Removing Forecasting Errors with White Gaussian Noise after Square Root Transformation

An analytical model has been developed in the present paper based on a square root transformation of white Gaussian noise. The mathematical expectation and variance of the new asymmetric distribution generated by white Gaussian noise after a square root transformation are analytically deduced from the preceding four terms of the Taylor expansion. The model was first evaluated against numerical experiments and a good agreement was obtained. The model was then used to predict time series of wind speeds and highway traffic flows. The simulation results from the new model indicate that the prediction accuracy could be improved by 0.1–1% by removing the mean errors. Further improvement could be obtained for non‐stationary time series, which had large trends. Copyright © 2016 John Wiley & Sons, Ltd.     

Combining experts' opinions using a normal-wishart model

This paper examines how a Bayesian decision maker might update her distributions for continuous variables X_i, i=1, 2, …, upon hearing experts' forecasts expressed as quantiles. To utilize the relationship between the decision maker and experts, and to avoid problems associated with different scales and ranges of the variables, we assume that the decision maker transforms the experts' quantiles in terms of her own prior distribution for each X_i. A model using such a transformation is presented and its properties are examined.     

三维正压非线性潮汐潮流伴随同化模型开边界反演研究

在数学物理反问题的框架下,基于渤海、黄海M2分潮波的数值模拟,本文设计孪生实验研究了三维正压非线性潮汐潮流模型中开边界条件的伴随法反演问题,以验证所建立的伴随模型的有效性和正确性。本文同时讨论了开边界条件的空间分布、初值、观测误差以及观测数量对开边界反演的影响,对此参数估计反问题的适定性进行了初步研究.     

Bayesian Analysis of a Threshold Stochastic Volatility Model

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.     

A Bayesian time-varying autoregressive model for improved short-term and long-term prediction

Motivated by the application to German interest rates, we propose a time-varying autoregressive model for short-term and long-term prediction of time series that exhibit a temporary nonstationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the model and thereby regularize predictions in the far future. We use MCMC-based inference by deriving relevant full conditional distributions and employ a Metropolis-Hastings within Gibbs sampler approach to sample from the posterior (predictive) distribution. In combining data-driven short-term predictions with long-term distribution assumptions our model is competitive to the existing methods in the short horizon while yielding reasonable predictions in the long run. We apply our model to interest rate data and contrast the forecasting performance to that of a 2-Additive-Factor Gaussian model as well as to the predictions of a dynamic Nelson-Siegel model.     

Short‐term prediction of motorway travel time using ANPR and loop data

Travel time is a good operational measure of the effectiveness of transportation systems. The ability to accurately predict motorway and arterial travel times is a critical component for many intelligent transportation systems (ITS) applications. Advanced traffic data collection systems using inductive loop detectors and video cameras have been installed, particularly for motorway networks. An inductive loop can provide traffic flow at its location. Video cameras with image‐processing software, e.g. Automatic Number Plate Recognition (ANPR) software, are able to provide travel time of a road section. This research developed a dynamic linear model (DLM) model to forecast short‐term travel time using both loop and ANPR data. The DLM approach was tested on three motorway sections in southern England. Overall, the model produced good prediction results, albeit large prediction errors occurred at congested traffic conditions due to the dynamic nature of traffic. This result indicated advantages of use of the both data sources. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Predictive Content of Autoregression Residuals: A Semiparametric,Copula‐Based Approach to Time Series Prediction

This paper proposes an adjustment of linear autoregressive conditional mean forecasts that exploits the predictive content of uncorrelated model residuals. The adjustment is motivated by non‐Gaussian characteristics of model residuals, and implemented in a semiparametric fashion by means of conditional moments of simulated bivariate distributions. A pseudo ex ante forecasting comparison is conducted for a set of 494 macroeconomic time series recently collected by Dees et al. (Journal of Applied Econometrics 2007; 22: 1–38). In total, 10,374 time series realizations are contrasted against competing short‐, medium‐ and longer‐term purely autoregressive and adjusted predictors. With regard to all forecast horizons, the adjusted predictions consistently outperform conditionally Gaussian forecasts according to cross‐sectional mean group evaluation of absolute forecast errors and directional accuracy. Copyright © 2012 John Wiley & Sons, Ltd.     

The geometric combination of Bayesian forecasting models

A nonlinear geometric combination of statistical models is proposed as an alternative approach to the usual linear combination or mixture. Contrary to the linear, the geometric model is closed under the regular exponential family of distributions, as we show. As a consequence, the distribution which results from the combination is unimodal and a single location parameter can be chosen for decision making. In the case of Student t‐distributions (of particular interest in forecasting) the geometric combination can be unimodal under a sufficient condition we have established. A comparative analysis between the geometric and linear combinations of predictive distributions from three Bayesian regression dynamic linear models, in a case of beer sales forecasting in Zimbabwe, shows the geometric model to consistently outperform its linear counterpart as well as its component models. Copyright © 2008 John Wiley & Sons, Ltd.     

亚90nm沟道MOSFET亚阈值状态下二维电势和阈值电压的半解析模型

本文提出一个亚90nm沟道MOSFET在亚阈值状态下的二维电势和阈值电压的半解析模型．文章首先根据短沟道MOSFET在亚闽值状态下的物理模型提出定解问题,然后用特征函数将由氧化层和空间电荷区衔接条件所得到的超越方程组作正交展开,得到关于未知量的线性代数方程组．求出了氧化层和空间电荷区的二维电势、耗尽层厚度和阈值电压的表达式．该模型不需要适配参数,运算量小,避免了方程离散化,计算精度与数值解精度相同．文章给出了沟道长度为90nm以下MOSFET的电势分布、表面势、耗尽层厚度和阈值电压计算结果．计算值与二维数值模拟值高度吻合．     

Bayes Inference for Technological Substitution Data with Data-based Transformation

Bayesian inference via Gibbs sampling is studied for forecasting technological substitutions. The Box–Cox transformation is applied to the time series AR(1) data to enhance the linear model fit. We compute Bayes point and interval estimates for each of the parameters from the Gibbs sampler. The unknown parameters are the regression coefficients, the power in the Box–Cox transformation, the serial correlation coefficient, and the variance of the disturbance terms. In addition, we forecast the future technological substitution rate and its interval. Model validation and model choice issues are also addressed. Two numerical examples with real data sets are given.©1997 John Wiley & Sons, Ltd.     

Modeling and forecasting time series with a general non-normal distribution

We propose a model for time series with a general marginal distribution given by the Johnson family of distributions. We investigate for which Johnson distributions forecasting using the model is likely to be most effective compared to using a linear model. Monte Carlo simulation is used to assess the reliability of methods for determining which of the three Johnson forms is most appropriate for a given series. Finally, we give model fitting and forecasting results using the modeling procedure on a selection of simulated and real time series.     

Prediction intervals for exponential smoothing using two new classes of state space models

Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non‐linear structure in the observation equation as well as heteroscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods. We use these classes to provide exact analytic (matrix) expressions for forecast error variances that can be used to construct prediction intervals one or multiple steps ahead. These formulas are reduced to non‐matrix expressions for 15 state space models that underlie the most common exponential smoothing methods. We discuss relationships between our expressions and previous suggestions for finding forecast error variances and prediction intervals for exponential smoothing methods. Simpler approximations are developed for the more complex schemes and their validity examined. The paper concludes with a numerical example using a non‐linear model. Copyright © 2005 John Wiley & Sons, Ltd.     

Convergence and the Constant Dynamic Linear Model

It is well known that, as calculated using the Kalman filter recurrence relationships, the posterior parameter variance and the adaptive vector of observable constant dynamic linear models converge to limiting values. However, most proofs are tortuous, some have subtle errors and some relate only to specific cases. An elegant probabilistic convergence proof demonstrates that the limit is independent of the initial parametric prior. The result is extended to a class of multivariate dynamic linear models. Finally the proof is shown to apply to many non-observable constant DLMs. © 1997 John Wiley & Sons, Ltd.     

Hierarchical bayes forecasts of multinomial dirichlet data applied to coupon redemptions

This paper considers forecasting count data from a multinomial Dirichlet distribution. The forecasting procedure implements hierarchical Bayes methods in order to develop a prior distribution for a new series of data. The methodology is applied to the redemption of cents-off promotional coupons. In a forecasting experiment, early forecasts of new series are similar to those from pooling all redemptions from previous coupon promotions. However, the hierarchical Bayes model provides realistic estimates of forecasting errors, while those for the pooled forecasts are consistently optimistic. As the current series evolves, the hierarchical Bayes forecasts adapt more rapidly and are more accurate than pooled forecasts.     

Revisions in analysts' earnings forecasts: evidence of non‐linear adaptive expectations

Prior studies use a linear adaptive expectations model to describe how analysts revise their forecasts of future earnings in response to current forecast errors. However, research shows that extreme forecast errors are less likely than small forecast errors to persist in future years. If analysts recognize this property, their marginal forecast revisions should decrease with the forecast error's magnitude. Therefore, a linear model is likely to be unsatisfactory at describing analysts' forecast revisions. We find that a non‐linear model better describes the relation between analysts' forecast revisions and their forecast errors, and provides a richer theoretical framework for explaining analysts' forecasting behaviour. Our results are consistent with analysts' recognizing the permanent and temporary nature of forecast errors of differing magnitudes. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Sparse Bayesian vector autoregressions in huge dimensions

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global–local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to sample efficiently from high-dimensional multivariate Gaussian distributions. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities.     

On a dynamic mixture GARCH model

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non‐stationary volatility component. The VaR based on the new model performs better than traditional GARCH‐based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Financial Risk Management,Pre and Post the Global Financial Crisis

Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

Bayesian Analysis of Asymmetric Stochastic Conditional Duration Model

This paper proposes Markov chain Monte Carlo methods to estimate the parameters and log durations of the correlated or asymmetric stochastic conditional duration models. Following the literature, instead of fitting the models directly, the observation equation of the models is first subjected to a logarithmic transformation. A correlation is then introduced between the transformed innovation and the latent process in an attempt to improve the statistical fits of the models. In order to perform one‐step‐ahead in‐sample and out‐of‐sample duration forecasts, an auxiliary particle filter is used to approximate the filter distributions of the latent states. Simulation studies and application to the IBM transaction dataset illustrate that our proposed estimation methods work well in terms of parameter and log duration estimation. Copyright © 2014 John Wiley & Sons, Ltd.