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Due to the dramatic development of measuring instruments in recent years, a huge amount of large-scale data has been acquired in all research areas. Along with this, research method has changed, and data-driven methods are becoming important as the fourth scientific methodology. In the data-driven approach, the model is built according to the theory, knowledge, data, and further the purpose of the analysis. Once a model is built, useful information can be extracted from the data through the fitted model. In this data-driven method, it is crucial to use a good model and thud the evaluation of the model is essential in the success of the data-driven approach. This paper outlines the model evaluation criteria such as AIC, GIC, EIC, and so on, focusing on information criteria for evaluating prediction accuracy based on statistical models. Since \(L_1\) regularization is important in recent data analysis, the evaluation of the regularized model is also outlined.

A continuous-time generalized market microstructure (GMMS) model and its discretized model are proposed for characterizing a class of financial time series. The GMMS model is a kind of jump-diffusion model that may describe the dynamic behaviors of measurable market price, immeasurable market excess demand and market liquidity, as well as the interaction among the three variates in a market. The model includes a jump component that is used to capture the large abnormal variations of financial assets, which may occur when a market is affected by some special events happened suddenly, such as release of important financial information. On the basis of the discrete-time GMMS model, an online recursive jump detection algorithm is proposed, which is developed in accordance with the Markov property of financial time series and the Bayes theorem. Simulations and case studies demonstrate the feasibility and effectiveness of the model and its estimation approach presented in this paper.

This paper proposes a novel particle filter, namely, the auxiliary iterated extended Kalman particle filter (AIEKPF). To generate the importance density, based on the auxiliary particle filtering (APF) technique the proposed filter uses the iterated extended Kalman filter (IEKF) to integrate the latest measurements into state transition density. This new filter can match the posterior density well, because of the robustness of the APF and the importance density generated by the IEKF. The performance of the presented particle filter is evaluated by two different estimation problems with the noise of Gaussian distribution and Gamma distribution, respectively. The experimental results illustrate that the AIEKPF is superior to the extended Kalman filter and some existing particle filters, such as the standard particle filter (PF), the extended Kalman particle filter, the unscented Kalman particle filter (UKPF) and the auxiliary extended Kalman particle filter, where the number of particles is relatively small, such as 200 and 1,000. However, with an increase of particles, the superiority of the proposed method may decline compared with the PF and APF as showed in the experiments. Also, the AIEKPF has less running time than the UKPF under the same conditions, and from the viewpoint of the average effective sample sizes, it is clear that the AIEKPF has the slightest degeneracy in all filters presented in the experiments.

Progress in information technologies has enabled to apply computer- intensive methods to statistical analysis. In time series modeling, sequential Monte Carlo method was developed for general nonlinear non-Gaussian state-space models and it enables to consider very complex nonlinear non-Gaussian models for real-world problems. In this paper, we consider several computational problems associated with sequential Monte Carlo filter and smoother, such as the use of a huge number of parti- cles, two-filter formula for smoothing, and parallel computation. The posterior mean smoother and the Gaussian-sum smoother are also considered.

The time series utilized for geodetic signal analysis, such as strain and groundwater level data, usually is largely affected by barometric pressure, earth tide and precipitation, and also suffer from missing observations due to instrument maintenance or breakdown. To detect informative geodetic signal from heavily noise-affected data, one must build a time series model for decomposition of the data taking into account the characteristics of effects from these covariates. This paper proposes a new modeling method for detecting geodetic signal from earthquake-related time series data by introducing pole-restricted precipitation model, jump component and pre-processing with AR model for interpolating missing observations. Using the proposed method, a geodetic sample data can be decomposed stably into several components including geodetic trend signal, barometric pressure response, earth tidal response, precipitation response and data level shift due to mechanical maintenance or breakdown. The decomposition of the time series and the interpolation of the missing observations are performed very efficiently by using the state-space representation and the Kalman filter/smoother. Finally, case studies of real geodetic sample data demonstrate the effectiveness of the proposed modeling method that lead to some important findings in seismology.

A Sacks-Evertson borehole volumetric strainmeter (SE strainmeter) at a site located 105 km from the epicenter of the mainshock recorded a clear slow strain event following the 2003 M w 8.0 Tokachi-oki earthquake (September 25, 2003, 19:50:06 UTC). This consisted of an episode of contraction for 4 days followed by expansion for 23 days. GPS sites in southeastern Hokkaido also recorded displacement changes during the same time interval. We use quasi-static calculations to generate synthetic waveforms for the measured quantities. All the data are satisfied by a propagating line source 2-stage model of slow reverse slip, uniform amplitude of 50 cm, with rupture propagation velocities of constant 9 cm/s (first stage) and exponentially decreasing from 3 to 0.7 cm/s (second stage). This post-seismic slip event is taken to be coplanar with the main shock rupture on the upper plane of the double Wadati-Benioff seismic zone (DSZ), and largely overlaps the seismic rupture. Regular earthquakes release only about 30% of the plate motion in this section of the subduction zone; post-seismic slip appears to account for at least some of the deficit.

This paper presents two models for representing the ship's tracking dynamic behavior. The first model is a hybrid model combined by a state-dependent nonlinear time series model and a ship moving equation model, which has the advantage in long-term prediction. The second model is a pure state-dependent time series model, which has the advantage in short-term prediction. Both of them showed better simulation results than the model presented in Peng et al. [2010] did.

The Earth's surface is under the continuous influence of a variety of natural forces and human induced sources. Strain data are good examples of such disturbed signals. To determine the geodetic strain behavior before and after the 2003 Tokachi-oki earthquake (M8.0), we decomposed the disturbed strain data into trend, air pressure, earth tide, and precipitation responses components. The decomposition of the disturbed strain data and the interpolation of the missing observations are performed very effectively by using state-space modeling and the Kalman filter/smoother. The validity of the data processing is confirmed by the fact that the model derived to fit the strain data matches the GPS data extremely well. 1 The following contribution was presented at the WDS conference and presents a more complete explanation of the data processing and its implementation. Subsequent to the Conference, the authors completed their research and have published a comprehensive paper presenting their final results in [Modeling of the post-seismic slip of the 2003 Tokachi-oki earthquake M 8 off Hokkaido: constraints from volumetric strain, Earth, Planets and Space , doi: 10.5047/eps.2012.12.003, in press]. That paper includes not only a preliminary data processing presented here, but also contains many additional results concerned with a geophysical phenomenon. The CODATA Data Science Journal regrets the delay in publishing this conference paper.

For actualization of ship tracking control along a desired path with a constant velocity, a hybrid model is proposed to represent the ship's tracking dynamic behavior. Firstly, a single-input single-output nonlinear time series model is built for characterizing the responses between the ship's heading angle deviation and its rudder angle. To represent nonlinearity of the ship motion, the rolling angle is used as the model index to make the model parameters vary with the ship sailing states considering the yaw-heel-effect. The nonlinear time series model is identified offline by using previously observed real data. Then, a state-space model combined with the relationship between the heading angle deviations and the cross track errors is proposed to represent the tracking dynamic behavior. On the basis of the identified state-space type tracking motion model, a predictive controller is designed to steer the ship sailing forward with the constant velocity along the predefined reference path. The effectiveness of the nonlinear time series model-based method for the tracking control proposed in this paper is demonstrated by simulation studies and actual experiments.

For a class of smooth nonlinear multivariable systems whose working-points vary with time and the future working-points knowledge are unknown, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model is built to approximate the present and the future system’s nonlinear behavior, respectively. The combination models are constructed on the basis of a matrix polynomial multi-input multi-output (MIMO) RBF-ARX model identified offline for representing the underlying nonlinear system. A min–max robust MPC strategy is designed to achieve the systems’ output-tracking control based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator.

Monitoring and clustering of ship and main engine motions are urgent problems in order to realize energy saving navigation. In this paper, authors represent their motions by statistical autoregressive model using minimum AIC procedure. The modelling proceeds applying locally stationary fitting procedure. The watch officers and operators can automatically detect the change of ship's states by monitoring the spectra gained from the fitted model and detect the outlier, missing values of the data and predict the motions using Kalman filtering procedure. The most important feature of this system is to automatically cluster the ship's time series and save the results to the database. The watch officers and operators can analyse the past ship's and main engine's states and determine the next operating method of the navigation including the gain scheduling the ship's control system, for examples, autopilot, the tracking system, ship's governor system and so on.

A new optimal portfolio selection method within the Markowitz mean–variance framework is presented in this paper. The model proposed in the paper includes expected return, trading risk, and in particular, a quadratic form in the transaction costs of the portfolio. Using this model yields an optimal portfolio solution that maximizes return and minimizes risk as well as the transaction costs by moderating the transaction volume and smoothing the volume of traded securities in the trading process. A set of first-order autoregressive (AR) models is utilized to estimate the future returns of the securities in the portfolio, and the AR parameters are estimated by the least-squares method with a moving window. The optimization problem that results from this approach is convex and can thus be solved by quadratic programming (QP). A case study demonstrates the effectiveness and the significant performance improvements of the proposed optimal portfolio selection strategy. Copyright © 2010 John Wiley & Sons, Ltd.

We discuss the problem of constructing information criteria by applying the bootstrap methods. Various bias and variance reduction methods are presented for improving the bootstrap bias correction term in computing the bootstrap information criterion. The properties of these methods are investigated both in theoretical and numerical aspects, for which we use a statistical functional approach. It is shown that the bootstrap method automatically achieves the second-order bias correction if the bias of the first-order bias correction term is properly removed. We also show that the variance associated with bootstrapping can be considerably reduced for various model estimation procedures without any analytical argument. Monte Carlo experiments are conducted to investigate the performance of the bootstrap bias and variance reduction techniques.

狭い技術分野に限定した研究開発だけでは、社会や学問の現代的要請に応えられないとの認識が強まっています。2009年1月19日（月）産総研臨海副都心センターにて、産総研シンセシオロジー編集委員会、特定非営利活動法人横断型基幹科学技術研究団体連合（横幹連合）、大学共同利用機関法人情報・システム研究機構統計数理研究所（統数研）の3機関が合同で、「学問と技術の統合」に関するワークショップを開催しました。構成的研究方法論の理解や促進のために、また各機関の研究上の理念共有のために、本ワークショップにおける6名の講演概要を紹介します。

第Ⅱ部 招待講演による記念シンポジウム 研究機関の資料保存と歴史研究 第10章, 北川 源四郎 [統計数理研究所長]

Professor Hirotugu Akaike was awarded the 2006 Kyoto Prize for “his major contribution to statisticalscience and model ing with the Akaike Information Criterion (AIC)”. In 1973, he proposed the AIC as a naturalextension of the log-likelihood. The most natural way of applying the AIC is to use it as the model selection or order selection criterion. In the MAICE (minimum AIC estimation) procedure, the model with the minimum value of the AIC is selected as the best one among many possible models. This provided a versatile procedure for statistical modeling that is free from the ambiguities inherent in application of the hypothesis test procedure. However, the impact of the AIC is not limited to the realization of an automatic model selection procedure, and it eventually led to a paradigm shift in statisticalscience. In conventionalstatisticalinference, the theories of estimation and test are developed under the assumption of the presence of a true model. However, in statistical modeling, the model should be constructed based on the entire knowledge such as the established theory, empirical facts, current observations and even the objective of the analysis. Prof. Akaike gave a practical answer to the selection of the prior distribution of the Bayes model. Due to the development of information technologies, we can now access to huge amounts of data in various fields of science and social life. In this information and knowledge society, the Bayes modelis becoming a key technology. In this article, we shall look back at his research in five stages, namely, the launching period, frequency domain time series analysis, time series modeling, AIC and statistical modeling and Bayes modeling (Parzen et al. (1998)). It should be noted here that the reader will notice that his research was always performed based on the needs of researchers in the real-world.

SUMMARY Effects of small-scale heterogeneities on seismic waveform fluctuations were studied by physical model experiments. Using a laser Doppler vibrometer, we recorded elastic waves propagating through a granite block at 180 observation points that were arranged as an equally spaced circular array. A disc-shaped PZT source was attached on the other side surface of the circular array for realizing equivalent positions with respect to both source radiation pattern and travel distances of waves. Waveform pairs were selected out from the 180 waveforms, and cross spectra of time-windowed partial waveforms were calculated by applying the multivariate AR model. By comparing waveforms of two observation points, the cross-spectral amplitudes and phases are obtained with respect to the lapse time by moving the time window, or to the spatial distance by changing the pairs of observation points. We obtain distributions of cross-spectral phase values for frequency and the lapse time of waveforms. The distributions indicate phase fluctuation of waves in random media with respect to frequency and lapse time. Heterogeneity of the rock sample is expressed as a 1-D exponential autocorrelation functions (ACF); e2 exp(−|r|/a), where r is the distance, and a and e are the correlation length (0.22 mm) and the strength of heterogeneity (8.5 per cent), respectively. The distributions are plotted against ka; the product of wavenumber and correlation length. For small ka, the distributions of phase are close to the Gaussian distributions with small variances, but the variances quickly become large above ka≈ 0.2–0.3. Then the distributions become uniform between −π and π. This suggests that the incoherent scattered waves become dominant above a critical ka value (or a critical frequency for a medium), and phase information in later portions of waveforms will be lost. This may be important for extracting reflection, refraction or converted waves that are assigned as signals from geologic discontinuities because those signals may be strongly distorted by scattered waves produced from the small-scale heterogeneities of earth's media.

Nonstationary financial time series often observed in the real world, include a time series with a slowly shifting mean value function, a time series with time-varying variations around the mean value, and a time series with both a moving mean value and changing waveforms around the mean value. First, we briefly review nonstationary time series modeling, such as trend estimation, time-varying variance modeling, seasonal adjustment modeling, and non-Gaussian distribution modeling, which is closely related to our method for constructing a distribution-free index. Since the distribution of prices of a financial market is often non-Gaussian, we propose to transform the price observations by the Box–Cox transformation. Then, a distribution-free index is defined by taking the inverse Box–Cox transformation of the optimal long-term trend, which is estimated by fitting a trend model with time-varying observation noises to the Box–Cox transformed observations. The new index becomes impartial, regardless of the price distributions.