Monitoring foreclosure rates with a spatially risk-adjusted Bernoulli CUSUM chart for concurrent observations

Frequently in process monitoring, situations arise in which the order that events occur cannot be distinguished, motivating the need to accommodate multiple observations occurring at the same time, or concurrent observations. The risk-adjusted Bernoulli cumulative sum (CUSUM) control chart can be used to monitor the rate of an adverse event by fitting a risk-adjustment model, followed by a likelihood ratio-based scoring method that produces a statistic that can be monitored. In our paper, we develop a risk-adjusted Bernoulli CUSUM control chart for concurrent observations. Furthermore, we adopt a novel approach that uses a combined mixture model and kernel density estimation approach in order to perform risk-adjustment with regard to spatial location. Our proposed method allows for monitoring binary outcomes through time with multiple observations at each time point, where the chart is spatially adjusted for each Bernoulli observation's estimated probability of the adverse event. A simulation study is presented to assess the performance of the proposed monitoring scheme. We apply our method using data from Wayne County, Michigan between 2005 and 2014 to monitor the rate of foreclosure as a percentage of all housing transactions.     

Comment on testing for spurious and cointegrated regressions: a wavelet approach

In a recent paper, Leong and Huang [6] proposed a wavelet-correlation-based approach to test for cointegration between two time series. However, correlation and cointegration are two different concepts even when wavelet analysis is used. It is known that statistics based on non-stationary integrated variables have non-standard asymptotic distributions. However, wavelet analysis offsets the integrating order of non-stationary series so that traditional asymptotics on stationary variables suffices to ascertain the statistical properties of wavelet-based statistics. Based on this, this note shows that wavelet correlations cannot be used as a test of cointegration.     

SUBSAMPLING THE JOHANSEN TEST WITH STABLE INNOVATIONS

By taking into account the thick-tail property of the errors, cointegration analysis in vector error-correction models with infinite-variance stable errors is a natural generalization of cointegration analysis in error-correction models with normally distributed errors. We study the Johansen test for cointegrated systems under symmetric stable innovations with discrete spectral measures. The results show that the distributions of the Johansen test statistics under these innovations involve nuisance parameters. To overcome the problem of nuisance parameters, we implement a nonparametric subsampling procedure. We document some subsampling simulation results and demonstrate in an empirical example how the test can be used in practice.     

Generalized Linear Latent Variable Modeling for Multi-Group Studies

ABSTRACT

Latent variable modeling is commonly used in behavioral, social, and medical science research. The models used in such analysis relate all observed variables to latent common factors. In many applications, the observations are highly non normal or discrete, e.g., polytomous responses or counts. The existing approaches for non normal observations can be considered lacking in several aspects, especially for multi-group samples situations. We propose a generalized linear model approach for multi-sample latent variable analysis that can handle a broad class of non normal and discrete observations, and that furnishes meaningful interpretation and inference in multi-group studies through maximum likelihood analysis. A Monte Carlo EM algorithm is proposed for parameter estimation. The convergence assessment and standard error estimation is addressed. Simulation studies are reported to show the usefulness of the our approach. An example from a substance abuse prevention study is also presented.     

Time aggregation and skip sampling in cointegration tests

We examine the change of power of Johansen's VAR MLE cointegration test when samples are aggregated or skipped. We show by Monte Carlo simulation that although there are power gains when switching to high frequency data to gain more observations for a fixed time span, the power gains are much more significant when data with longer time span are used.     

A new nonlinear asymmetric cointegration approach using error correction models

In this article, two new powerful tests for cointegration are proposed. The general idea is based on an intuitively appealing extension of the traditional, rather restrictive cointegration concept. In this article, we allow for a nonlinear, but most importantly a different, asymmetric convergence process to account for negative and positive changes in our cointegration approach. Using Monte Carlo simulations we verify, that the estimated size of the first test depends on the unknown value of a signal-to-noise ratio q. However, our second test—which is based on the original ideas of Kanioura and Turner—is more successful and robust in the sense that it works in all of the different evaluated situations. Furthermore it is shown to be more powerful than the traditional residual based Enders and Siklos method. The new optimal test is also applied in an empirical example in order to test for potential nonlinear asymmetric price transmission effects on the Swedish power market. We find that there is a higher propensity for power retailers to rapidly and systematically increase their retail electricity prices subsequent to increases in Nordpool's wholesale prices, than there is for them to reduce their prices subsequent to a drop in wholesale spot prices.     

Sensitivity of the portmanteau statistic in time series modeling

The portmanteau statistic is commonly used for testing goodness-of-fit of time series models. However, this lack of fit test may depend on one or several atypical observations in the series. We investigate the sensitivity of the portmanteau statistic in the presence of additive outliers. Diagnostics are developed to assess both local and global influence. Three practical examples demonstrate the usefulness of the proposed diagnostics.     

A default Bayesian procedure for the generalized Pareto distribution

The generalized Pareto distribution is used to model the exceedances over a threshold in a number of fields, including the analysis of environmental extreme events and financial data analysis. We use this model in a default Bayesian framework where no prior information is available on unknown model parameters. Using a large simulation study, we compare the performance of our posterior estimations of parameters with other methods proposed in the literature. We show that our procedure also allows to make inferences in other quantities of interest in extreme value analysis without asymptotic arguments. We apply the proposed methodology to a real data set.     

Cointegration analysis with state space models

This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration, and polynomial cointegration are defined. Based upon these definitions, the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By detailing the cases most relevant for empirical applications, the I(1), multiple frequency I(1), and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly discussed.     

Johansen和Juselius协整检验应注意的几个问题

Johansen和Juselius的似然比检验多变量协整关系的方法在实证分析中得到了广泛应用。在总结该方法的基础上,针对国内使用该方法存在比较混乱的状况指出了一些注意事项,譬如根据经济时间序列的数据生成过程选择确定性成分,检验临界值的使用以及协整关系个数的非唯一性等问题,还简要论述了阶数的确定、外生性与因果关系检验等问题,最后指出了该检验的一些不足。通过对上述问题的讨论,试图为实证研究人员在使用该方法时提供简单有效的指导性建议。     

Test for cointegration based on two-stage least squares

A residual-based test for cointegration is proposed. The method of two-stage least squares is used to estimate the cointegration model parameters. The residuals are then tested for the existence of a unit root using the augmented Dickey-Fuller test.     

Testing equality of survival distributions when the population marks are missing

This paper introduces a nonparametric approach for testing the equality of two or more survival distributions based on right censored failure times with missing population marks for the censored observations. The standard log-rank test is not applicable here because the population membership information is not available for the right censored individuals. We propose to use the imputed population marks for the censored observations leading to fractional at-risk sets that can be used in a two sample censored data log-rank test. We demonstrate with a simple example that there could be a gain in power by imputing population marks (the proposed method) for the right censored individuals compared to simply removing them (which also would maintain the right size). Performance of the imputed log-rank tests obtained this way is studied through simulation. We also obtain an asymptotic linear representation of our test statistic. Our testing methodology is illustrated using a real data set.     

Atypical observations in linear models

The problem of ‘atypical data point’ in the estimation of model parameters and its effect on prediction are discussed. A cross-validity procedure is then proposed to accommodate the unusual observations in the estimation and thereby to improve the prediction of future data points. Each atypical point, weighted according to cross-validitory procedure, is used in the estimation of model parameters.     

A vector of quarters representation for bivariate time series

In this paper it is shown that several models for a bivariate nonstationary quarterly time series are nested in a vector autoregression with cointegration restrictions for the eight annual series of quarterly observations. Or, the Granger Representation Theorem is extended to incorporate, e.g., seasonal and periodic cointegration.     

A vector of quarters representation for bivariate time series

In this paper it is shown that several models for a bivariate nonstationary quarterly time series are nested in a vector autoregression with cointegration restrictions for the eight annual series of quarterly observations. Or, the Granger Representation Theorem is extended to incorporate, e.g., seasonal and periodic cointegration.     

The 1970 US draft lottery revisited: a spatial analysis

Summary.  We revise the result of the 1970 selective service draft lottery in the USA following an open question that was suggested by Fienberg in a paper published in Science in 1971. The result of the drawings can be viewed as a particular spatial pattern which can be analysed by using general spatial tools adapted to our context. Approaches for assessing the complete spatial randomness for this spatial process on a finite support are proposed. More specifically, these approaches involve the number of events in a square window and a k ( r )-based function used to analyse stationary spatial point processes.     

Robust estimation of dynamic fixed-effects panel data models

This paper extends an existing outlier-robust estimator of linear dynamic panel data models with fixed effects, which is based on the median ratio of two consecutive pairs of first-order differenced data. To improve its precision and robustness properties, a general procedure based on higher-order pairwise differences and their ratios is designed. The asymptotic distribution of this class of estimators is derived. Further, the breakdown point properties are obtained under contamination by independent additive outliers and by the patches of additive outliers, and are used to select the pairwise differences that do not compromise the robustness properties of the procedure. The proposed estimator is additionally compared with existing methods by means of Monte Carlo simulations.     

Quasi-likelihood ratio tests for cointegration,cobreaking, and cotrending

We consider a set of variables with two types of nonstationary features, stochastic trends and broken linear trends. We develop tests that can determine whether there is a linear combination of these variables under which the nonstationary features can be canceled out. The first test can determine whether stochastic trends can be eliminated and thus whether cointegration holds, regardless of whether structural breaks in linear trends are eliminated. The second test can determine whether both stochastic trends and breaks in linear trends are simultaneously removed and thus whether cointegration and cobreaking simultaneously hold. The third test can determine whether not only breaks in linear trends but also linear trends themselves are eliminated along with stochastic trends and thus whether both cointegration and cotrending hold.     

Cointegration and Long-Run Asset Allocation

We show that economic restrictions of cointegration between asset cash flows and aggregate consumption have important implications for return dynamics and optimal portfolio rules, particularly at long investment horizons. When cash flows and consumption share a common stochastic trend (i.e., are cointegrated), temporary deviations between their levels forecast long-horizon dividend growth rates and returns, and consequently, alter the term profile of risks and expected returns. We show that the optimal asset allocation based on the error-correction vector autoregression (EC-VAR) specification can be quite different relative to a traditional VAR that ignores the cointegrating relation. Unlike the EC-VAR, the commonly used VAR approach to model expected returns focuses on short-run forecasts and can considerably miss on long-horizon return dynamics, and hence, the optimal portfolio mix in the presence of cointegration. We develop and implement methods to account for parameter uncertainty in the EC-VAR setup and highlight the importance of the error-correction channel for optimal portfolio decisions at various investment horizons.     

Cointegration in VAR(1) process: Characterization and testing

In this paper we taken a rather different approach to the concept of cointegration (comparated to existing literature) by focusing on the distance norm of an appropriately defined stochastic process (the first differences of one series) and a closed linear subspace defined from the first differences of the other series. The main result contained in Theorem 2 states that, within a VAR(l) framework, two series are cointegrated if and only if this distance is smaller than the standard deviation of the former process. It links cointegration to the evaluation of the distance between two information sets concerning the short-run dynamic paths of the variables. Hence cointegration can be detected by the differenced series. We, also propose a test for cointegration