A simulation study and evaluation of multivariate forecast based control charts applied to ARMA processes

Much research had been performed in the area of control charting techniques for monitoring autocorrelated processes, especially regarding forecast based monitoring schemes. Forecast based monitoring schemes involve fitting an appropriate time-series model to the process, generating one step ahead forecast errors, and monitoring the forecast errors with traditional control charts. Another method introduced into the literature involves using multivariate control charts to monitor the ARMA derived one-step-ahead (OSA) and two-step-ahead (TSA) forecast errors. This article provides a broad simulation study and evaluation of the suggested multivariate approaches in regards to various ARMA(1,1) and AR(1) processes, and a comparison to their univariate counterparts.     

基于联系数贴近度的区间型组合预测模型及其有效性

利用区间数和二元联系数的相互转化关系,把区间数组合预测问题转换成二元联系数组合预测问题。在联系数贴近度的最优准则下,建立基于联系数贴近度的区间型组合预测模型,分析了该模型的有效性理论,包括:基于联系数贴近度的区间型组合预测模型是非劣性组合预测、优性组合预测的充分条件定理,基于联系数贴近度的区间型组合预测模型的冗余预测方法的存在性和冗余方法的判定定理。对某省社会保障水平适度区间值进行组合预测的实证分析,结果显示所建立的模型能有效提高预测的精度。     

Forecasting time series of economic processes by model averaging across data frames of various lengths

This paper presents an extension of mean-squared forecast error (MSFE) model averaging for integrating linear regression models computed on data frames of various lengths. Proposed method is considered to be a preferable alternative to best model selection by various efficiency criteria such as Bayesian information criterion (BIC), Akaike information criterion (AIC), F-statistics and mean-squared error (MSE) as well as to Bayesian model averaging (BMA) and naïve simple forecast average. The method is developed to deal with possibly non-nested models having different number of observations and selects forecast weights by minimizing the unbiased estimator of MSFE. Proposed method also yields forecast confidence intervals with a given significance level what is not possible when applying other model averaging methods. In addition, out-of-sample simulation and empirical testing proves efficiency of such kind of averaging when forecasting economic processes.     

基于平衡轮换样本调查的季节调整方法研究

传统季节调整方法对时间序列数据进行季节调整时,往往假定误差项为白噪声,不考虑其序列相关关系。为了进行更准确地季节调整分析,本文从连续性抽样调查的角度出发,研究基于平衡轮换样本调查的抽样误差对季节调整的影响,建立一般化的季节调整模型,利用卡尔曼滤波进行参数估计,并从预测误差、误差方差等角度评价模型精度。最后以中国城镇住户调查采用的12～0平衡轮换模式为例,对考虑抽样误差结构特征的季节调整模型进行实证分析,验证这套季节调整方法的有效性。     

Evaluation of realized volatility predictions from models with leptokurtically and asymmetrically distributed forecast errors

Accurate volatility forecasting is a key determinant for portfolio management, risk management and economic policy. The paper provides evidence that the sum of squared standardized forecast errors is a reliable measure for model evaluation when the predicted variable is the intra-day realized volatility. The forecasting evaluation is valid for standardized forecast errors with leptokurtic distribution as well as with leptokurtic and asymmetric distributions. Additionally, the widely applied forecasting evaluation function, the predicted mean-squared error, fails to select the adequate model in the case of models with residuals that are leptokurtically and asymmetrically distributed. Hence, the realized volatility forecasting evaluation should be based on the standardized forecast errors instead of their unstandardized version.     

Empirical Likelihood Intervals for Conditional Value‐at‐Risk in Heteroscedastic Regression Models

Abstract. Non‐parametric regression models have been studied well including estimating the conditional mean function, the conditional variance function and the distribution function of errors. In addition, empirical likelihood methods have been proposed to construct confidence intervals for the conditional mean and variance. Motivated by applications in risk management, we propose an empirical likelihood method for constructing a confidence interval for the pth conditional value‐at‐risk based on the non‐parametric regression model. A simulation study shows the advantages of the proposed method.     

Forecasting Study of Shanghai’s and Shenzhen’s Stock Markets Using a Hybrid Forecast Method

In this article, a novel hybrid method to forecast stock price is proposed. This hybrid method is based on wavelet transform, wavelet denoising, linear models (autoregressive integrated moving average (ARIMA) model and exponential smoothing (ES) model), and nonlinear models (BP Neural Network and RBF Neural Network). The wavelet transform provides a set of better-behaved constitutive series than stock series for prediction. Wavelet denoising is used to eliminate some slight random fluctuations of stock series. ARIMA model and ES model are used to forecast the linear component of denoised stock series, and then BP Neural Network and RBF Neural Network are developed as tools for nonlinear pattern recognition to correct the estimation error of the prediction of linear models. The proposed method is examined in the stock market of Shanghai and Shenzhen and the results are compared with some of the most recent stock price forecast methods. The results show that the proposed hybrid method can provide a considerable improvement for the forecasting accuracy. Meanwhile, this proposed method can also be applied to analysis and forecast reliability of products or systems and improve the accuracy of reliability engineering.     

Measuring Nonlinear Granger Causality in Mean

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive the asymptotic normality of nonparametric estimator of causality measures, which we use to build tests for their statistical significance. We establish the validity of smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. Monte Carlo simulations reveal that the proposed test has good finite sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, the empirical importance of measuring nonlinear causality in mean is also illustrated. We quantify the degree of nonlinear predictability of equity risk premium using variance risk premium. Our empirical results show that the variance risk premium is a very good predictor of risk premium at horizons less than 6 months. We also find that there is a high degree of predictability at the 1-month horizon, that can be attributed to a nonlinear causal effect. Supplementary materials for this article are available online.     

Bias-corrected estimations in varying-coefficient partially nonlinear models with measurement error in the nonparametric part

In this paper, we consider the statistical inference for the varying-coefficient partially nonlinear model with additive measurement errors in the nonparametric part. The local bias-corrected profile nonlinear least-squares estimation procedure for parameter in nonlinear function and nonparametric function is proposed. Then, the asymptotic normality properties of the resulting estimators are established. With the empirical likelihood method, a local bias-corrected empirical log-likelihood ratio statistic for the unknown parameter, and a corrected and residual adjusted empirical log-likelihood ratio for the nonparametric component are constructed. It is shown that the resulting statistics are asymptotically chi-square distribution under some suitable conditions. Some simulations are conducted to evaluate the performance of the proposed methods. The results indicate that the empirical likelihood method is superior to the profile nonlinear least-squares method in terms of the confidence regions of parameter and point-wise confidence intervals of nonparametric function.     

Empirical Likelihood for a Heteroscedastic Partial Linear Errors-in-Variables Model

The purpose of this article is to use the empirical likelihood method to study construction of the confidence region for the parameter of interest in heteroscedastic partially linear errors-in-variables model with martingale difference errors. When the variance functions of the errors are known or unknown, we propose the empirical log-likelihood ratio statistics for the parameter of interest. For each case, a nonparametric version of Wilks’ theorem is derived. The results are then used to construct confidence regions of the parameter. A simulation study is carried out to assess the performance of the empirical likelihood method.     

Estimation and Inference in Two-Step Econometric Models

A commonly used procedure in a wide class of empirical applications is to impute unobserved regressors, such as expectations, from an auxiliary econometric model. This two-step (T-S) procedure fails to account for the fact that imputed regressors are measured with sampling error, so hypothesis tests based on the estimated covariance matrix of the second-step estimator are biased, even in large samples. We present a simple yet general method of calculating asymptotically correct standard errors in T-S models. The procedure may be applied even when joint estimation methods, such as full information maximum likelihood, are inappropriate or computationally infeasible. We present two examples from recent empirical literature in which these corrections have a major impact on hypothesis testing.     

Estimating the parameters of Poisson-exponential models

This paper proposes two methods of estimation for the parameters in a Poisson-exponential model. The proposed methods combine the method of moments with a regression method based on the empirical moment generating function. One of the methods is an adaptation of the mixed-moments procedure of Koutrouvelis & Canavos (1999). The asymptotic distribution of the estimator obtained with this method is derived. Finite-sample comparisons are made with the maximum likelihood estimator and the method of moments. The paper concludes with an exploratory-type analysis of real data based on the empirical moment generating function.     

Empirical Likelihood for Linear Models Under Linear Process Errors

In this article, we study the construction of confidence intervals for regression parameters in a linear model under linear process errors by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ²-type distributed. The result is used to obtain EL based confidence regions for regression parameters. The finite-sample performance of the method is evaluated through a simulation study.     

Bayesian inference and forecasting in the stationary bilinear model

A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk, first-order autoregressive AR(1), and autoregressive moving average ARMA(1,1) models in terms of root mean squared forecast errors. In addition, the SB model is superior to these three models in terms of predictive likelihood for the majority of forecast observations.     

Comparison of Bayesian Model Selection Criteria and Conditional Kolmogorov Test as Applied to Spot Asset Pricing Models

We compare Bayesian and sample theory model specification criteria. For the Bayesian criteria we use the deviance information criterion and the cumulative density of the mean squared errors of forecast. For the sample theory criterion we use the conditional Kolmogorov test. We use Markov chain Monte Carlo methods to obtain the Bayesian criteria and bootstrap sampling to obtain the conditional Kolmogorov test. Two non nested models we consider are the CIR and Vasicek models for spot asset prices. Monte Carlo experiments show that the DIC performs better than the cumulative density of the mean squared errors of forecast and the CKT. According to the DIC and the mean squared errors of forecast, the CIR model explains the daily data on uncollateralized Japanese call rate from January 1, 1990 to April 18, 1996; but according to the CKT, neither the CIR nor Vasicek models explains the daily data.     

Road trafficking description and short term travel time forecasting,with a classification method

The purpose of this work is, on the one hand, to study how to forecast road trafficking on highway networks and, on the other hand, to describe future traffic events. Here, road trafficking is measured by vehicle velocities. The authors propose two methodologies. The first is based on an empirical classification method, and the second on a probability mixture model. They use an SAEM‐type algorithm (a stochastic approximation of the EM algorithm) to select the densities of the mixture model. Then, they test the validity of their methodologies by forecasting short term travel times.     

Bootstrapping Periodic State-Space Models

This article is concerned with how the bootstrap can be applied to study conditional forecast error distributions and construct prediction regions for future observations in periodic time-varying state-space models. We derive, first, an algorithm for assessing the precision of quasi-maximum likelihood estimates of the parameters. As a result, the derived algorithm is exploited for numerically evaluating the conditional forecast accuracy of a periodic time series model expressed in state space form. We propose a method which requires the backward, or reverse-time, representation of the model for assessing conditional forecast errors. Finally, the small sample properties of the proposed procedures will be investigated by some simulation studies. Furthermore, we illustrate the results by applying the proposed method to a real time series.     

Empirical likelihood inference for semiparametric model with linear process errors

The purpose of this article is to use the empirical likelihood method to study the confidence regions construction for the parameters of interest in semiparametric model with linear process errors under martingale difference. It is shown that the adjusted empirical log-likelihood ratio at the true parameters is asymptotically chi-squared. A simulation study indicates that the adjusted empirical likelihood works better than a normal approximation-based approach.     

Label switching and its solutions for frequentist mixture models

In this article, the label switching problem and the importance of solving it are discussed for frequentist mixture models if a simulation study is used to evaluate the performance of mixture model estimators. Two effective labelling methods are proposed by using true label for each observation. The empirical studies demonstrate that the new proposed methods work well and provide better results than the rule of thumb method of order constraint labelling. In addition, a Monte Carlo study also demonstrates that simple order constraint labelling can sometimes produce severely biased, and possibly meaningless, estimated bias and standard errors.