On the structure of moving average processes

This paper uses Hilbert space methods to develop a rigorous proof that the sum of two uncorrelated moving average processes of order q₁ and q₂ is an MA process of order q ≦ max (q₁, q₂). The methods establish the existence of suitable random shocks for the summed process, they illuminate relationships between the coefficients of such processes and their random shocks, and they provide means for proving that the random shocks of the summed processes are normal when the shocks of the underlying processes are normal. The role of the Wold decomposition is examined in terms of multiple representations of an MA process.     

Improved stein-rule estimator for regression problems

Stein-Rule estimator for regression problems has been studied by several authors including Sclove (1968) and others listed in Vinod's (1978) survey. Ullah and Ullah (1978) provide the expressions for the mean squared error (MSE) of a double k-class (KK) estimator with parameters k₁ and k₂. When k₂=1 the Stein-Rule estimator becomes a special case of KK and an optimal choice of k₁ is known. This paper explores optimal theoretical choice of k₁ and k₂. We note that negative choices of k₂ are permissible, and that thereis a large range of choices for K₁ and k₂ where the MSE of the Stein-Rule estimator can be reduced for regression problems based on multicollinear data. A simulation experiment is included.     

Estimation in a disequilibrium model and the value of information

Suits' model of the watermelon market is reformulated as a disequilibrium model and the likelihood function is derived under various assumptions concerning the amount of available information. Such models are characterized by a min condition as in y_t = min(D_t, S_t) for an ordinary demand-supply model, where the observed quantity y_t is the smaller demand and supply. Varying amounts of information may be available depending on which variables are observed and on whether prior information is available for separating the sample into subsets for which D_t < S_t and conversely. The likelihood function corresponding to the least amount of prior information is shown to be unbounded without a certain variance ratio restriction. Computations are successfully carried out both with the original model and Monte Carlo experiments and the effect of different amounts of information on MSE's is analyzed.     

Forecasting contemporal aggregates of multiple time series

The paper considers forecasting a contemporal linear aggregate y_t of a vector time series Z^'_t =(Z_1t,...,Z_kt). We first disciss the case where Z_t follows a stationary multiple moving average process and propose a measure of the efficiency of aggregation. A necessary and sufficient condition is given for the case of no gain by employing the component series. Extension of the results to stationary multiple autoregressive process and some non-stationarity processes is discussed, and an illustrative example is given.     

On the maximum number of balancing subsets

Let a₁,…,a_n be a finite sequence of n real numbers. A subset {i₁,…,i_r} of the set {1,…,n } is called a balancing subset for a₁,…,a_n if a_i1 + … + a_ir = 0. We discuss in this paper the maximum number of balancing subsets for given n.     

Estimation in the first-order moving average model through the finite autoregressive approximation: Some asymptotic results

To estimate α in the model y_t = u_t+αu_t?1, we consider a proposal by Durbin (Biometrika, 1969). It consists in fitting an autoregression of order k to the data, and deriving from there an estimate α^. The probability limit and the variance of the limiting normal distribution of α^ are presented and discussed in detail, when the sample size T → ∞, but k remains fixed. The differences between the resulting values and those corresponding to the maximum likelihood estimator are exponentially decreasing functions of k. Several modifications of the estimator are discussed and found consistent, but asymptotically inefficient.     

The distribution of the maximum of a first order autoregressive process: the continuous case

We give the cumulative distribution function of M _n , the maximum of a sequence of n observations from an autoregressive process of order 1. Solutions are first given in terms of repeated integrals and then for the case, where the underlying random variables are absolutely continuous. When the correlation is positive, $$P \left( M_n \leq x \right)\ =a_{n,x},$$ where $$a_{n,x}= \sum_{j=1}^\infty \beta_{jx}\ \nu_{jx}^{n} = O \left( \nu_{1x}^{n}\right),$$ where {?? _jx } are the eigenvalues of a non-symmetric Fredholm kernel, and ?? _1x is the eigenvalue of maximum magnitude. When the correlation is negative $$P \left( M_n \leq x \right)\ =a_{n,x} +a_{n-1,x}.$$ The weights ?? _jx depend on the jth left and right eigenfunctions of the kernel. These are given formally by left and right eigenvectors of an infinite Toeplitz matrix whose eigenvalues are just {?? _jx }. These results are large deviations expansions for extremes, since the maximum need not be standardized to have a limit. In fact, such a limit need not exist. The use of the derived expansion for P(M _n ?? x) is illustrated using both simulated and real data sets.     

Revelations of a gambler

Knowing that a decision maker maximizes expected utility with respect to some (unknown) utility U and some (unknown) probability P, what can one tell about P by observing his decisions? We discuss this revealed preference question primarily in the simple case of a two-element (H and T) state space, and show that the possible revelations of P_T/P_H are precisely those of the form P_T/P_Hε∪^K_k=1 (γ_k,δ_k), for some algebraic numbers γ_k,δ_k.     

Two kinds of variance/covariance estimates in linear mixed models

For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D ₁ and the error variance σ ² in linear mixed models. One is to estimate D ₁ first and then to estimate σ ²; the other kind is to estimate σ ² first and then for D ₁. Both kinds of estimators are consistent. The covariance matrices of these covariance estimators and the variances of these two error variance estimators are calculated. In particular, the mean square errors of these estimators are also derived for one dimensional random effects. Besides, a simulation study is conducted to investigate the performances of these estimators.     

Moments structure of ? 1-stochastic volatility models

We consider Taylor??s stochastic volatility model (SVM) when the innovations of the hidden log-volatility process have a Laplace distribution (? ₁ exponential density), rather than the standard Gaussian distribution (? ₂) usually employed. Recently many investigations have employed ? ₁ metric to allow better modeling of the abrupt changes of regime observed in financial time series. However, the estimation of SVM is known to be difficult because it is a non-linear with an hidden markov process. Moreover, an additional difficulty yielded by the use of ? ₁ metric is the not differentiability of the likelihood function. An alternative consists in using a generalized or efficient method-of-moments (GMM/EMM) estimation. For this purpose, we derive here the moments and autocovariance function of such ? ₁-based stochastic volatility models.     

An evaluation framework for developing green infrastructure by using a new hybrid multiple attribute decision-making model for promoting environmental sustainability

With the expansion of urbanization caused by the growth of population and industrial activities, the urban/city and suburban areas are facing a variety of environmental threats. Although more research and urban policy has advocated and practiced the development of green infrastructure (GI) to support urban sustainable environment, the evaluation framework for the development of GI for promoting environmental sustainability is still insufficient. Moreover, the Analytic Hierarchy Process (AHP) commonly applied in published literature, makes an unrealistic assumption of independent relationships among dimensions/criteria in decision making for satisfying the real-world problem. Therefore, the purpose of this study is to construct the evaluation framework, including four dimensions and related ten criteria, using a new hybrid-modified multiple attribute decision-making (MADM) model for developing and improving the GI for promoting environmental sustainability. This MADM model is combined with three different methodologies of MADM, including the Decision-Making Trial and Evaluation Laboratory (DEMATEL) for constructing the influential network relation map (INRM) to explore the complex influential inter-relationships and DEMATEL based on Analytic Network Process (DANP) for determining the influential weights with the VIse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) for evaluating and presenting improvement strategies for six different GIs. The empirical study indicates that DEMATEL and DANP Results suggest that decision-makers should pay more attention to the improvement of Design (D₄) and Materials (D₂) in terms of dimensions when utilizing the GI to promote environmental sustainability. Because these dimensions are enhanced, Species (D₁) and Energy (D₃) will be improved in synchronization. From the perspective of criteria, five are key core criteria and need to be focused on first: increasing the green coverage rate (B₉), utilizing sustainable materials (B₄), using ecological engineering (B₈), shaping species biodiversity (B₁), and reducing energy consumption (B₅). Modified VIKOR reveals that “grass swales” are a comparatively better choice among six GIs for promoting environmental sustainability toward achieving the aspiration level. Therefore, this MADM model is beneficial to provide a more convincing assessment framework and improvement strategies for the development of GI for promoting environmental sustainability. As a result, these modified MADM models can be shown more conveniently and reasonably than traditional methods such as traditional AHP or ANP method.     

Correcting for truncation bias caused by a latent truncation variable

We discuss estimation of the model Y_i=X_ib_Y+e_Yi, T_i=X_ib_T+ e_Ti, when data on the continuous dependent variable Y and on the independent variables X are observed iff the ‘truncation variable’ T>0 and when T is latent. This case is distinct from both (i) the‘censored sample’ case, in which Y data are available iff T>0, T is latent and X data are available for all observations, and (ii) the ‘observed truncation variable’ case, in which both Y and X are observed iff T>0 and in which the actual value of T is observed whenever T>0. We derive a maximum-likelihood procedure for estimating this model and discuss identification and estimation.     

Feedback orientation: A meta-analysis

Feedback orientation reflects an individual difference in one's receptivity to feedback. We present the results of a meta-analysis of the feedback orientation literature. Based on k = 46 independent samples, representing n = 12,478 workers, meta-analytic results suggest that feedback orientation is positively related to learning goal orientation (r_c = 0.39), job satisfaction (r_c = 0.33), work performance (r_c = 0.35), and feedback seeking (r_c = 0.43). Meta-analytic regression and dominance analysis was used to tease apart how related informal feedback constructs (i.e., feedback seeking, feedback environment, & feedback orientation) aid in the prediction of outcomes, above and beyond two established predictors of job attitudes and work performance: role clarity and leader-member exchange. We also present an interactive exploratory data analysis tool to aid in developing future research questions regarding the connection between informal feedback constructs and work outcomes.     

Causality in temporal systems: Characterization and a survey

A time series {Y_t} ‘causes’ another time series {Y_t}, in the sense defined by C.W.J. Granger, if present Y can be predicted better by using past values of X than by not doing so, other relevant information (including the past of Y) being used in either case. In this paper we (1) classify the possible causality relationships between two series X and Y, using an analogy to events in a sample space; (2) review existing work and present some new results on alternative characterizations of the more important causality events; and (3) compare several recent procedures for the empirical detection of causality.     

Steiner minimal trees and urban service networks

The optimal configuration of urban service networks has recently been shown to be a computationally difficult problem. However, there are efficient and effective techniques by which this optimal configuration of urban service networks can be approximated. In this paper, we analyze the L_p Steiner Network problem in the plane R² and demonstrate its applicability to the urban service network problem. We present a simple algorithm for estimating the L_p metric parameter for random points in the plane, then utilize it to find the L_p values for four different American cities. Finally, we apply the L_pSMT algorithm described within the text to one of the cities in order to demonstrate the effectiveness of our algorithm for determining optimal network configurations.     

Tests of significance for the mean of a finite lot

Let ξ₁, ξ₂, ξ₃, ... be independent identically distributed random variables each with normal distribution with mean μ and variance σ². Tests for the process mean μ are well-known elements of statistical analysis: the Gauß test under known process variance σ², Student’st-test under unknown process variance σ². Let the process be partitioned in lots (ξ₁, ..., ξ _N ), (ξ _N+1, ..., ξ_2N ), ... of sizeN. Consider (ξ₁, ..., ξ _N ) as a stochastic representative of this lot sequence and let the lot be characterized by the lot mean $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } $ . The lot mean can be considered as a parameter of the joint conditional distribution function of the lot variables under $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ . The present paper investigates the analogies of the Gauß test and Student’st-test for the lot situation, i.e. tests of significance for the lot meanz under known and unknown process variance σ². This approach is of special interest for the statistical control of product quality in situations where the quality of a lot of items 1, 2, ...,N with quality characteristics ξ₁, ξ₂, ..., ξ _N is identified with the lot average $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ .     

Proportional distribution schemes

An amount of income can be obtained jointly by m agents, the ith agent's share of income being θ_i. The income and the utilities of each agent are functions of the state of nature. Each agent has a probability measure over the states of nature. An efficient proportional distribution is one which is (1) Pareto optimal and for which (2) the expected proportion of income agent i recieves divided by θ_i is independent of i. It is shown that if the attitudes are strictly concave then there exists exactly one proportional distribution scheme. Furthermore, in special cases, each agent expects to recieve an income that exceeds his share.     

Sulle operazioni associative tra variabili casuali

Si mostra che, sotto condizioni di regolarità, seo è un’operazione associativa tra variabili casuali reali e indipendenti, è definibile una trasformata integrale ξ delle loro funzioni di ripartizione con la proprietà: ξx ₀ Y (t)=ξx(t)·ξ _y (t). Si indicano alcune proprietà di tale trasformata e si tratta della possibilità di estendere a un’operazione associativa risultati noti per l’addizione tra variabili casuali. In particolare ci si occupa dell’« infinita divisibilità » fornendo condizioni perché una variabile casualeX ammetta la rappresentazioneX=X _1O X _2O … _o X _n per ognin naturale con leX _i indipendenti e identicamente ditribuite.     

Cointegration and distance between differenced processes

In this note, it is argued that cointegration augments the distance between the differenced series. If two series, x _t and y _t , are integrated of order one and cointegrated and v _t and w _t are integrated of order one but not cointegrated then, under certain conditions, the distance between ??x _t and ??y _t is more than the distance between ??v _t and ??w _t .