Gains in efficiency from joint estimation of systems of autoregressive-moving average processes

The paper examines gains in efficiency from joint estimation of systems of ARMA processes where cross-correlation is due to contemporaneous correlation among disturbances. The asymptotic variance of joint estimates is derived and it involves only variances and covariances among purely AR processes corresponding to the AR and MA parts of the constituent processes. Small sample gains are evaluated by Monte Carlo methods. Application of joint estimation to two short-term interest rates is shown to result in more accurate post-sample predictions relative to both univariate models and the FMP econometric model.     

A general asymptotic theory for time-series models

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.     

A representation of risk measures

We provide a representation theorem for risk measures satisfying (1) monotonicity, (2) positive homogeneity and (3) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition, sub-additive; see Artzner et al. in Math Finance 9:203–228, 1999).     

稳健的HAC法在多元平稳时间序列之间伪回归中的应用

本文在传统HAC法的基础上,将截断参数M设定为样本容量T,并推导新的模型显著性检验Wald*统计量的极限分布。通过比较分析,表明Wald*统计量能大大减少伪回归概率,且新统计量比传统检验统计量更加稳健,但是也发现新的统计量具有一定程度的检验水平扭曲,原因在于截断参数M的设定忽略了AR过程的持久性、MA过程的滞后阶等因素,从而导致Wald*存在检验水平扭曲,说明M的设定不当会产生伪回归和检验水平扭曲现象。     

The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors

We consider the normalized least squares estimator of the parameter in a nearly integrated first-order autoregressive model with dependent errors. In a first step we consider its asymptotic distribution as well as asymptotic expansion up to order O_p(T⁻¹). We derive a limiting moment generating function which enables us to calculate various distributional quantities by numerical integration. A simulation study is performed to assess the adequacy of the asymptotic distribution when the errors are correlated. We focus our attention on two leading cases: MA(1) errors and AR(1) errors. The asymptotic approximations are shown to be inadequate as the MA root gets close to −1 and as the AR root approaches either −1 or 1. Our theoretical analysis helps to explain and understand the simulation results of Schwert (1989) and DeJong, Nankervis, Savin, and Whiteman (1992) concerning the size and power of Phillips and Perron's (1988) unit root test. A companion paper, Nabeya and Perron (1994), presents alternative asymptotic frameworks in the cases where the usual asymptotic distribution fails to provide an adequate approximation to the finite-sample distribution.     

Direct and iterated multistep AR methods for difference stationary processes

The paper focuses on a comparison between the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors. The methods are based on an encompassing representation for the two predictors, which enables us to derive their properties quite easily under a maintained model. The paper provides an analytical expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From an empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule-Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values are obtained using the bootstrap method.     

Multivariate stable ARMA processes with time dependent coefficients

This paper considers the class of m-variate autoregressive moving average (ARMA) processes with stable innovations and time dependent coefficients. A set of suitable AR and MA regularity conditions is given to ensure existence and uniqueness of valid solutions. A simple form of the above solution is expressed in terms of one sided Green's matrix functions associated with the AR operator. We solve the prediction problem arising in this class of models. A few examples are added to support the general theory.     

Autocovariance functions of series and of their transforms

We derive a method to link exactly the autocovariance functions of two arbitrary instantaneous transformations of a time series. For example, this is useful when one wants to derive the autocovariance of the logarithm of a series from the known autocovariance of the original series and, more generally, when one wishes to describe the time-series effects of applying a nonlinear transformation to a process whose properties are known. As an illustration, we provide two corollaries and three examples. The first corollary is on the commonly used logarithmic transformation, and is applied to a geometric auto-regressive (AR) process, as well as to a positive moving-average (MA) process. The second corollary is on the tan⁻¹(·) transformation which will turn possibly unstable series into stable ones. As an illustration, we obtain the autocovariance function of the tan⁻¹(·) of an arithmetic AR process. This filter, while always producing a bounded process, preserves the stability/instability distinction of the original series, a feature that can be turned to an advantage in the design of tests. We then present a probabilistic interpretation of the main features of the new autocovariance function. We also provide a mathematical lemma on a general integral which is of independent interest.     

Derivation of the unconditional state-covariance matrix for exact maximum-likelihood estimation of ARMA models

Analytical expressions for the unconditional state-covariance matrix are combined with an efficient scheme for computing theoretical autocovariances, to simplify the exact maximum-likelihood estimation of multivariate ARMA models. Alternative state-space representations for pure AR and pure MA processes, giving rise to straightforward expressions for their unconditional state covariance, are suggested.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

A dynamic analysis of moving average rules

The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper, we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the MA rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.     

Multivariate subset autoregressive modelling with zero constraints for detecting ‘overall causality’

The necessary and sufficient condition to test for ‘overall causality’, i.e., the presence of Granger- causality and instantaneous causal relations, in a bivariate and trivariate autoregressive model with recursive form is discussed. It is argued that the conventional AR model (the reduced form AR) is a more straightforward and effective means of testing for ‘overall causality’. To detect instanta- neous causality it is proposed to select the best subset system in a residual regression system in conjunction with model selection criteria. The Canadian money-income-bank rate system is re-examined in this way and by using a previously proposed algorithm we identify the optimum multivariate subset AR with constraints to detect whether there is ‘overall causality’ in that system.     

Distribution-free tests for time series models specification

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box–Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.     

Expected utility theory with non-commutative probability theory

In this paper, we extend von Neumann and Morgenstern’s expected utility approach to a non-commutative probability theory. We introduce a new representation of the decision maker’s set of events which extends the canonical representation. We reformulate von Neumann and Morgenstern’s approach to modeling decision maker behavior by non-commutative probability theory. We introduce a set of preference axioms similar to von Neumann and Morgenstern’s axioms, and show that they lead to a generalization of the expected utility theorem. Our generalization allows for decision makers to make an intuitive distinction between representations of a set of events. We find that this methodology enables several paradoxes and inconsistencies in traditional expected utility theory (e.g., Allais paradox, etc.) to be solved or better understood.     

三角Bezier曲面光滑拼接研究

文章在研究三角Bezier曲面原理的基础上,提出在曲面绘制阶段采用一种新的明暗处理算法,这种明暗处理算法综合了Gouroud算法处理速度快的优点和Phong算法对法矢量进行插值优化的思想,并且该算法采用法矢量二次插值方法,用此法矢量代替原三角片的线性法矢量参与光照计算,可构造出视觉连续的三角Bezier曲面。此算法简单可靠,并可推广到高次三角Bezier曲面的光滑拼接。     

BI-REGIONAL SAM LINKAGES: A MODIFIED BACKWARD AND FORWARD DISPERSION APPROACH

The aim of the paper is to apply a new backward and forward dispersion approach, starting from the original Rasmussen definition, which can give further insight into the interactions between industries and institutional sectors in a multiregional framework. The method is based on identification of the Macro Multipliers and the related impact components of a model based on a bi-regional SAM, which allows for the representation of the bi-regional multisectoral and multi-industry model in a two-dimensional space defined by the two dominating impact components. From such representation, we derive a set of indices of intraregional and interregional backward and forward dispersion that identifies key groups of industries and institutional sectors. The strength of these groups is further evaluated in terms of correlation of the impact components within the groups and cross-correlation between industry and institutional sectors groups. Comparative analysis among regional results gives a full picture of regional income policies.     

Absence and Variant Modes of Presence of Management Accounting in New Product Development – Theoretical Refinement and Some Empirical Evidence

Abstract

The purpose of this explorative multi-organisation study is to describe and explain absence and variant modes of presence of management accounting (MA) in new product development (NPD), and to problematise further the equivocal results and paradigm shift regarding the role and relevance of management control system (MCS) packages in innovative and uncertain environments, in particular, why there are environments without formal management controls such as MA. The study refines, and in certain respects develops the theory of MA absence by combining it with the theory base of MA change and stability. The theoretical analysis suggests that a wide variety of factors may explain the absence or the mode of presence of MA in NPD. These identified explanatory factors are analysed further within the developed theoretical framework. The strongest empirical evidence for MA absence arises from technical, economic and functional factors. Furthermore, lack of reasons-for-adoption of MA systems and other forms of control associated with engineering-oriented culture lead to MA absence in NPD. The empirical findings also reveal a number of variant modes of MA presence with only the ‘accounting thinking’ and concepts adopted in NPD. The contribution of the study extends from the refinement of the theory of MA absence towards increasing the understanding of the evolution, change, stability and relationship of various elements of MA systems, and the dynamics of MCS in general.     

基于组合权重的绿色度三角模糊函数模糊综合评价研究

首先建立了一套生产型节点企业绿色度综合评价指标体系,然后综合运用熵权值法、德尔菲法、层次分析法、三角模糊函数法形成的模糊综合评价方法对绿色度的评价问题进行研究,提出了基于组合权重的三角模糊函数模糊综合评价方法及其完整的评价过程,最后以供应链上多家企业的实际数据为例进行了实证研究。     

A geometric approach to temptation

We provide a simple geometric proof of the Gul and Pesendorfer’s (Gul and Pesendorfer, 2001) utility representation theorem about choice under temptation without self-control. We extract two incomplete orders from preferences: temptation relation and resistance relation. We characterize those relations geometrically and obtain temptation utility using a separation method à la Aumann (Aumann, 1962).     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.