient estimates for the autoregressive matrix coefficients and moving average covariance matrices of the vector autoregressive moving average (VARMA) models in both time and frequency domains. To do this we shall apply the Newton-Raphson and scoring methods to the maximum likelihood equations derived from modified likelihood functions under the Gaussian Assumption.
Download or read book Dynamic Models for Volatility and Heavy Tails written by Andrew C. Harvey and published by Cambridge University Press. This book was released on 2013-04-22 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.
