A semiparametric method for predicting bankruptcy

Bankruptcy prediction methods based on a semiparametric logit model are proposed for simple random (prospective) and case–control (choice‐based; retrospective) data. The unknown parameters and prediction probabilities in the model are estimated by the local likelihood approach, and the resulting estimators are analyzed through their asymptotic biases and variances. The semiparametric bankruptcy prediction methods using these two types of data are shown to be essentially equivalent. Thus our proposed prediction model can be directly applied to data sampled from the two important designs. One real data example and simulations confirm that our prediction method is more powerful than alternatives, in the sense of yielding smaller out‐of‐sample error rates. Copyright © 2007 John Wiley & Sons, Ltd.     

Fitting of growth curves over time when the data are obtained from a single realization

This paper focuses on the general problem of forecasting the maximum value of a time series which by the nature of the data must approach an asymptotic value. Examples of such series include the growth of organisms, the concentration of a chemical reagent during a reaction occurring over time or the amount of a fossil fuel resource which has been discovered or produced as a function of time. The approach taken below differs from the usual models for this type of data in that it assumes that an unobserved time series is actually driving the process, and that the observed data series is a function of the unobserved process. In the case of fossil fuels the unobserved series might be a measure of the exploratory drilling, the number of production days in a given time period or even the amount of fiscal resources devoted to exploratory activities. A maximum likelihood method is developed for estimating the parameters of the process, especially the maximum S, and the covariance structure of the estimators is developed. The methodology is illustrated on an example of oil production. Finally, methods are developed for forecasting the data into the near future.     

Forecasting multivariate time series with linear restrictions using constrained structural state‐space models

This paper presents a methodology for modelling and forecasting multivariate time series with linear restrictions using the constrained structural state‐space framework. The model has natural applications to forecasting time series of macroeconomic/financial identities and accounts. The explicit modelling of the constraints ensures that model parameters dynamically satisfy the restrictions among items of the series, leading to more accurate and internally consistent forecasts. It is shown that the constrained model offers superior forecasting efficiency. A testable identification condition for state space models is also obtained and applied to establish the identifiability of the constrained model. The proposed methods are illustrated on Germany's quarterly monetary accounts data. Results show significant improvement in the predictive efficiency of forecast estimators for the monetary account with an overall efficiency gain of 25% over unconstrained modelling. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Forecasting and trading strategies based on a price trend model

In this paper, we consider the price trend model in which it is assumed that the time series of a security's prices contain a stochastic trend component which remains constant on each of a sequence of time intervals, with each interval having random duration. A quasi‐maximum likelihood method is used to estimate the model parameters. Optimal one‐step‐ahead forecasts of returns are derived. The trading rule based on these forecasts is constructed and is found to bear similarity to a popular trading rule based on moving averages. When applying the methods to forecast the returns of the Hang Seng Index Futures in Hong Kong, we find that the performance of the newly developed trading rule is satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

Statistical surveillance of cyclical processes with application to turns in business cycles

On‐line monitoring of cyclical processes is studied. An important application is early prediction of the next turn in business cycles by an alarm for a turn in a leading index. Three likelihood‐based methods for detection of a turn are compared in detail. One of the methods is based on a hidden Markov model. The two others are based on the theory of statistical surveillance. One of these is free from parametric assumptions of the curve. Evaluations are made of the effect of different specifications of the curve and the transitions. The methods are made comparable by alarm limits, which give the same median time to the first false alarm, but also other approaches for comparability are discussed. Results are given on the expected delay time to a correct alarm, the probability of detection of a turning point within a specified time, and the predictive value of an alarm. Copyright © 2005 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.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

A bootstrap simulation study in ARMA (p,q) structures

In 1979 Efron proposed a new general statistical procedure known as ‘Bootstrap’, a computer-intensive method used when finite-sample theory is impossible or difficult to derive, or when only asymptotic theory is available. It is recommended in the estimation of measures of both location and scale for any statistical model without making any distributional assumptions about the data. This technique has been successfully used in various applied statistical problems, although not many applications have been reported in the area of time series. In this paper we present a new application of Bootstrap to time series. We consider a simulation study where artificial time series corresponding to AR(1), AR(2), MA(1), MA(2) and ARMA(1, 1) structures were generated, covering important regions of the parameter space of each one of them. The conventional Box-Jenkins parametric estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimators, obtained by 500 Bootstrap repetitions for each series.     

Methods for backcasting,nowcasting and forecasting using factor‐MIDAS: With an application to Korean GDP

We utilize mixed‐frequency factor‐MIDAS models for the purpose of carrying out backcasting, nowcasting, and forecasting experiments using real‐time data. We also introduce a new real‐time Korean GDP dataset, which is the focus of our experiments. The methodology that we utilize involves first estimating common latent factors (i.e., diffusion indices) from 190 monthly macroeconomic and financial series using various estimation strategies. These factors are then included, along with standard variables measured at multiple different frequencies, in various factor‐MIDAS prediction models. Our key empirical findings as follows. (i) When using real‐time data, factor‐MIDAS prediction models outperform various linear benchmark models. Interestingly, the “MSFE‐best” MIDAS models contain no autoregressive (AR) lag terms when backcasting and nowcasting. AR terms only begin to play a role in “true” forecasting contexts. (ii) Models that utilize only one or two factors are “MSFE‐best” at all forecasting horizons, but not at any backcasting and nowcasting horizons. In these latter contexts, much more heavily parametrized models with many factors are preferred. (iii) Real‐time data are crucial for forecasting Korean gross domestic product, and the use of “first available” versus “most recent” data “strongly” affects model selection and performance. (iv) Recursively estimated models are almost always “MSFE‐best,” and models estimated using autoregressive interpolation dominate those estimated using other interpolation methods. (v) Factors estimated using recursive principal component estimation methods have more predictive content than those estimated using a variety of other (more sophisticated) approaches. This result is particularly prevalent for our “MSFE‐best” factor‐MIDAS models, across virtually all forecast horizons, estimation schemes, and data vintages that are analyzed.     

Neural model identification,variable selection and model adequacy

In recent years an impressive array of publications has appeared claiming considerable successes of neural networks in modelling financial data but sceptical practitioners and statisticians are still raising the question of whether neural networks really are ‘a major breakthrough or just a passing fad’. A major reason for this is the lack of procedures for performing tests for misspecified models, and tests of statistical significance for the various parameters that have been estimated, which makes it difficult to assess the model's significance and the possibility that any short‐term successes that are reported might be due to ‘data mining’. In this paper we describe a methodology for neural model identification which facilitates hypothesis testing at two levels: model adequacy and variable significance. The methodology includes a model selection procedure to produce consistent estimators, a variable selection procedure based on statistical significance and a model adequacy procedure based on residuals analysis. We propose a novel, computationally efficient scheme for estimating sampling variability of arbitrarily complex statistics for neural models and apply it to variable selection. The approach is based on sampling from the asymptotic distribution of the neural model's parameters (‘parametric sampling’). Controlled simulations are used for the analysis and evaluation of our model identification methodology. A case study in tactical asset allocation is used to demonstrate how the methodology can be applied to real‐life problems in a way analogous to stepwise forward regression analysis. Neural models are contrasted to multiple linear regression. The results indicate the presence of non‐linear relationships in modelling the equity premium. Copyright © 1999 John Wiley & Sons, Ltd.     

Generalised Estimators for Seasonal Forecasting by Combining Grouping with Shrinkage Approaches

In this paper, generalised estimators are proposed to estimate seasonal indices for certain forms of additive and mixed seasonality. The estimators combine one of two group seasonal indices methods—Dalhart's group method and Withycombe's group method—with a shrinkage method in different ways. Optimal shrinkage parameters are derived to maximise the performance of the estimators. Then, the generalised estimators, with the optimal shrinkage parameters, are evaluated based on forecasting accuracy. Moreover, the effects of three factors are examined, namely, the length of data history, variance of random components and the number of series. Finally, a simulation experiment is conducted to support the evaluation. Copyright © 2011 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.     

Transformations and dynamic linear models

The dynamic linear model (DLM) with additive Gaussian errors provides a useful statistical tool that is easily implemented because of the simplicity of updating a normal model that has a natural conjugate prior. If the model is not linear or if it does not have additive Gaussian errors, then numerical methods are usually required to update the distributions of the unknown parameters. If the dimension of the parameter space is small, numerical methods are feasible. However, as the number of unknown parameters increases, the numerial methods rapidly grow in complexity and cost. This article addresses the situation where a state dependent transformation of the observations follows the DLM, but a priori the appropriate transformation is not known. The Box-Cox family, which is indexed by a single parameter, illustrates the methodology. A prior distribution is constructed over a grid of points for the transformation parameter. For each value of the grid the relevant parameter esitmates and forecasts are obtained for the transformed series. These quantities are then integrated by the current distribution of the transformation parameter. When a new observation becomes available, parallel Kalman filters are used to update the distributions of the unknown parameters and to compute the likelihood of the transformation parameter at each grid point. The distribution of the transformation parameter is then updated.     

New proposals for the quantification of qualitative survey data

In this paper we propose and evaluate two new methods for the quantification of business surveys concerning the qualitative assessment of the state of the economy. The first is a nonparametric method based on the spectral envelope, originally proposed by Stoffer, Tyler and McDougall (Spectral analysis for categorical time series: scaling and the spectral envelope, Biometrika 80 : 611–622) to the multivariate time series of the counts in each response category. Secondly, we fit by maximum likelihood a cumulative logit unobserved components models featuring a common cycle. The conditional mean of the cycle, which can be evaluated by importance sampling, offers the required quantification. We assess the validity of the two methods by comparing the results with a standard quantification based on the balance of opinions and with a quantitative economic indicator. Copyright ? 2010 John Wiley & Sons, Ltd.     

Weighted Empirical Likelihood Estimator for Vector Multiplicative Error Model

The vector multiplicative error model (vector MEM) is capable of analyzing and forecasting multidimensional non‐negative valued processes. Usually its parameters are estimated by generalized method of moments (GMM) and maximum likelihood (ML) methods. However, the estimations could be heavily affected by outliers. To overcome this problem, in this paper an alternative approach, the weighted empirical likelihood (WEL) method, is proposed. This method uses moment conditions as constraints and the outliers are detected automatically by performing a k‐means clustering on Oja depth values of innovations. The performance of WEL is evaluated against those of GMM and ML methods through extensive simulations, in which three different kinds of additive outliers are considered. Moreover, the robustness of WEL is demonstrated by comparing the volatility forecasts of the three methods on 10‐minute returns of the S&P 500 index. The results from both the simulations and the S&P 500 volatility forecasts have shown preferences in using the WEL method. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction in a duration model

Predictors of mean duration and an arbitrary quantile are given for the Weibull regression model for duration data. Associated prediction variances arising from maximum likelihood and least squares estimation are given. In an empirical example, based on duration of employment data, the uses of various model diagnostics and the predictors are illustrated.     

Specification versus data fitting: SEM prediction and the Q‐class estimator

We propose a new class of limited information estimators built upon an explicit trade‐off between data fitting and a priori model specification. The estimators offer the researcher a continuum of estimators that range from an extreme emphasis on data fitting and robust reduced‐form estimation to the other extreme of exact model specification and efficient estimation. The approach used to generate the estimators illustrates why ULS often outperforms 2SLS‐PRRF even in the context of a correctly specified model, provides a new interpretation of 2SLS, and integrates Wonnacott and Wonnacott's (1970) least weighted variance estimators with other techniques. We apply the new class of estimators to Klein's Model I and generate forecasts. We find for this example that an emphasis on specification (as opposed to data fitting) produces better out‐of‐sample predictions. Copyright © 1999 John Wiley & Sons, Ltd.     

基于模型突变检测的管道泄漏检测定位方法

为了改进负压波法在管道微弱泄漏的检测和定位中的效果,提出了基于模型突变检测的特征提取和泄漏定位算法。首先运用广义似然比检测理论,建立压力信号变化的统计检验模型,计算广义似然比比率r和下降幅度d作为压力信号突变发生的敏感特征,并通过求得的压力变化时间点进行泄漏定位。针对缓慢泄漏时压力信号变化的特点,提出了相应的改进模型,更精确的求出缓慢泄漏压力信号的下降拐点。实验证明,参数r和d对不同变化类型的压力信号有较好的区分度,利用管道内压力和流量信号的特征值作为神经网络的特征向量可以实现管道的微弱泄漏识别,且基于改进模型的定位算法在缓慢泄漏定位中有较好的定位结果和稳定度。     

A Study of Value‐at‐Risk Based on M‐Estimators of the Conditional Heteroscedastic Models

In this paper, we investigate the performance of a class of M‐estimators for both symmetric and asymmetric conditional heteroscedastic models in the prediction of value‐at‐risk. The class of estimators includes the least absolute deviation (LAD), Huber's, Cauchy and B‐estimator, as well as the well‐known quasi maximum likelihood estimator (QMLE). We use a wide range of summary statistics to compare both the in‐sample and out‐of‐sample VaR estimates of three well‐known stock indices. Our empirical study suggests that in general Cauchy, Huber and B‐estimator have better performance in predicting one‐step‐ahead VaR than the commonly used QMLE. Copyright © 2011 John Wiley & Sons, Ltd.