A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity

Statistical tests routinely adopted for detecting nonlinear components in time series rely on the auxiliary regression of ARMA lagged residuals, and the Lagrange multiplier test to detect ARCH components is an example. The size distortion of such test suggests adopting a weighted test, where the weights are computed through a forward search algorithm. Simulations show that the forward weighted robust test is preferable to the classical Lagrange test and to existing robust tests, which are based on backward weighted regression or on estimated autocorrelation function. The forward weighted robust test is applied to daily financial and quarterly macroeconomic time series, showing its usefulness in detecting ARCH effects, even when outliers are present.     

Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis

Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the Gram-Charlier (GC) density and the skewed-t density. The Gram-Charlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen’s skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate.     

Adaptable arbitration of behaviours: some simulation results

During the last few years, in an attempt to provide an efficient alternative to classical methods to designing robot control structures, the behaviour-based approach has emerged. Its success has largely been a result of the bottom-up development of a number of fast, tightly coupled control processes. This new approach, however, has some important limitations because of its lack of goal directedness and flexibility. This paper describes a self-improving control system that would deal with some of these problems. The system is based on two levels of arbitration, a local level which enables the robot to survive in a particular real-world situation, and a global level which ensures that the robot reactions be consistent with the required goal. Emphasis is put on the local arbitration level: it is shown how the local priorities can be computed and learnt and some simulation results are presented.     

Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model

Recent developments in multivariate volatility modeling suggest that the conditional correlation matrix can be described by a time series recursion, where the total number of parameters grows by the power-of-two of the dimension of financial returns. The power of two computational requirement makes high-dimensional multivariate volatility modeling very time consuming. In this paper, we propose two simplified specifications in a multivariate autoregressive conditional heteroscedasticity model. The first specification computes an unconditional correlation matrix from standardized residuals of the model. The second specification restricts the sum of the weights in a time-varying conditional correlation equation to be one. Applying a Bayesian sampling scheme allows the number of parameters to be reduced from the power of two of the dimension to the linear order of the dimension only and simultaneously provides us a framework for model comparison. We test our simplified specifications using simulated and real data from three sectoral indices in Hong Kong, three market indices and four exchange rates. The results suggest that our simplified specifications are more effective than the original formulation.     

Quantum minimization for adapting ANFIS outputs to its nonlinear generalized autoregressive conditional heteroscedasticity

Volatility clustering degrades the efficiency and effectiveness of time series prediction and gives rise to large residual errors. This is because volatility clustering suggests a time series where successive disturbances, even if uncorrelated, are yet serially dependent. Traditional time-series forecast model such as grey model (GM) or auto-regressive moving-average (ARMA) has often encountered the overshoot effect, thus leading to the deterioration of its predictive accuracy. To overcome the overshoot and volatility clustering problems at the same time, an adaptive neuro-fuzzy inference system (ANFIS) is combined with a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model that is adapted by quantum minimization (QM) so as to tackle the problem of overshooting situation and time-varying conditional variance residual errors. The proposed method significantly reduces large residual errors in forecasts because the overshoot and volatility clustering effects are regulated to trivial levels. Two experiments using real financial and geographic data series, respectively, compare the proposed method and a number of well-known alternative methods. Results show that forecasting performance by the proposed method produces superior results, with good speed of computation. Goodness of fit of the proposed method is tested by Ljung-Box Q-test. It is concluded that the ANFIS/NGARCH composite model adapted by QM performs very well for improved predictive accuracy of irregular non-periodic short-term time series forecast and will be of interest to the science of statistical prediction of time series.

Diagnostics analysis for log-Birnbaum-Saunders regression models

In this paper, several diagnostics measures are proposed based on case-deletion model for log-Birnbaum-Saunders regression models (LBSRM), which might be a necessary supplement of the recent work presented by Galea et al. [2004. Influence diagnostics in log-Birnbaum-Saunders regression models. J. Appl. Statist. 31, 1049-1064] who studied the influence diagnostics for LBSRM mainly based on the local influence analysis. It is shown that the case-deletion model is equivalent to the mean-shift outlier model in LBSRM and an outlier test is presented based on mean-shift outlier model. Furthermore, we investigate a test of homogeneity for shape parameter in LBSRM, which is a problem mentioned by both Rieck and Nedelman [1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60] and Galea et al. [2004. Influence diagnostics in log-Birnbaum-Saunders regression models. J. Appl. Statist. 31, 1049-1064]. We obtain the likelihood ratio and score statistics for such test. Finally, a numerical example is given to illustrate our methodology and the properties of likelihood ratio and score statistics are investigated through Monte Carlo simulations.     

Empirical likelihood based diagnostics for heteroscedasticity in partial linear models

In this paper, we propose a diagnostic technique for checking heteroscedasticity based on empirical likelihood for the partial linear models. We construct an empirical likelihood ratio test for heteroscedasticity. Also, under mild conditions, a nonparametric version of Wilk’s theorem is derived, which says that our proposed test has an asymptotic chi-square distribution. Simulation results reveal that the finite sample performance of our proposed test is satisfactory in both size and power. An empirical likelihood bootstrap simulation is also conducted to overcome the size distortion in small sample sizes.     

Composite of adaptive support vector regression and nonlinear conditional heteroscedasticity tuned by quantum minimization for forecasts

Adaptive support vector regression (ASVR) applied to the forecast of complex time series is superior to the other traditional prediction methods. However, the effect of volatility clustering occurred in time-series actually deteriorates ASVR prediction accuracy. Therefore, incorporating nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model into ASVR is employed for dealing with the problem of volatility clustering to best fit the forecast’s system. Interestingly, quantum-based minimization algorithm is proposed in this study to tune the resulting coefficients between ASVR and NGARCH, in such a way that the ASVR/NGARCH composite model can achieve the best accuracy of prediction. Quantum optimization here tackles so-called NP-completeness problem and outperforms the real-coded genetic algorithm on the same problem because it accomplishes better approach to the optimal or near-optimal coefficient-found. It follows that the proposed method definitely obtains the satisfactory results because of highly balancing generalization and localization for composite model and thus improving forecast accuracy. Bao Rong Chang is currently an Associate Professor in the Department of Computer Science and Information Engineering at National Taitung University in Taitung, Taiwan. He completed his BS degree from the Department of Electronic Engineering, Tam Kang University, Taiwan. In 1990, he earned his ME degree from the Department of Electrical Engineering, University of Missouri-Columbia, USA, and his Ph.D. in 1994 at the same University. His current research interests include Intelligent Computations, Applied Computer Network, and Financial Engineering. Hsiu-Fen Tsai is currently a Senior Lecturer in the Department of International Business at Shu Te University in Kaohsiung, Taiwan. She completed her BA degree from the Department of International Business, National Taiwan University, Taiwan. In 1995, she earned her MBA degree from the Department of Business Administration, National Taiwan University, Taiwan. At present, she is a Ph. D. Candidate in Department of International Business since 2004 at the same University. Her current research interests include Intelligent Analysis of Business Models and Applications of Strategy Management.     

The complete realization problem for hidden Markov models: a survey and some new results

Suppose m is a positive integer, and let ${\mathcal{M} = \{1, \ldots ,m\}}$ . Suppose ${\{\mathcal{Y}_t \}}$ is a stationary stochastic process assuming values in ${\mathcal{M}}$ . In this paper we study the question: When does there exist a hidden Markov model (HMM) that reproduces the statistics of this process? This question is more than forty years old, and as yet no complete solution is available. In this paper, we begin by surveying several known results, and then we present some new results that provide ??almost?? necessary and sufficient conditions for the existence of a HMM for a mixing and ultra-mixing process (where the notion of ultra-mixing is introduced here). In the survey part of the paper, consisting of Sects. 2 through 8, we rederive the following known results: (i) Associate an infinite matrix H with the process, and call it a ??Hankel?? matrix (because of some superficial similarity to a Hankel matrix). Then the process has a HMM realization only if H has finite rank. (ii) However, the finite Hankel rank condition is not sufficient in general. There exist processes with finite Hankel rank that do not admit a HMM realization. (iii) An abstract necessary and sufficient condition states that a frequency distribution has a realization as an HMM if and only if it belongs to a ??stable polyhedral?? convex set within the set of all frequency distributions on ${\mathcal{M}^{*}}$ , the set of all finite strings over ${\mathcal{M}}$ . While this condition may be ??necessary and sufficient,?? it virtually amounts to a restatement of the problem rather than a solution of it, as observed by Anderson (Math Control Signals Syst 12(1):80?C120, 1999). (iv) Suppose a process has finite Hankel rank, say r. Then there always exists a ??regular quasi-realization?? of the process. That is, there exist a row vector, a column vector, and a set of matrices, each of dimension r or r ×?r as appropriate, such that the frequency of arbitrary strings is given by a formula that is similar to the corresponding formula for HMM??s. Moreover, all quasi-regular realizations of the process can be obtained from one of them via a similarity transformation. Hence, given a finite Hankel-rank process, it is a simple matter to determine whether or not it has a regular HMM in the conventional sense, by testing the feasibility of a linear programming problem. (v) If in addition the process is ??-mixing, every regular quasi-realization has additional features. Specifically, a matrix associated with the quasi-realization (which plays the role of the state transition matrix in a HMM) is ??quasi-row stochastic?? (in that its rows add up to one, even though the matrix may not be nonnegative), and it also satisfies the ??quasi-strong Perron property?? (its spectral radius is one, the spectral radius is a simple eigenvalue, and there are no other eigenvalues on the unit circle). A corollary is that if a finite Hankel rank ??-mixing process has a regular HMM in the conventional sense, then the associated Markov chain is irreducible and aperiodic. While this last result is not surprising, it does not seem to have been stated explicitly. While the above results are all ??known,?? they are scattered over the literature; moreover, the presentation here is unified and occasionally consists of relatively simpler proofs than are found in the literature. Next we move on to present some new results. The key is the introduction of a property called ??ultra-mixing.?? The following results are established: (a) Suppose a process has finite Hankel rank, is both ??-mixing as well as ??ultra-mixing,?? and in addition satisfies a technical condition. Then it has an irreducible HMM realization (and not just a quasi-realization). Moreover, the Markov process underlying the HMM is either aperiodic (and is thus ??-mixing), or else satisfies a ??consistency condition.?? (b) In the other direction, suppose a HMM satisfies the consistency condition plus another technical condition. Then the associated output process has finite Hankel rank, is ??-mixing and is also ultra-mixing. Moreover, it is shown that under a natural topology on the set of HMMs, both ??technical?? conditions are indeed satisfied by an open dense set of HMMs. Taken together, these two results show that, modulo two technical conditions, the finite Hankel rank condition, ??-mixing, and ultra-mixing are ??almost?? necessary and sufficient for a process to have an irreducible and aperiodic HMM.     

Shared kernel models for class conditional density estimation

We present probabilistic models which are suitable for class conditional density estimation and can be regarded as shared kernel models where sharing means that each kernel may contribute to the estimation of the conditional densities of an classes. We first propose a model that constitutes an adaptation of the classical radial basis function (RBF) network (with full sharing of kernels among classes) where the outputs represent class conditional densities. In the opposite direction is the approach of separate mixtures model where the density of each class is estimated using a separate mixture density (no sharing of kernels among classes). We present a general model that allows for the expression of intermediate cases where the degree of kernel sharing can be specified through an extra model parameter. This general model encompasses both the above mentioned models as special cases. In all proposed models the training process is treated as a maximum likelihood problem and expectation-maximization algorithms have been derived for adjusting the model parameters.     

On the use of optimization models for portfolio selection: A review and some computational results

Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.     

A conditional independence algorithm for learning undirected graphical models

When it comes to learning graphical models from data, approaches based on conditional independence tests are among the most popular methods. Since Bayesian networks dominate research in this field, these methods usually refer to directed graphs, and thus have to determine not only the set of edges, but also their direction. At least for a certain kind of possibilistic graphical models, however, undirected graphs are a much more natural basis. Hence, in this area, algorithms for learning undirected graphs are desirable, especially, since first learning a directed graph and then transforming it into an undirected one wastes resources and computation time. In this paper I present a general algorithm for learning undirected graphical models, which is strongly inspired by the well-known Cheng–Bell–Liu algorithm for learning Bayesian networks from data. Its main advantage is that it needs fewer conditional independence tests, while it achieves results of comparable quality.     

Neural network models for conditional distribution under bayesian analysis

We use neural networks (NN) as a tool for a nonlinear autoregression to predict the second moment of the conditional density of return series. The NN models are compared to the popular econometric GARCH(1,1) model. We estimate the models in a Bayesian framework using Markov chain Monte Carlo posterior simulations. The interlinked aspects of the proposed Bayesian methodology are identification of NN hidden units and treatment of NN complexity based on model evidence. The empirical study includes the application of the designed strategy to market data, where we found a strong support for a nonlinear multilayer perceptron model with two hidden units.     

Mixture periodic autoregressive conditional heteroskedastic models

Mixture Periodically Correlated Autoregressive Conditionally Heteroskedastic (MPARCH) model, which extends the ARCH model, is proposed. The primary motivation behind this extension is to make the model consistent with high kurtosis, outliers and extreme events, and at the same time, able to capture the periodicity feature exhibited by the autocovariance structure. The second and the fourth moment periodically stationary conditions and their closed-forms are derived. Maximum likelihood estimation is obtained via the iterative Expectation Maximization algorithm and the performance of this algorithm is shown via a simulation studies and the MPARCH models are fitted to a real data set.     

Mixture periodic autoregressive conditional heteroskedastic models

Mixture Periodically Correlated Autoregressive Conditionally Heteroskedastic (MPARCH) model, which extends the ARCH model, is proposed. The primary motivation behind this extension is to make the model consistent with high kurtosis, outliers and extreme events, and at the same time, able to capture the periodicity feature exhibited by the autocovariance structure. The second and the fourth moment periodically stationary conditions and their closed-forms are derived. Maximum likelihood estimation is obtained via the iterative Expectation Maximization algorithm and the performance of this algorithm is shown via a simulation studies and the MPARCH models are fitted to a real data set.     

Analysis of conditional covariance structure models

This paper presents a statistical development for analyzing covariance structure models with certain variables held constant. The theory enables one to assess partial correlations among variables. Models are defined based on the conditional covariance matrices, and they are studied by the maximum likelihood approach with the appropriate conditional sample covariance matrices. It is shown that existing computer package programs and statistical methods can be easily applied to analyze the new models. Examples from two real data sets are reported to illustrate the theory.     

Structured learning with constrained conditional models

Making complex decisions in real world problems often involves assigning values to sets of interdependent variables where an expressive dependency structure among these can influence, or even dictate, what assignments are possible. Commonly used models typically ignore expressive dependencies since the traditional way of incorporating non-local dependencies is inefficient and hence leads to expensive training and inference. The contribution of this paper is two-fold. First, this paper presents Constrained Conditional Models (CCMs), a?framework that augments linear models with declarative constraints as a way to support decisions in an expressive output space while maintaining modularity and tractability of training. The paper develops, analyzes and compares novel algorithms for CCMs based on Hidden Markov Models and Structured Perceptron. The proposed CCM framework is also compared to task-tailored models, such as semi-CRFs. Second, we propose CoDL, a?constraint-driven learning algorithm, which makes use of constraints to guide semi-supervised learning. We provide theoretical justification for CoDL along with empirical results which show the advantage of using declarative constraints in the context of semi-supervised training of probabilistic models.     

Bayesian causal effects in quantiles: Accounting for heteroscedasticity

Testing for Granger non-causality over varying quantile levels could be used to measure and infer dynamic linkages, enabling the identification of quantiles for which causality is relevant, or not. However, dynamic quantiles in financial application settings are clearly affected by heteroscedasticity, as well as the exogenous and endogenous variables under consideration. GARCH-type dynamics are added to the standard quantile regression model, so as to more robustly examine quantile causal relations between dynamic variables. An adaptive Bayesian Markov chain Monte Carlo scheme, exploiting the link between quantile regression and the skewed-Laplace distribution, is designed for estimation and inference of the quantile causal relations, simultaneously estimating and accounting for heteroscedasticity. Dynamic quantile linkages for the international stock markets in Taiwan and Hong Kong are considered over a range of quantile levels. Specifically, the hypothesis that these stock returns are Granger-caused by the US market and/or the Japanese market is examined. The US market is found to significantly and positively Granger-cause both markets at all quantile levels, while the Japanese market effect was also significant at most quantile levels, but with weaker effects.     

Prototyping: some new results

This research describes a survey of experienced software development practitioners in large organizations for their perceptions of the relative merits of the prototyping and waterfall approaches. Some results of earlier research are confirmed but a number of new insights are obtained. Prototyping is used by developers who are mainly concerned with early life cycle issues; improved communication with users, increased flexibility of the design produced and for early discovery of problems. Non-prototypers prefer to use a waterfall approach because they are more concerned with later life cycle issues—level of control provided, good communication with IS personnel, and the robustness and maintainability of the systems produced.     

Implementation of conditional simulation by successive residuals

Conditional simulation of ergodic and stationary Gaussian random fields using successive residuals is a new approach used to overcome the size limitations of the LU decomposition algorithm as well as provide fast updating of existing simulated realizations with new data. This paper discusses two different implementations of this approach. The implementations differ in the use of the new information available; in the first implementation new information is partially used to generate updated realizations; however, in the second implementation, the realizations are updated using all the new information available. The implementations are validated using the Walker Lake data set, and compared through a case study at a stockwork gold deposit.