Estimation and Forecasting of Locally Stationary Processes

This paper develops a state space framework for the statistical analysis of a class of locally stationary processes. The proposed Kalman filter approach provides a numerically efficient methodology for estimating and predicting locally stationary models and allows for the handling of missing values. It provides both exact and approximate maximum likelihood estimates. Furthermore, as suggested by the Monte Carlo simulations reported in this work, the performance of the proposed methodology is very good, even for relatively small sample sizes. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation and forecasting of long-memory processes with missing values

This paper addresses the issues of maximum likelihood estimation and forecasting of a long-memory time series with missing values. A state-space representation of the underlying long-memory process is proposed. By incorporating this representation with the Kalman filter, the proposed method allows not only for an efficient estimation of an ARFIMA model but also for the estimation of future values under the presence of missing data. This procedure is illustrated through an analysis of a foreign exchange data set. An investment scheme is developed which demonstrates the usefulness of the proposed approach. © 1997 John Wiley & Sons, Ltd.     

Bayesian modelling of ARFIMA processes by Markov chain Monte Carlo methods

This article describes Bayesian inference for autoregressive fractionally integrated moving average (ARFIMA) models using Markov chain Monte Carlo methods. The posterior distribution of the model parameters, corresponding to the exact likelihood function is obtained through the partial linear regression coefficients of the ARFIMA process. A Metropolis-Rao-Blackwellizallization approach is used for implementing sampling-based Bayesian inference. Bayesian model selection is discussed and implemented.     

Bayesian Analysis of Vector ARMA Models using Gibbs Sampling

We present a methodology for estimation, prediction, and model assessment of vector autoregressive moving-average (VARMA) models in the Bayesian framework using Markov chain Monte Carlo algorithms. The sampling-based Bayesian framework for inference allows for the incorporation of parameter restrictions, such as stationarity restrictions or zero constraints, through appropriate prior specifications. It also facilitates extensive posterior and predictive analyses through the use of numerical summary statistics and graphical displays, such as box plots and density plots for estimated parameters. We present a method for computationally feasible evaluation of the joint posterior density of the model parameters using the exact likelihood function, and discuss the use of backcasting to approximate the exact likelihood function in certain cases. We also show how to incorporate indicator variables as additional parameters for use in coefficient selection. The sampling is facilitated through a Metropolis–Hastings algorithm. Graphical techniques based on predictive distributions are used for informal model assessment. The methods are illustrated using two data sets from business and economics. The first example consists of quarterly fixed investment, disposable income, and consumption rates for West Germany, which are known to have correlation and feedback relationships between series. The second example consists of monthly revenue data from seven different geographic areas of IBM. The revenue data exhibit seasonality, strong inter-regional dependence, and feedback relationships between certain regions.© 1997 John Wiley & Sons, Ltd.     

Modelling a traffic network with missing data

Whitlock and Queen (1998) developed a dynamic graphical model for forecasting traffic flows at a number of sites at a busy traffic junction in Kent, UK. Some of the data collection sites at this junction have been faulty over the data collection period and so there are missing series in the multivariate problem. Here we adapt the model developed in Whitlock and Queen ( 1998 ) to accommodate these missing data. Markov chain Monte Carlo methods are used to provide forecasts of the missing series, which in turn are used to produce forecasts for some of the other series. The methods are used on part of the network and shown to be very promising. Copyright © 2000 John Wiley & Sons, Ltd.     

Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory

This paper presents an autoregressive fractionally integrated moving‐average (ARFIMA) model of nominal exchange rates and compares its forecasting capability with the monetary structural models and the random walk model. Monthly observations are used for Canada, France, Germany, Italy, Japan and the United Kingdom for the period of April 1973 through December 1998. The estimation method is Sowell's (1992) exact maximum likelihood estimation. The forecasting accuracy of the long‐memory model is formally compared to the random walk and the monetary models, using the recently developed Harvey, Leybourne and Newbold (1997) test statistics. The results show that the long‐memory model is more efficient than the random walk model in steps‐ahead forecasts beyond 1 month for most currencies and more efficient than the monetary models in multi‐step‐ahead forecasts. This new finding strongly suggests that the long‐memory model of nominal exchange rates be studied as a viable alternative to the conventional models. Copyright © 2006 John Wiley & Sons, Ltd.     

Predictions in Overdispersed Series of Counts Using an Approximate Predictive Likelihood

The generalized autoregression model or GARM, originally used to model series of non-negative data measured at irregularly spaced time points (Lambert, 1996a), is considered in a count data context. It is first shown how the GARM can be expressed as a GLM in the special case of a linear model for some transform of the location parameter. The Butler approximate predictive likelihood (Butler, 1986, Rejoinder) is then used to define likelihood prediction envelopes. The width of these intervals is shown to be slightly wider than the Fisher (1959, pp. 128–33) and Lejeune and Faulkenberry (1982) predictive likelihood-based envelopes which assume that the parameters have fixed known values (equal to their maximum likelihood estimates). The method is illustrated on a small count data set showing overdispersion.© 1997 John Wiley & Sons, Ltd.     

A non‐Gaussian generalization of the Airline model for robust seasonal adjustment

In their seminal book Time Series Analysis: Forecasting and Control, Box and Jenkins (1976) introduce the Airline model, which is still routinely used for the modelling of economic seasonal time series. The Airline model is for a differenced time series (in levels and seasons) and constitutes a linear moving average of lagged Gaussian disturbances which depends on two coefficients and a fixed variance. In this paper a novel approach to seasonal adjustment is developed that is based on the Airline model and that accounts for outliers and breaks in time series. For this purpose we consider the canonical representation of the Airline model. It takes the model as a sum of trend, seasonal and irregular (unobserved) components which are uniquely identified as a result of the canonical decomposition. The resulting unobserved components time series model is extended by components that allow for outliers and breaks. When all components depend on Gaussian disturbances, the model can be cast in state space form and the Kalman filter can compute the exact log‐likelihood function. Related filtering and smoothing algorithms can be used to compute minimum mean squared error estimates of the unobserved components. However, the outlier and break components typically rely on heavy‐tailed densities such as the t or the mixture of normals. For this class of non‐Gaussian models, Monte Carlo simulation techniques will be used for estimation, signal extraction and seasonal adjustment. This robust approach to seasonal adjustment allows outliers to be accounted for, while keeping the underlying structures that are currently used to aid reporting of economic time series data. Copyright © 2006 John Wiley & Sons, Ltd.     

Forecasting non-seasonal time series with missing observations

Most forecasting methods are based on equally spaced data. In the case of missing observations the methods have to be modified. We have considered three smoothing methods: namely, simple exponential smoothing; double exponential smoothing; and Holt's method. We present a new, unified approach to handle missing data within the smoothing methods. This approach is compared with previously suggested modifications. The comparison is done on 12 real, non-seasonal time series, and shows that the smoothing methods, properly modified, usually perform well if the time series have a moderate number of missing observations.     

安全信息缺失事故致因理论的初步研究

为更好解释事故致因,在分析已有事故致因理论的基础上,分析了安全信息与事故致因因素之间的联系,认为安全信息是各种致因因素的信息化表述,安全信息缺失将直接或间接导致事故的发生并影响事故的发展.继而用安全信息的概念统一人、物、环境、能量和管理等事故致因因素,提出了安全信息缺失的概念和安金信息缺失事故致因理论.新理论认为安全信息缺失是造成事故发生的主要潜在原因,也是导致事故扩大的主要原因,避免关键性安全信息的缺失是预防事故发生和防止事故扩大的重点.建立了新理论的理论模型和可用于定量风险评价的数学模型.该理论为事故有效预防和系统风险评价提供了一种新思路和方法.     

Implications of ancient DNA for phylogenetic studies

The utility of DNA sequence characters from fossil specimens is examined from a phylogenetic perspective. Four ways that fossil characters can alter phylogenetic hypotheses are discussed. Two empirical examples and a third hypothetical example concerning amber-preserved insects are presented to illustrate these phenomena. Fossil DNA sequences as characters will be affected by the problem of missing data and missing taxa. In general, cladogram accuracy will be more greatly affected by missing taxa and cladogram resolution will be affected more acutely by missing data. Due to these points, an examination of the importance of the phylogenetic question being addressed, the utility of the fossil DNA sequences and the rarity of the fossil should be considered before damage of a fossil is undertaken.     

Regression forecasts when disturbances are autocorrelated

A Monte Carlo simulation is used to study the quality of forecasts obtained from regression models with various degrees of autocorrelation present in the disturbances. The methods used to estimate the model parameters include least squares, full maximum likelihood, Prais-Winsten, Cochrane-Orcutt and Bayesian estimation. Results indicate that the Cochrane-Orcutt method should be avoided. The full maximum likelihood, Prais-Winsten and Bayesian methods are relatively more efficient than least squares when the degree of autocorrelation is high (greater than or equal to 0.5) and show little efficiency loss when the degree is low. These results hold for both trended and untrended independent variables.     

Puzzling over orphan enzymes

Despite the current availability of several hundreds of thousands of amino acid sequences, more than 39% of the well-defined enzyme activities (EC numbers) are not associated with any sequence in major public databases. This wide gap separating knowledge of biochemical function and sequence information is found in nearly all classes of enzymes. Thus, there is an urgent need to explore the 1525 orphan enzymes (EC numbers without associated sequences), in order to progressively bridge this unwanted gap. Improving genome annotation could unveil a significant proportion of sequenceless enzymes. Peptide mass mapping and further genome mining would be useful to identify proper sequence for enzymes found in species for which genetic tools are missing. Finally, the whole community must help major public databases to begin addressing the problem of missing or incomplete information. Received 31 October 2005; received after revision 8 December 2005; accepted 20 December 2005     

Have we lost spacetime on the way? Narrowing the gap between general relativity and quantum gravity

Important features of space and time are taken to be missing in quantum gravity, allegedly requiring an explanation of the emergence of spacetime from non-spatio-temporal theories. In this paper, we argue that the explanatory gap between general relativity and non-spatio-temporal quantum gravity theories might significantly be reduced with two moves. First, we point out that spacetime is already partially missing in the context of general relativity when understood from a dynamical perspective. Second, we argue that most approaches to quantum gravity already start with an in-built distinction between structures to which the asymmetry between space and time can be traced back.     

Forecast Combination and Bayesian Model Averaging: A Prior Sensitivity Analysis

In this study we evaluate the forecast performance of model‐averaged forecasts based on the predictive likelihood carrying out a prior sensitivity analysis regarding Zellner's g prior. The main results are fourfold. First, the predictive likelihood does always better than the traditionally employed ‘marginal’ likelihood in settings where the true model is not part of the model space. Secondly, forecast accuracy as measured by the root mean square error (RMSE) is maximized for the median probability model. On the other hand, model averaging excels in predicting direction of changes. Lastly, g should be set according to Laud and Ibrahim (1995: Predictive model selection. Journal of the Royal Statistical Society B 57 : 247–262) with a hold‐out sample size of 25% to minimize the RMSE (median model) and 75% to optimize direction of change forecasts (model averaging). We finally apply the aforementioned recommendations to forecast the monthly industrial production output of six countries, beating for almost all countries the AR(1) benchmark model. Copyright © 2011 John Wiley & Sons, Ltd.     

Einstein Equations and Hilbert Action: What is missing on page 8 of the proofs for Hilbert's First Communication on the Foundations of Physics?

The history of the publication of the gravitational field equations of general relativity in November 1915 by Einstein and Hilbert is briefly reviewed. An analysis of the internal structure and logic of Hilbert's theory as expounded in extant proofs and in the published version of his relevant paper is given with respect to the specific question what information would have been found on a missing piece of Hilbert's proofs. The existing texts suggest that the missing piece contained the explicit form of the Riemann curvature scalar in terms of the Ricci tensor as a specification of the axiomatically underdetermined Lagrangian in Hilbert's action integral. An alternative reading that the missing piece of the proofs already may have contained the Einstein tensor, i.e. an explicit calculation of the gravitational part of Hilbert's Lagrangian is argued to be highly implausible.     

Forecasting with missing data: application to coastal wave heights

This paper presents a comparative analysis of linear and mixed models for short‐term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay. The series is interpolated with a linear predictor which minimizes the forecast mean square error. The linear models are seasonal ARIMA models and the mixed models have a linear component and a non‐linear seasonal component. The non‐linear component is estimated by a non‐parametric regression of data versus time. Short‐term forecasts, no more than two days ahead, are of interest because they can be used by the port authorities to notify the fleet. Several models are fitted and compared by their forecasting behaviour. Copyright © 1999 John Wiley & Sons, Ltd.     

Single‐season heteroscedasticity in time series

We consider seasonal time series in which one season has variance that is different from all the others. This behaviour is evident in indices of production where variability is highest for the month with the lowest level of production. We show that when one season has different variability from others there are constraints on the seasonal models that can be used; neither dummy and trigonometric models are effective in modelling this type of behaviour. We define a general model that provides an appropriate representation of single‐season heteroscedasticity and suggest a likelihood ratio test for the presence of periodic variance in one season. Copyright © 2007 John Wiley & Sons, Ltd.     

我国农户入户调查数据预处理及在农户收入模型中的应用

使用Grubbs检验法对直接入户采集获得的农村住户资料进行异常值检验，并对异常值进行删除，而后使用EM法对数据集由于无回答和异常值删除产生的缺失数据进行插补；并利用处理后的数据进行衣户收入关于其劳动力投入和资本投入的微观计量分析，得到结论：农户可用劳动力数量对农户收入影响最大，而农户家庭经营支出对农户收入的影响大于农户家庭生产性固定资产拥有量对农户收入的影响。     

Using accounting‐based information on young firms to predict bankruptcy

This study analyzes the nonlinear relationships between accounting‐based key performance indicators and the probability that the firm in question will become bankrupt or not. The analysis focuses particularly on young firms and examines whether these nonlinear relationships are affected by a firm's age. The analysis of nonlinear relationships between various predictors of bankruptcy and their interaction effects is based on a structured additive regression model and on a comprehensive data set on German firms. The results of this analysis provide empirical evidence that a firm's age has a considerable effect on how accounting‐based key performance indicators can be used to predict the likelihood that a firm will go bankrupt. More specifically, the results show that there are differences between older firms and young firms with respect to the nonlinear effects of the equity ratio, the return on assets, and the sales growth on their probability of bankruptcy.