Robust testing procedures of process locations

In many manufacturing and service industries, the quality department of the organization works continuously to ensure that the mean or location of the process is close to the target value. In order to understand the process, it is necessary to provide numerical statements of the processes that are being investigated. That is why the researcher needs to check the validity of the hypotheses that are concerned with some physical phenomena. It is usually assumed that the collected data behave well. However, sometimes the data may contain outliers. The presence of one or more outliers might seriously distort the statistical inference. Since the sample mean is very sensitive to outliers, this research will use the smooth adaptive (SA) estimator to estimate the population mean. The SA estimator will be used to construct testing procedures, called smooth adaptive test (SA test), for testing various null hypotheses. A Monte Carlo study is used to simulate the values of the probability of a Type I error and the power of the SA test. This is accomplished by constructing confidence intervals of the process mean by using the SA estimator and bootstrap methods. The SA test will be compared with other tests such as the normal test, t test and a nonparametric statistical method, namely, the Wilcoxon signed-rank test. Also, the cases with and without outliers will be considered. For the right-skewed distributions, the SA test is the best choice. When the population is a right-skewed distribution with one outlier, the SA test controls the probability of a Type I error better than other tests and is recommended.     

Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)

We analyse the dynamic dependence structure between broad stock market indexes from the United States (S&P500), Britain (FTSE100), Brazil (BOVESPA) and Mexico (PCMX). We employ Patton’s [Int. Econ. Rev., 2006, 2, 527–556] conditional copula setting and additionally observe the impact of different copula functions on Value at Risk (VaR) estimation. We conclude that the dependence between BOVESPA and the other indexes has intensified since the beginning of 2007. In our case the particular copula form is not crucial for VaR estimation. A goodness-of-fit test based on the parametric bootstrap is also applied. The best fits are obtained via time constant Student-t and time-varying Normal copulas.     

Diagonal effects in claims reserving

In this paper we present two different approaches to how one can include diagonal effects in non-life claims reserving based on run-off triangles. Empirical analyses suggest that the approaches in Zehnwirth (2003) and Kuang et al. (2008a, 2008b) do not work well with low-dimensional run-off triangles because estimation uncertainty is too large. To overcome this problem we consider similar models with a smaller number of parameters. These are closely related to the framework considered in Verbeek (1972) and Taylor (1977, 2000); the separation method. We explain that these models can be interpreted as extensions of the multiplicative Poisson models introduced by Hachemeister & Stanard (1975) and Mack (1991).     

Nonlinear dynamical structural equation models

Structural equation models (SEMs) have been widely used in behavioural, educational, medical and socio-psychological research for exploring and confirming relations among observed and latent variables. In the existing SEMs, the unknown coefficients in the measurement and structural equations are assumed to be constant with respect to time. This assumption does not always hold, as the relation among the observed and latent variables varies with time for some situations. In this paper, we propose nonlinear dynamical structural equation models to cope with these situations, and explore the nonlinear dynamic of the relation between the variables involved. A local maximum likelihood-based estimation procedure is proposed. We investigate a bootstrap resampling-based test for the hypothesis that the coefficient is constant with respect to time, as well as confidence bands for the unknown coefficients. Intensive simulation studies are conducted to show the empirical performance of the proposed estimation procedure, hypothesis test statistic and confidence band. Finally, a real example in relation to the stock market of Hong Kong is presented to demonstrate the proposed methodologies.     

The performance of enhanced-return index funds: evidence from bootstrap analysis

We apply the bootstrap technique proposed by Kosowski et al. [J. Finance, 2006, 61, 2551–2595] in conjunction with Carhart's [J. Finance, 1997, 52, 57–82] unconditional and Ferson and Schadt's [J. Finance, 1996, 51, 425–461] conditional four-factor models of performance to examine whether the performances of enhanced-return index funds over the 1996 to 2007 period are based on luck or superior ‘enhancing’ skills. The advantages of using the bootstrap to rank fund performance are many. It eliminates the need to specify the exact shape of the distribution from which returns are drawn and does not require estimating correlations between portfolio returns. It also eliminates the need to explicitly control for potential ‘data snooping’ biases that arise from an ex-post sort. Our results show evidence of enhanced-return index funds with positive and significant alphas after controlling for luck and sampling variability. The results are robust to both stock-only and derivative-enhanced index funds, although the spread of cross-sectional alphas for derivative-enhanced funds is slightly more pronounced. The study also examines various sub-periods within the sample horizon.     

Inferring fundamental value and crash nonlinearity from bubble calibration

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it is not possible to distinguish between an exponentially growing fundamental price and an exponentially growing bubble price. In this paper, we present a series of new models based on the Johansen–Ledoit–Sornette (JLS) model, which is a flexible tool to detect bubbles and predict changes of regime in financial markets. Our new models identify the fundamental value of an asset price and a crash nonlinearity from a bubble calibration. In addition to forecasting the time of the end of a bubble, the new models can also estimate the fundamental value and the crash nonlinearity, meaning that identifying the presence of a bubble is enabled by these models. In addition, the crash nonlinearity obtained in the new models presents a new approach to possibly identify the dynamics of a crash after a bubble. We test the models using data from three historical bubbles ending in crashes from different markets. They are the Hong Kong Hang Seng index 1997 crash, the S&P 500 index 1987 crash (Black Monday) and the Shanghai Composite index 2009 crash. All results suggest that the new models perform very well in describing bubbles, forecasting their ending times and estimating fundamental value and the crash nonlinearity. The performance of the new models is tested under both the Gaussian residual assumption and non-Gaussian residual assumption. Under the Gaussian residual assumption, nested hypotheses with the Wilks' statistics are used and the p-values suggest that models with more parameters are necessary. Under the non-Gaussian residual assumption, we use a bootstrap method to obtain type I and II errors of the hypotheses. All tests confirm that the generalized JLS models provide useful improvements over the standard JLS model.     

兼具截面相依性和重尾性面板单位根检验方法研究及应用

Block Bootstrap方法因其适用范围广和操作简单等众多优点成为面板单位根检验的理想工具之一。然而,由于要求误差项服从独立同分布的假设条件,该方法仍具有一定的局限性。为此,本文发展Wild Bootstrap方法来解决误差项可能具有截面相依性和重尾性等更一般情形下的面板单位根检验问题。 Monte Carlo模拟结果表明,当重尾性存在时,Wild Bootstrap检验相对Block Bootstrap检验有更小的水平扭曲和更高的功效。最后对中国股票市场的有效性问题进行了实证检验,并得出其为弱式有效性的结论。     

A Comparison of two Robust Estimation Methods for Business Surveys

Two alternative robust estimation methods often employed by National Statistical Institutes in business surveys are two‐sided M‐estimation and one‐sided Winsorisation, which can be regarded as an approximate implementation of one‐sided M‐estimation. We review these methods and evaluate their performance in a simulation of a repeated rotating business survey based on data from the Retail Sales Inquiry conducted by the UK Office for National Statistics. One‐sided and two‐sided M‐estimation are found to have very similar performance, with a slight edge for the former for positive variables. Both methods considerably improve both level and movement estimators. Approaches for setting tuning parameters are evaluated for both methods, and this is a more important issue than the difference between the two approaches. M‐estimation works best when tuning parameters are estimated using historical data but is serviceable even when only live data is available. Confidence interval coverage is much improved by the use of a bootstrap percentile confidence interval.     

Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes

In this paper, we suggest a blockwise bootstrap wavelet to estimate the regression function in the nonparametric regression models with weakly dependent processes for both designs of fixed and random. We obtain the asymptotic orders of the biases and variances of the estimators and establish the asymptotic normality for a modified version of the estimators. We also introduce a principle to select the length of data block. These results show that the blockwise bootstrap wavelet is valid for general weakly dependent processes such as α-mixing, φ-mixing and ρ-mixing random variables.     

Bootstrapping structural VARs: Avoiding a potential bias in confidence intervals for impulse response functions

Constructing bootstrap confidence intervals for impulse response functions (IRFs) from structural vector autoregression (SVAR) models has become standard practice in empirical macroeconomic research. The accuracy of such confidence intervals can deteriorate severely, however, if the bootstrap IRFs are biased. We document an apparently common source of bias in the estimation of the VAR error covariance matrix which can be easily reduced by a scale adjustment. This bias is generally unrecognized because it only affects the bootstrap estimates of the error variance, not the original OLS estimates. Nevertheless, as we illustrate here, analytically, with sampling experiments, and in an example from the literature, the bootstrap error variance bias can have significant distorting effects on bootstrap IRF confidence intervals. We also show that scale-adjusted bootstrap confidence intervals can be expected to exhibit improved coverage accuracy.