A k-Factor GARMA Long-memory Model

Long-memory models have been used by several authors to model data with persistent autocorrelations. The fractional and fractional autoregressive moving-average (FARMA) models describe long-memory behavior associated with an infinite peak in the spectrum at f = 0. The Gegenbauer and Gegenbauer ARMA (GARMA) processes of Gray, Zhang and Woodward (On generalized fractional processes. J. Time Ser. Anal. 10 (1989), 233–57) can model long-term periodic behavior for any frequency 0 ≤ f ≤ 0.5. In this paper we introduce a k -factor extension of the Gegenbauer and GARMA models that allows for long-memory behavior to be associated with each of k frequencies in [0, 0.5]. We prove stationarity conditions for the k -factor model and discuss issues such as parameter estimation, model iden- tification, realization generation and forecasting. A two-factor GARMA model is then applied to the Mauna Loa atmospheric CO₂ data. It is shown that this model provides a reasonable fit to the CO₂ data and produces excellent forecasts.     

Integration of machine learning and first principles models

Model building and parameter estimation are traditional concepts widely used in chemical, biological, metallurgical, and manufacturing industries. Early modeling methodologies focused on mathematically capturing the process knowledge and domain expertise of the modeler. The models thus developed are termed first principles models (or white-box models). Over time, computational power became cheaper, and massive amounts of data became available for modeling. This led to the development of cutting edge machine learning models (black-box models) and artificial intelligence (AI) techniques. Hybrid models (gray-box models) are a combination of first principles and machine learning models. The development of hybrid models has captured the attention of researchers as this combines the best of both modeling paradigms. Recent attention to this field stems from the interest in explainable AI (XAI), a critical requirement as AI systems become more pervasive. This work aims at identifying and categorizing various hybrid models available in the literature that integrate machine-learning models with different forms of domain knowledge. Benefits such as enhanced predictive power, extrapolation capabilities, and other advantages of combining the two approaches are summarized. The goal of this article is to consolidate the published corpus in the area of hybrid modeling and develop a comprehensive framework to understand the various techniques presented. This framework can further be used as the foundation to explore rational associations between several models.     

Measuring the Advantages of Multivariate vs. Univariate Forecasts

Abstract. Suppose we are interested in forecasting a time series and, in addition to the time series data, we have data from many time series related to the one we want to forecast. Since building a dynamic multivariate model for the set of time series can be a complex task, it is important to measure in advance the increase in precision to be attained by using multivariate forecasts with respect to univariate ones. This article presents a simple procedure designed to obtain a consistent estimate of this measure. Its performance is illustrated with Monte Carlo simulations and examples.     

A STUDY OF THE APPLICATION OF STATE-DEPENDENT MODELS IN NON-LINEAR TIME SERIES ANALYSIS

Abstract. The theory of state-dependent models was developed by Priestley (1980), and a few simple applications were given in Priestley (1981). In this paper, an extensive study of the application of state-dependent models to a wide variety of non-linear time series data is carried out. Both real and simulated data are used in the study, and the problems encountered are highlighted. The method is demonstrated to be successful in practice in many cases, and suggestions for the further development of the algorithm are also given.     

Long Memory,Realized Volatility and Heterogeneous Autoregressive Models

The presence of long memory in realized volatility (RV) is a widespread stylized fact. The origins of long memory in RV have been attributed to jumps, structural breaks, contemporaneous aggregation, nonlinearities, or pure long memory. An important development has been the heterogeneous autoregressive (HAR) model and its extensions. This article assesses the separate roles of fractionally integrated long memory models, extended HAR models and time varying parameter HAR models. We find that the presence of the long memory parameter is often important in addition to the HAR models.     

IDENTIFICATION OF UNOBSERVED COMPONENTS MODELS

Abstract. Unobserved components ARIMA models are common in time series applications. However, fitting models of this type leads to problems of model identification. In this paper we derive a methodology to check whether a proposed model is identifiable. We show that this kind of identification can be checked using the autocovariance generating function and/or the (pseudo-)spectral generating function.     

Identification of uncertain MIMO Wiener and Hammerstein models

Several approaches can be found in the literature to perform the identification of block oriented models (BOMs). In this sense, an important improvement is to achieve robust identification to cope with the presence of uncertainty.In this work, two special and widely used BOMs are considered: Hammerstein and Wiener models. The models herein treated are assumed to be described by parametric representations. The approach introduced in this work for the identification of the multiple input-multiple output (MIMO) uncertain model is performed in a single step. The uncertainty is described as a set of parameters which is found through the solution of an optimization problem.A distillation column simulation model is presented to illustrate the robust identification approach. This process is an interesting benchmark due to its well-known nonlinear dynamics. Both Hammerstein and Wiener models are used to represent this plant in the presence of uncertainty. A comparative study between these models is established.     

Designability and thermal stability of protein structures

Only about 1000 qualitatively different protein folds are believed to exist in nature. Here, we review theoretical studies which suggest that some folds are intrinsically more designable than others, i.e. are lowest energy states of an unusually large number of sequences. The sequences associated with these folds are also found to be unusually thermally stable. The connection between highly designable structures and highly stable sequences is generally known as the ‘designability principle’. The designability principle may help explain the small number of natural folds, and may also guide the design of new folds.     

地理信息系统与环境模型集成的探讨

文章从地理信息系统与环境模型集成的必要性入手,对GIS与环境模型集成的方式、步骤等问题作了一些探讨,并指出了其未来的发展趋势.     

Outlier Detection And Estimation In NonLinear Time Series

Abstract. The problem of identifying the time location and estimating the amplitude of outliers in nonlinear time series is addressed. A model‐based method is proposed for detecting the presence of additive or innovational outliers when the series is generated by a general nonlinear model. We use this method for identifying and estimating outliers in bilinear, self‐exciting threshold autoregressive and exponential autoregressive models. A simulation study is performed to test the proposed procedures and comparing them with the methods based on linear models and linear interpolators. Finally, our results are applied for detecting outliers in the Canadian lynx trappings and in the sunspot numbers data.     

A COMPARATIVE STUDY OF VARIOUS UNIVARIATE TIME SERIES MODELS FOR CANADIAN LYNX DATA

Abstract. This paper describes the results of a simulation study aimed at comparing the various time series models, both linear and non-linear, fitted to the annual Canadian lynx trappings for the years 1821–1934.     

广义线性模型与非线性模型参数的统计推断

概述了广义线性模型(含半参数广义线性模型)与非线性模型研究的新进展,着重讨论了它们参数估计的统计推断。近年来,广义线性模型与非线性模型的研究发展迅速,有着广泛的应用前景。     

Aggregation and Disaggregation of Structural Time Series Models

The aggregation/disaggregation problem has been widely studied in the time series literature. Some main issues related to this problem are modelling, prediction and robustness to outliers. In this paper we look at the modelling problem with particular interest in the local level and local trend structural time series models together with their corresponding ARIMA(0, 1, 1) and ARIMA(0, 2, 2) representations. Given an observed time series that can be expressed by a structural or autoregressive integrated moving-average (ARIMA) model, we derive the necessary and sufficient conditions under which the aggregate and/or disaggregate series can be expressed by the same class of model. Harvey's cycle and seasonal components models (Harvey, Forecasting, Structural Time Series Models and the Kalman Filter , Cambridge: Cambridge University Press, 1989) are also briefly discussed. Systematic sampling of structural and ARIMA models is also discussed.     

空洞蠕变的理论模型

综述了最近30年文献上报道的适用于陶瓷材料的蠕变空洞成核、生长的理论模型,剖析了这些模型的成功和不足之处,展望了该领域的研究前景。     

Time‐Varying Transition Probabilities for Markov Regime Switching Models

We propose a new Markov switching model with time‐varying transitions probabilities. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time‐varying probability is generated by the score of the predictive likelihood function. We show how the model dynamics can be readily interpreted. We investigate the performance of the model in a Monte Carlo study and show that the model is successful in estimating a range of different dynamic patterns for unobserved regime switching probabilities. We also illustrate the new methodology in an empirical setting by studying the dynamic mean and variance behaviour of US industrial production growth.     

On stationarity and ergodicity of the bilinear model with applications to GARCH models

We establish sufficient conditions for the bilinear time‐series model to be strictly stationary and ergodic in terms of its associated Lyapunov exponent. In two special cases, we verify that the conditions are also necessary. We then use these results to give necessary and sufficient conditions for stationarity of specific generalized autoregressive conditionally heteroskedastic (GARCH) models which can be written as a bilinear model, including linear GARCH, Power GARCH, EGARCH among others. These results generalize the ones found in the studies of, among others, Bougerol and Picard [Journal of Econometrics 52 (1992) 115], Duan [Journal of Econometrics 79 (1997) 97] and Nelson [Econometric Theory 6 (1990) 318]. In many cases, the conditions are weaker than the ones found elsewhere in the literature.     

Determination of reaction models from experimental measurements

It is demonstrated through the use of transformation relations, function approximation and error limits that it is impossible to distinguish among rival gasification models using just a single temperature programmed reaction experiment. Two experiments at different heating rates must be used and the ratio between rates is important. These depend on the models to be distinguished.     

Inventory pinch gasoline blend scheduling algorithm combining discrete- and continuous-time models

This work introduces multi-period inventory pinch-based algorithm to solve continuous-time scheduling models (MPIP-C algorithm), a three level method which combines discrete-time approximate scheduling with continuous-time detailed scheduling and with inventory pinch-based optimization of operating states. When applied to gasoline blending, the top level computes optimal recipes for aggregated blends over periods initially delineated by inventory pinch points. Discrete-time middle level uses fixed blend recipes to compute an approximate schedule, i.e. what, when, and how much to produce; it also allocates swing storage and associated product shipments with specific storage. Continuous-time model at the third level computes when exactly to start/stop an operation (blend, tank transfer, shipment). MPIP-C algorithm solves linear or nonlinear problems 2–3 orders of magnitude faster than full-space models.     

LARGE SAMPLE ANALYSIS OF AUTOREGRESSIVE MOVING-AVERAGE MODELS WITH ERRORS IN VARIABLES

Abstract. We consider estimation of parameters of an unobservable ARMA(p, q) process {U_t; t= 1,2,…} based on a set of n observables, X₁, …, X_n, where X_t=U_t, +ε_t, 1 ≤t≤n, it being assumed that {ε_t} is independent of {U_t}. We examine the asymptotic properties of these ARMA estimators under a set of weak regularity conditions on {ε_t}.