Automatic modal parameters identification and uncertainty quantification based on block-bootstrap and multi-stage clustering under ambient excitation

This study proposes an algorithm for autonomous modal estimation to automatically eliminate false modes and quantify the uncertainty caused by the clustering algorithm and ambient factors. This algorithm belongs to the stochastic subspace identification (SSI) techniques and is based on the Block-Bootstrap and multi-stage clustering analysis. First, the Block-Bootstrap is introduced to decompose the response signal of the structure into M blocks of data. The covariance-driven stochastic subspace identification (SSI-Cov) method is used to process a random sample of data and obtain the corresponding M stabilization diagrams. In addition, the hierarchical clustering method is adopted to carry out the secondary clustering of the picked stable axis according to the defined distance threshold. Then, false modes are eliminated according to the proposed true and false modal discrimination index ( MDI). Finally, the above steps are repeated B times, and MDI is used to modify the initial modal parameters of group B. The mean value of elements in the cluster is taken as the recognition result of modal parameters, and the standard deviation is used to measure the accuracy of the recognition result. The numerical simulation results and the modal parameter identification of the Jing-yuan Yellow River Bridge show that, for identifying true and false modals, the proposed modal discrimination index is more effective than the threshold value of the traditional index. Also, it was found that the proposed method can eliminate the uncertainty introduced in the clustering process. In addition, this method can remove the influence of ambient noises, and it can improve the identification accuracy. It will be shown that this method has better anti-noise performance.

Controlled Sampling Approach in Improving Multiple Imputation for Missing Seasonal Rainfall Data

Missingness in rainfall data is one of the well-known and challenging issues faced by meteorologists and researchers from all over the world. The problem would affect the quality of the data which is very important in representing the actual meteorological characteristics of a particular location. Therefore, the missing data should be properly treated in order to provide good quality dataset for the public domain. In furtherance of ensuring the accuracy of imputed missing data, the original structure of the rainfall data series must be specifically preserved when the data are having seasonal patterns. Most of the environmental datasets are generally characterized by outliers and seasonal patterns. These characteristics have certainly affected the performance of missing data imputation methods. The problem of missing data can be treated, but a specific structured approach must be employed when involving dataset that contains outliers and seasonal patterns. This study has highlighted and discussed the structured and comprehensive procedures on how to tackle the problem of missing data by emphasizing on controlled sampling approach for their implementation. The missing values were estimated by using multiple imputation based on block bootstrap approach associated with normal ratio methods compared to the conventional sampling (i.e. general bootstrap approach). The analysis and experimentation are illustrated using several datasets obtained for several locations in Peninsular Malaysia. The block bootstrap approach has revealed its advantage of preserving time series structure in its process and successfully improved the estimates of missing rainfall data imputation.

Semiparametric Block Bootstrap Prediction Intervals for Parsimonious Autoregression

This paper investigates the research question of whether the principle of parsimony carries over into interval forecasting, and proposes new semiparametric prediction intervals that apply the block bootstrap to the first-order autoregression. The AR(1) model is parsimonious in which the error term may be serially correlated. Then, the block bootstrap is utilized to resample blocks of consecutive observations to account for the serial correlation. The Monte Carlo simulations illustrate that, in general, the proposed prediction intervals outperform the traditional bootstrap intervals based on nonparsimonious models.

How to Explain the Cross-Section of Equity Returns through Common Principal Components

In this paper, we propose a procedure to obtain and test multifactor models based on statistical and financial factors. A major issue in the factor literature is to select the factors included in the model, as well as the construction of the portfolios. We deal with this matter using a dimensionality reduction technique designed to work with several groups of data called Common Principal Components. A block-bootstrap methodology is developed to assess the validity of the model and the significance of the parameters involved. Data come from Reuters, correspond to nearly 1250 EU companies, and span from October 2009 to October 2019. We also compare our bootstrap-based inferential results with those obtained via classical testing proposals. Methods under assessment are time-series regression and cross-sectional regression. The main findings indicate that the multifactor model proposed improves the Capital Asset Pricing Model with regard to the adjusted-R2 in the time-series regressions. Cross-section regression results reveal that Market and a factor related to Momentum and mean of stocks’ returns have positive risk premia for the analyzed period. Finally, we also observe that tests based on block-bootstrap statistics are more conservative with the null than classical procedures.

Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest.

Models for Expected Returns with Statistical Factors

In this paper, we propose multifactor models for the pan-European Equity Market using a block-bootstrap method and compare the results with those of traditional inferential techniques. The new factors are built from statistical measurements on stock prices—in particular, coefficient of variation, skewness, and kurtosis. Data come from Reuters, correspond to nearly 2000 EU companies, and span from January 2008 to February 2018. Regarding methodology, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics). Methods under assessment are time-series regression, cross-sectional regression, and the Fama–MacBeth procedure. The main findings indicate that the two factors that better improve the Capital Asset Pricing Model with regard to the adjusted R2 in the time-series regressions are the skewness and the coefficient of variation. For this reason, a model including those two factors together with the market is thoroughly studied. We also observe that our block-bootstrap methodology seems to be more conservative with the null of the GRS test than classical procedures.

Block bootstrap optimality and empirical block selection for sample quantiles with dependent data

Summary We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. The conclusion that bootstrap samples should be of smaller size than the original sample has significant implications for computational efficiency and scalability of bootstrap methodologies with dependent data. Our main theorem determines the optimal number of blocks and block length to achieve the best possible convergence rate for the block bootstrap distribution estimator for sample quantiles. We propose an intuitive method for empirical selection of the optimal number and length of blocks, and demonstrate its value in a nontrivial example.