A GENERALIZED LEAST-SQUARES APPROACH FOR ESTIMATION OF AUTOREGRESSIVE MOVING-AVERAGE MODELS

Abstract. In this paper we present a generalized least-squares approach for estimating autoregressive moving-average (ARMA) models. Simulation results based on different model structures with varying numbers of observations are used to contrast the performance of our procedure with that of maximum likelihood estimates. Existing software packages can be utilized to derive these estimates.     

Structure and estimation of a class of nonstationary yet nonexplosive GARCH models

This article considers GARCH(1,1) models in which the time‐varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi‐maximum likelihood estimator are derived under mild assumptions.     

A mixed portmanteau test for ARMA‐GARCH models by the quasi‐maximum exponential likelihood estimation approach

This paper investigates the joint limiting distribution of the residual autocorrelation functions and the absolute residual autocorrelation functions of ARMA‐GARCH models. This leads a mixed portmanteau test for diagnostic checking of the ARMA‐GARCH model fitted by using the quasi‐maximum exponential likelihood estimation approach in Zhu and Ling (2011) . Simulation studies are carried out to examine our asymptotic theory, and assess the performance of this mixed test and other two portmanteau tests in Li and Li (2008) . A real example is given.     

Least squares estimation of ARCH models with missing observations

A least squares estimator for ARCH models in the presence of missing data is proposed. Strong consistency and asymptotic normality are derived. Monte Carlo simulation results are analysed and an application to real data of a Chilean stock index is reported.     

Estimation of Parameters in the NLAR(p) Model

Abstract. In this article, we study a new Laplace autoregressive model of order p– NLAR(p). Conditional least squares, weighted conditional least squares and maximum quasi‐likelihood are used to estimate the model parameters. Comparisons among these estimates of the NLAR(2) model are given via simulation studies.     

The Effect of the Estimation on Goodness‐of‐Fit Tests in Time Series Models

Abstract. We analyze, by simulation, the finite‐sample properties of goodness‐of‐fit tests based on residual autocorrelation coefficients (simple and partial) obtained using different estimators frequently used in the analysis of autoregressive moving‐average time‐series models. The estimators considered are unconditional least squares, maximum likelihood and conditional least squares. The results suggest that although the tests based on these estimators are asymptotically equivalent for particular models and parameter values, their sampling properties for samples of the size commonly found in economic applications can differ substantially, because of differences in both finite‐sample estimation efficiencies and residual regeneration methods.     

Comparing the bias and misspecification in ARFIMA models

We investigate the bias in both the short-term and long-term parameters for a range of autoregressive fractional integrated moving-average (ARFIMA) models using both semi-parametric and maximum likelihood (ML) estimation methods. The results suggest that, provided the correct model is estimated, the ML method outperforms the semi-parametric methods in terms of the bias and smaller mean square errors in both the long-term and short-term parameter estimates. These biases often cause model selection criteria to select an incorrect ARFIMA specification. Taking account of the potential misspecification the biases associated with the ML procedure tend to increase, although it continues to have a smaller worst-case bias than either of the semi-parametric procedures.     

Maximum quasi-likelihood estimation for the near(2) model

Abstract.  Maximum quasi-likelihood estimation is investigated for the NEAR(2) model, an autoregressive time series model with marginal exponential distributions. In certain regions of the parameter space, simulations indicate that maximum quasi-likelihood estimators perform better than two-stage conditional least squares estimators in terms of the per cent of estimates falling in the parameter space. The problem of out-of-range estimates is shown to be caused by the lack of information in the data rather than the characteristics of the method of estimation.     

A note on estimation by least squares for harmonic component models

Abstract. Let observations ( X ₁,…, X _n ) be generated by a harmonic model such that X _t = A ₀ cos  ω ₀ t + B ₀ sin  ω ₀ t + ε _t , where A ₀, B ₀, ω ₀ are constants and ( ε _t ) is a stationary process with zero mean and finite variance. The estimation of A ₀, B ₀, ω ₀ by the method of least squares is considered. It is shown that, without any restriction on ω in the minimization procedure, the estimate     is an n -consistent estimate of ω ₀, and hence (     ) has the usual asymptotic distribution.
The extension to a harmonic model with k >1 components is discussed. The case k =2 is considered in detail, but it was only found possible to establish the result under the restriction that both angular frequencies lie in the interval         

Comparative study of estimation methods for continuous time stochastic processes

In this paper we investigate the finite sample performances of five estimation methods for a continuous-time stochastic process from discrete observations. Applying these methods to two examples of stochastic differential equations, one with linear drift and state-dependent diffusion coefficients and the other with nonlinear drift and constant diffusion coefficients, Monte Carlo experiments are carried out to evaluate the finite sample performance of each method. The Monte Carlo results indicate that the differences between the methods are large when the discrete- time interval is large. In addition, these differences are noticeable in estimations of the diffusion coefficients.     

气体传感器Weibull分布下的一种有效参数估计

通过几种统计方法的比较,选用Weibull分布来对气体传感器的试验数据进行统计分析.针对Weibull分布的参数估计并结合气体传感器试验数据的特殊性,采用威布尔概率纸法和最小二乘法对试验数据进行初步处理,之后利用极大似然估计法对分布参数进行估计.     

Weighted scatter estimation method of the GO‐GARCH models

We propose a new estimation method for the factor loading matrix in modelling multivariate volatility processes. The key step of the method is based on the weighted scatter estimators, which does not involve optimizing any objective function. The method can therefore be easily applied to high‐dimensional systems without running into computational problems. The estimation is proved to be consistent and the asymptotic distribution is derived. The method inherits robust properties in dealing with ‘outlier’ clusters generated by GARCH processes. Through both simulation and real‐world case studies, we show that the method works well.     

Network‐induced supervised learning: Network‐induced classification (NI‐C) and network‐induced regression (NI‐R)

Current supervised approaches, such as classification and regression methodologies, are strongly focused on optimizing estimation accuracy metrics, leaving the interpretation of the results produced as a secondary concern. However, in the analysis of complex systems, one of the main interests is precisely the induction of relevant associations, to understand or clarify the way the system operates. Two related frameworks for addressing supervised learning problems (classification and regression) are presented, that incorporate interpretational‐oriented analysis features right from the onset of the analysis. These features constrain the predictive space, in order to introduce interpretable elements in the final model. Interestingly, such constraints do not usually compromise the methods' performance, when compared to their unconstrained versions. The frameworks, called network‐induced classification (NI‐C), and network‐induced regression (NI‐R), share a common methodological backbone, and are described in detail, as well as applied to real‐world case studies. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1570–1587, 2013     

Development of calibration models for estimation of monomer concentration by Raman spectroscopy during emulsion polymerization: Facing the medium heterogeneity

This work compares different calibration models for the estimation of monomer concentrations by Raman spectroscopy during semicontinuous emulsion copolymerization reactions. The limitations of these models are discussed in terms of a complex reaction, namely the copolymerization of vinyl acetate and butyl acrylate, whose monomers present overlapping Raman spectra, especially the C=C stretching band. Additionally, the copolymerization was monitored in a spectroscopic setup arranged for fast spectral acquisition, which resulted in a low signal‐to‐noise ratio. These realistic conditions for in‐line monitoring of emulsion copolymerization, i.e., considerable noise level in the spectra and medium heterogeneity, are discussed in the context of different approaches for adjusting the calibration model and the ensuing model limitations. It was verified that combining data obtained during reactions with synthetic samples is interesting from the statistical point of view, since in this way it is possible to produce data sets with a wide range of variation, allowing the accurate estimation of statistical parameters. These parameters are of major importance for process variables and product property estimations, especially if they are to be used for process control and decision making purposes. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1136–1150, 2004     

Predicting plant yields using soil testing for phosphorus: Effects of error in the estimation of the maximum yield on interseasonal comparisons of yield prediction

Results from long-term field experiments in south-western Australia are presented in the form of relationships between yield, expressed as a percentage of the maximum yield, and soil test for phosphorus (P) values. Maximum yields were not always indicated by well defined yield plateaux. Different methods have been used to estimate the maximum yield value which is used to calculate yield as a percentage of the maximum yield so as to remove interseasonal variation. For all of these methods and for the same site, the same P fertilizer (superphosphate), and the same plant species, the relationship between yield and soil test P differed for different years. Consequently fertilizer recommendations based on the assumption that this relationship is constant are likely to be incorrect. We therefore question the validity of the common practice in soil testing programmes of using percentage yield values to remove interseasonal variation.     

Parameter and state estimation in nonlinear stochastic continuous‐time dynamic models with unknown disturbance intensity

Approximate Maximum Likelihood Estimation (AMLE) is an algorithm for estimating the states and parameters of models described by stochastic differential equations (SDEs). In previous work (Varziri et al., Ind. Eng. Chem. Res., 47 (2), 380‐393, (2008); Varziri et al., Comp. Chem. Eng., in press), AMLE was developed for SDE systems in which process‐disturbance intensities and measurement‐noise variances were assumed to be known. In the current article, a new formulation of the AMLE objective function is proposed for the case in which measurement‐noise variance is available but the process‐disturbance intensity is not known a priori. The revised formulation provides estimates of the model parameters and disturbance intensities, as demonstrated using a nonlinear CSTR simulation study. Parameter confidence intervals are computed using theoretical linearization‐based expressions. The proposed method compares favourably with a Kalman‐filter‐based maximum likelihood method. The resulting parameter estimates and information about model mismatch will be useful to chemical engineers who use fundamental models for process monitoring and control.     

Nonparametric adaptive change point estimation and on line detection

Under standard conditions of change point problems with one or both distributions being unknown, we propose efficient on line and off line nonparametric algorithms for detecting and estimating the change point. They are based on histogram density estimators, which allows applications involving ordinal and categorical data. Also, they are designed to detect any changes in distribution, not necessarily related to the location or scale parameters. EfFiciency of the proposed schemes is demonstrated by relevant inequalities for the mean delay and the mean time between false alarms. Asymptotically, they are shown to behave similarly to the most efficient procedures based on the known distributions. The stopping rule achieves an asymptotically linear rnean delay and an exponential mean time between false alarms. The guidelines on selecting the threshold and the partition for the histogram density estimation are given, based on the obtained results. Proposed methods are applied to the England temperatures data and the Vostok ice core record to detect the global climate changes     

Inference for pth‐order random coefficient integer‐valued autoregressive processes

Abstract. A pth‐order random coefficient integer‐valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi‐likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.     

On the three-step non-Gaussian quasi-maximum likelihood estimation of heavy-tailed double autoregressive models

This note considers a three-step non-Gaussian quasi-maximum likelihood estimation (TS-NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy-tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy-tailed.