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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。

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.

In the previous chapter, we presented three types of autopilot system based on the stationary linear AR model. However, actual sea conditions may change gradually or abruptly due to various factors, and in such a situation, we must consider a nonstationary time series. Furthermore, it may become necessary to consider the nonlinear response of the ship, which will be of particular importance to tracking control. In this chapter, we propose extensions of our statistical optimal controller based on the locally stationary AR model and the RBF-ARX model and develop a noise-adaptive autopilot and a path-tracking autopilot.

A method for constructing a distribution-free index is applied to financial and economic time series data and causations are analyzed based on power contributions . Highlighting the current sequential financial crises, the applications focus primarily on credit default swap (CDS) markets, which often have heavy-tailed spread distributions. The first application detects that the European debt crisis has already spilled over worldwide in terms of sovereign CDS (SCDS) markets. The second application measures the impact of the US subprime crisis on Japanese domestic markets. Finally, in order to examine the usability of a distribution-free index, the clear polarization between advanced and emerging regions by GDP growth regional distribution-free indices, and the importance of examining sovereign risks in estimating the economic growth, are observed. Moreover, the Japanese SCDS distribution-free index can be regarded as an underlying SCDS spread level reflecting a domestic credit strength. These applications verify the effectiveness of a distribution-free index and confirm that applying our method to markets with insufficient information, such as fast-growing or immature markets, can be effective.

A critical problem in applying the optimal control theory to a large-scale complex system that is subject to large disturbances, such as a ship, an electric power plant, or a large chemical plant, is that it is sometimes difficult to obtain a precise state-space model from the theory of the subject area. For such systems, Akaike, H.: Ann. Inst. Stat. Math. 23, 163–180 (1971) proposed the ARX model for the identification of the controlled system. In this chapter, we propose a method for obtaining optimal control laws based on the linear stationary state-space model of the controlled system for two performance criteria. Based on this linear quadratic optimal controller, we develop three types of optimal controllers for a ship: an AR model-based autopilot, a roll reduction control system, and an engine governor control system.

The features of dynamic phenomena can be described using time series models. In this chapter, we present various types of autoregressive models for the analysis of time series, such as univariate and multivariate autoregressive models, an autoregressive model with exogenous variables, a locally stationary autoregressive model, and a radial basis function autoregressive model. Various tools for analyzing dynamic systems such as the impulse response function, the power spectrum, the characteristic roots, and the power contribution are obtained through these models (Akaike and Nakagawa 1989; Kitagawa 2010).

The globalization of financial and economic systems has brought attention to the significant ramifications of price fluctuations in both domestic and international financial markets, which may cause inextricable difficulties such as the global economic crisis triggered by the bankruptcy of Lehman Brothers in 2008. In order to detect such causations, we propose the application of the generalized power contribution, which extends the original Akaike’s power contribution by decomposing a variance covariance matrix of the noises. This application reveals the frequency-wise effect of multi-dimensional noise sources on the power of the fluctuation of each variable in a multivariate feedback system . Therefore, multi-directional causations between variables can simultaneously be evaluated. The causations detected by power contribution analysis verify the effectiveness of a distribution-free index and provide valuable information flows.

In the coming post IT era, the problems of signal extraction and knowledge discovery from huge data sets will become very important. For these problems, the use of good model is crucial and thus the statistical modeling will play an important role. In this paper, we show two basic tools for statistical modeling, namely the information criteria for the evaluation of the statistical models and generic state-space model which provides us with a very flexible tool for modeling complex and time-varying systems. As examples of these methods we shall show some applications in seismology and macro economics.

The execution of price and/or display promotion has a significant effect on the sales of a brand sold in a supermarket. Information on price and/or sales is available from POS data. However, unless an investigator collects information on the execution of display promotions from every retail store, such information is unavailable. This paper presents a method of identifying whether display promotion has been executed without having to visit individual stores. We treat the execution/non-execution of a display promotion as a state variable. An unknown stationary probability matrix is assumed to describe the probability of a transition between states. Each state is characterized by a different stationary time series model with unknown parameters. The objective of the analysis is to identify the model and to assign a probability model for each state at each time instant. Finally, we provide a high precision estimator of a past execution/non-execution of a display promotion based on the proposed model.

Most of the previously developed information criteria are based on the asymptotic bias correction of the log-likelihood and have common weakness in accuracy and reliability for relatively small sample sizes. We develop a general theory for bias reduction technique in the context of smooth functional statistics and propose an information-theoretic criterion in model evaluation and selection problems. The method can be applied to a wide variety of statistical models obtained by various estimation procedures. The efficiency of the proposed criterion is investigated through a Monte Carlo simulation.

This article is addressed to the problem of modeling and exploring mean value structure of large-scale time series data and time-space data. A smoothness prior modeling approach (Smoothness Prior Analysis of Time Series, Lecture Notes in Statistics, vol. 116, Springer, New York, 1996.) is taken. In this approach, the observed series are decomposed into several components each of which are expressed by smoothness priors models. In the analysis of POS and GPS data, various useful information were extracted by this decomposition, and result in discoveries in these areas.

SUMMARY Using laboratory-scale physical models, we studied seismic waveform fluctuation in 3-D heterogeneous media, and evaluated the effects of short-wavelength random heterogeneity on seismic waves. We made two series of experiments: (1) waves are excited by the same source signal and propagate through three kinds of granitic rocks with different scales of heterogeneity, and (2) waves are excited by different frequencies but propagating through the same rock. A compression-mode piezoelectric transducer was attached to one side of the block, and the waveforms were measured at a 10 mm radius circular array with a 2 ° spacing, located on the other side. 180 waveforms are obtained at equal source–receiver distances with an equal wave radiation from the source. The source signals are one- or two-cycle sine-wave pulse with 0.5 MHz for different heterogeneities, and 0.25, 0.5, 1 and 2 MHz for the same heterogeneity. Waveforms were recorded by using a system equipped with a laser Doppler vibrometer as a sensor of elastic waves. The rock heterogeneities were investigated as the 1-D velocity fluctuations obtained from the 2-D microstructure images of the rock. By applying the exponential autocorrelation function, heterogeneities in the three rocks are characterized by similar fluctuation intensities (7.9–9.3 per cent) but different scale lengths ranging from 0.22 to 0.92 mm. We calculated the spatial correlation of waveforms, the correlation between an averaged waveform and observed waveforms, the energy partition with respect to lapse time, and the statistical distributions of the waveform parameters: correlation coefficients, traveltimes of P wave, and the log values of the P-phase energy. Correlation of waveforms, energy partition and statistical parameters of waveforms are investigated as a function of the normalize scale parameter ka: the product of wave number and the characteristic scale length of heterogeneity. We found that waveform parameters change the trends at ka∼0.2–0.3. When ka exceeds 0.2–0.3, scattered waves become strong and waveforms become more complicated. This may indicate a transition from an equivalent homogeneous medium to a scattering medium for seismic waves propagating through random heterogeneous medium.

It is known that the execution of a price and non-price promotion has a strong influence on the sales of a brand sold in a supermarket. Usually, we can easily obtain information on the degree of price promotion from POS data. On the other hand, unless the investigator collects information on the execution of non-price promotion in every retail store, we can not obtain this information. In this article, we consider the problem of identifying whether or not non-price promotion is conducted. We treat a non-price promotion execute/non-execute as a ‘state’. In that case, we assume that there is an unknown stationary probability matrix which describes the probability of a transition between states. Each state is characterized by a different stationary time series with unknown parameters. The objective of the analysis is to identify the regression model and to assign a state probability to each time instant. Finally, we give a high precision estimator of a past non-price promotion based on the proposed model.

A web-based mobile application was developed to investigate cooking oil use and disposal of households in Indonesia, and released in February, 2014. The application was designed as an interactive program visualizing Green House Gas emission calculated by individual cooking oil consumption and disposals, as well as a potential GHG reduction if the same amountof waste cooking oil was recycled. On 13 and 14 February, 2014, the released mobile application was demonstrated at three high schools, SMA2, SMA3, SMAPGRI4 in Bogor, Indonesia. The responses of 188 households were collected by a mobile application and paper questionnaires. The results showed that 51% of households disposed waste cooking oil to drainage.17%to soil, and 15% gave it to maids for further use. The average monthly consumption and disposal of cooking oil were 3.6L and 0.8L respectively. The feedback of the GHG emission by user's own cooking oil consumption and disposal seemed to have enhanced users' environmental recognition and incentive to participate in Bogor City's waste cooking oil recycling program. The application was proved as an environmental informatics and feedback system of daily food consumption and disposal.

Access to daily store level scanner data has been increasingly easier in recent years in Japan and time series analysis based on a sales response model is becoming realistic. Introduces a new method of combining time series analysis and regression analysis on the price promotion effect, which enables simultaneous decomposition of store level scanner sales into trend (including seasonality), day‐of‐the‐week effect and explanatory variable effect due to price promotion. The method was applied to daily store level scanner sales of milk, showing evidence of the existence of day‐of‐the‐week effect. Further, a method of incorporating several kinds of price‐cut variables in regression analysis and the analyzed results were presented.

The statistical information processing can be characterized by the likelihood function defined by giving an explicit form for an approximation to the true distribution. This mathematical representation, which is usually called a model, is built based on not only the current data but also prior knowledge on the object and the objective of the analysis. Akaike2,3) showed that the log-likelihood can be considered as an estimate of the Kullback-Leibler (K-L) information which measures the similarity between the predictive distribution of the model and the true distribution. Akaike information criterion (AIC) is an estimate of the K-L information and makes it possible to evaluate and compare the goodness of many models objectively. In consequence, the minimum AIC procedure allows us to develop automatic modeling and signal extraction procedures. In this article, we give a simple explanation of statistical modeling based on the AIC and demonstrate four examples of applying the minimum AIC procedure to an automatic transaction of signals observed in the earth sciences.