Exponentially Weighted Multivariate HAR Model with Applications in the Stock Market

This paper considers a multivariate time series model for stock prices in the stock market. A multivariate heterogeneous autoregressive (HAR) model is adopted with exponentially decaying coefficients. This model is not only suitable for multivariate data with strong cross-correlation and long memory, but also represents a common structure of the joint data in terms of decay rates. Tests are proposed to identify the existence of the decay rates in the multivariate HAR model. The null limiting distributions are established as the standard Brownian bridge and are proven by means of a modified martingale central limit theorem. Simulation studies are conducted to assess the performance of tests and estimates. Empirical analysis with joint datasets of U.S. stock prices illustrates that the proposed model outperforms the conventional HAR models via OLSE and LASSO with respect to residual errors.     

Trimmed stable AR(1) processes

In this paper we investigate the distribution of trimmed sums of dependent observations with heavy tails. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. We show if the $d$ largest (in magnitude) terms are removed from the sample, then the sum of the remaining elements satisfies a functional central limit theorem with random centering provided $d=d\left(n\right)\ge n^{\gamma }$ (for some $\gamma >0$) and $d\left(n\right)/n\to 0$. This result is used to get asymptotics for the widely used CUSUM process in case of dependent heavy tailed observations.     

A Hidden-Markov estimation method for mean-shift detection of fraction defective in production process control

This paper considers a statistical method of estimating mean shift for a fraction defective of population. One traditional method for this estimation problem has been known as the CUSUM (cumulative sum) method, and it provides a method of estimating the occurrence of a shift in the mean from the observed data. We consider this estimation problem of shift occurrence in a production process. It is assumed that the process has two states, one is good (fraction defective low) and the other bad (fraction defective high), and starts in good state with probability one. We are interested in judging when the state has moved to the bad state by analyzing the observed data.In this paper, we model such a phenomenon as a hidden-Markov model. The states which are unobservable in a hidden-Markov model can be analyzed from the sequence of observed results. Hence, the advantage of this modeling technique is that the unknown parameters which are included in the hidden states can be estimated. We compare the performance of this hidden-Markov model with the CUSUM method based on several simulation data sets.     

CUSUM control charts based on likelihood ratio for preliminary analysis

To detect and estimate a shift in either the mean and the deviation or both for the preliminary analysis, the statistical process control (SPC) tool, the control chart based on the likelihood ratio test (LRT), is the most popular method. Sullivan and woodall pointed out the test statistic lrt(n1, n2) is approximately distributed as x2(2) as the sample size n,n1 and n2 are very large, and the value of n1 = 2,3,..., n - 2 and that of n2 = n - n1. So it is inevitable that n1 or n2 is not large. In this paper the limit distribution of lrt(n1, n2) for fixed n1 or n2 is figured out, and the exactly analytic formulae for evaluating the expectation and the variance of the limit distribution are also obtained. In addition, the properties of the standardized likelihood ratio statistic slr(n1, n) are discussed in this paper. Although slr(n1, n) contains the most important information, slr(i, n)(i≠n1) also contains lots of information. The cumulative sum (CUSUM) control chart can obtain more information in this condition. So we propose two CUSUM control charts based on the likelihood ratio statistics for the preliminary analysis on the individual observations. One focuses on detecting the shifts in location in the historical data and the other is more general in detecting a shift in either the location and the scale or both. Moreover, the simulated results show that the proposed two control charts are, respectively, superior to their competitors not only in the detection of the sustained shifts but also in the detection of some other out-of-control situations considered in this paper.     

Steady-state-optimal adaptive control charts based on variable sampling intervals

Variable sampling interval (VSI) control charts vary the sampling rate adaptively as a function of the data coming from the process in order to reduce the detection delay of process changes. Zero-time performance refers to the detection delay of a process change that is present during the onset of the chart at time zero. Steady-state performance refers to the detection delay of a process change that occurs after the chart has been operating for some time. The zero-time performance of a VSI control chart can differ considerably from the chart's steady-state performance, which is generally more important than the zero-time performance. We develop an efficient quadratic-programming algorithm for the construction and investigation of steady-state-optimal sampling policies for various VSI charts. We show that a steady-state-optimal VSI scheme is fundamentally different from the respective zero-time-optimal VSI scheme, and recommend VSI policies based on two sampling intervals for the various types of control charts considered.     

Diagnosis for uncertain,dynamic and hybrid domains using Bayesian networks and arithmetic circuits

System failures, for example in electrical power systems, can have catastrophic impact on human life and high-cost missions. Due to an electrical fire in Swissair flight 111 on September 2, 1998, all 229 passengers and crew on board sadly lost their lives. A battery failure most likely took place on the Mars Global Surveyor, which unfortunately last communicated with Earth and thus ended its mission on November 2, 2006. Fault diagnosis techniques that seek to hinder similar accidents in the future are being developed in this article. We present comprehensive fault diagnosis methods for dynamic and hybrid domains with uncertainty, and validate them using electrical power system data. Our approach relies on the use of Bayesian networks, which model the electrical power system, compiled to arithmetic circuits. We handle in an integrated way varying fault dynamics (both persistent and intermittent faults), fault progression (both abrupt and drift faults), and fault behavior cardinality (both discrete and continuous behaviors). Our work has resulted in a software system for fault diagnosis, ProDiagnose, that has been the top performer in three of the four international diagnostics competitions in which it participated. In this paper we comprehensively present our methods as well as novel and extensive experimental results on data from a NASA electrical power system.     

Change Point Test for the Conditional Mean of Time Series of Counts Based on Support Vector Regression

This study considers support vector regression (SVR) and twin SVR (TSVR) for the time series of counts, wherein the hyper parameters are tuned using the particle swarm optimization (PSO) method. For prediction, we employ the framework of integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) models. As an application, we consider change point problems, using the cumulative sum (CUSUM) test based on the residuals obtained from the PSO-SVR and PSO-TSVR methods. We conduct Monte Carlo simulation experiments to illustrate the methods’ validity with various linear and nonlinear INGARCH models. Subsequently, a real data analysis, with the return times of extreme events constructed based on the daily log-returns of Goldman Sachs stock prices, is conducted to exhibit its scope of application.     

An adaptation of Page’s CUSUM test for change detection

Summary Page’s CUSUM test for detecting change in a sequence of independent observations is extended to the general parametric model involving nuisance parameters. The test statistic is the standardized efficient score vector. The model of nested random effects is analyzed in detail.     

On testing for no effect of the predictor on response

1.Introduction'Givenasequenceofpairdata(yi1ti),'t(aam,t.),',itisimportanttocheckwhetherornotthepredictorvariablethasaneffectontheresponsevariabley,sincethisisessentialinstudyingthebehaviouroftheprocessandpredictingthefuturevalueofy.Alongthisdirection,therearetwokindsofmodels,namely,regressionmodelandtimeseriesmodelwhichareoftenconsidered:i)Regressionmodelyi~p g(ti) fi,i~1,...?n,(1.1)wheretiarefixeddesignedpointsorrandompoilltscorrespondingtovariousconcretesituations.n)Timeseriesmodelyi~P …