POWER OF THE NEURAL NETWORK LINEARITY TEST

Abstract. Recently, a new linearity test for time series was introduced based on concepts from the theory of neural networks. Lee et al. have already studied the power properties of this test and they are further investigated here. They are compared by simulation with those of a Lagrange multiplier (LM) type test that we derive from the same single-hidden-layer neural network model. The auxiliary regression of our LM type test is a simple cubic 'dual' of the Volterra expansion of the original series, and the power of the test appears superior overall to that of the other test.     

TESTING SEPARATE TIME SERIES MODELS

Abstract. We develop simple procedures for testing the adequacy of separate time series models. The test statistics may be calculated using auxiliary regressions that are very similar to those used for calculating Lagrange multiplier test statistics. While the separate tests are designed to yield high power against separate alternatives, they are also powerful as diagnostic checks against a range of inappropriate alternatives. The small-sample properties of the separate and Lagrange multiplier tests are compared on the basis of a Monte Carlo experiment. In these experiments it is found that the separate tests are frequently more powerful than the Lagrange multiplier tests, even for alternatives against which the latter are asymptotically optimal.     

Trend Adjustment Prior to Testing for the Cointegrating Rank of a Vector Autoregressive Process

Testing the cointegrating rank of a vector autoregressive process that may have a deterministic linear trend is considered. Previous proposals for dealing with such a situation are either to allow for a deterministic trend term in computing a suitable test statistic or else to remove the linear trend first and then derive the test statistic from the trend-adjusted data. In this study the latter approach is considered and a new method for trend removal is proposed that is based on estimating the trend parameters under the null hypothesis. Likelihood ratio and Lagrange multiplier type test statistics are derived on the basis of the trend-adjusted data and their asymptotic distributions are considered under the null hypothesis and under local alternatives. A simulation comparison with other proposals is performed.     

New Improved Tests for Cointegration with Structural Breaks

Abstract. This article proposes Lagrange multiplier‐based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small‐sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests.     

Testing Composite Hypotheses for Locally Stationary Processes

For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to a χ² distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.     

Dickey–Fuller, Lagrange Multiplier and Combined Tests for a Unit Root in Autoregressive Time Series

In this paper we investigate (augmented) Dickey–Fuller (DF) and Lagrange multiplier (LM) type unit root tests for autoregressive time series through comprehensive Monte Carlo simulations. We consider two sorts of null and alternative hypotheses: a unit root without drift versus level stationarity and a unit root with drift versus trend stationarity. The DF-type coef ficient tests are found to show the best overall performance in both cases, at least if the sample size is sufficiently large. How ever, it is also found that the DF and LM tests are roughly complementary with regard to their finite-sample power. We therefore consider combining these two types of unit root tests to obtain ( ad hoc 'but') 'robust' test procedures. Critical values for the proposed tests are provided     

Evaluating Specification Tests for Markov‐Switching Time‐Series Models

Abstract. We evaluate the performance of several specification tests for Markov regime‐switching time‐series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung–Box tests based on both the generalized residual and a standard‐normal residual constructed using the Rosenblatt transformation. The size and power of the tests are studied using Monte Carlo experiments. We find that the LM tests have the best size and power properties. The Ljung–Box tests exhibit slight size distortions, though tests based on the Rosenblatt transformation perform better than the generalized residual‐based tests. The tests exhibit impressive power to detect both autocorrelation and autoregressive conditional heteroscedasticity (ARCH). The tests are illustrated with a Markov‐switching generalized ARCH (GARCH) model fitted to the US dollar–British pound exchange rate, with the finding that both autocorrelation and GARCH effects are needed to adequately fit the data.     

On the Consistency of Bootstrap Testing for a Parameter on the Boundary of the Parameter Space

It is well known that with a parameter on the boundary of the parameter space, such as in the classic cases of testing for a zero location parameter or no autoregressive conditional heteroskedasticity (ARCH) effects, the classic nonparametric bootstrap – based on unrestricted parameter estimates – leads to inconsistent testing. In contrast, we show here that for the two aforementioned cases, a nonparametric bootstrap test based on parameter estimates obtained under the null – referred to as ‘restricted bootstrap’ – is indeed consistent. While the restricted bootstrap is simple to implement in practice, novel theoretical arguments are required in order to establish consistency. In particular, since the bootstrap is analysed both under the null hypothesis and under the alternative, non‐standard asymptotic expansions are required to deal with parameters on the boundary. Detailed proofs of the asymptotic validity of the restricted bootstrap are given and, for the leading case of testing for no ARCH, a Monte Carlo study demonstrates that the bootstrap quasi‐likelihood ratio statistic performs extremely well in terms of empirical size and power for even remarkably small samples, outperforming the standard and bootstrap Lagrange multiplier tests as well as the asymptotic quasi‐likelihood ratio test.     

Stationarity testing under nonlinear models. Some asymptotic results

Stationarity testing for nonlinear time series models which include several smooth trend components with (possibly) unknown parameters is considered. A pseudo‐Lagrange multiplier stationarity test is proposed and its asymptotic behaviour is derived. The limiting null distribution generally depends on the unknown parameters of the model. A bootstrap approach permits this problem to be circumvented and consistency of the bootstrapped test is obtained. The theoretical analysis is complemented with a simulation study which allows us to check the performance of the test in finite samples. The article ends with an empirical application.     

Diagnostic Checking in a Flexible Nonlinear Time Series Model

This paper considers a sequence of misspecification tests for a flexible nonlinear time series model. The model is a generalization of both the smooth transition autoregressive (STAR) and the autoregressive artificial neural network (AR-ANN) models. The tests are Lagrange multiplier (LM) type tests of parameter constancy against the alternative of smoothly changing ones, of serial independence, and of constant variance of the error term against the hypothesis that the variance changes smoothly between regimes. The small sample behaviour of the proposed tests is evaluated by a Monte-Carlo study and the results show that the tests have size close to the nominal one and a good power.     

Test for the null hypothesis of cointegration with reduced size distortion

Abstract. This article considers a single‐equation cointegrating model and proposes the locally best invariant and unbiased (LBIU) test for the null hypothesis of cointegration. We derive the local asymptotic power functions and compare them with the standard residual‐based test, and show that the LBIU test is more powerful in a wide range of local alternatives. Then, we conduct a Monte Carlo simulation to investigate the finite sample properties of the tests and show that the LBIU test outperforms the residual‐based test in terms of both size and power. The advantage of the LBIU test is particularly patent when the error is highly autocorrelated. Furthermore, we point out that finite sample performance of existing tests is largely affected by the initial value condition while our tests are immune to it. We propose a simple transformation of data that resolves the problem in the existing tests.     

采用结构进化策略的Lagrange乘子法优化换热网络

针对罚函数法处理有约束问题时存在的不足,采用Lagrange乘子法优化换热网络.为求解Lagrange函数方程组,根据确定性方法,提出最速下降法求解策略以及Powell法求解策略.通过极小值判断机制,保证Lagrange函数方程组的解是原换热网络目标函数值的极小值.根据实际工况,提出结构进化策略,与Lagrange乘子法相结合,实现了换热网络全局最优化.通过经典算例验证了两种求解策略的有效性、准确性以及结构进化策略的通用性.与文献结果进行对比,结果表明本算法具有较强的局部搜索能力以及全局搜索能力,能够找到更优的换热网络结构,有利于在工业生产中节约成本.     

On threshold moving-average models

In this paper the class of discrete self-exciting threshold moving-average (SETMA) models is studied in some detail. In particular, we consider various problems associated with the identification, estimation and testing of these models. A simple method for distinguishing between low order moving average (MA) and low order SETMA models is presented. Some simulation results illustrate the performance of the proposed method. We also derive a Lagrange multiplier (LM) test statistic for testing a linear MA model against a SETMA model. The small sample performance of the LM test is evaluated in a Monte Carlo study. A real example is used to illustrate the results.     

A surface model‐based simulation for warpage of injection‐molded parts

The mid‐plane model for warpage simulation of injection‐molded parts requires a mid‐plane mesh whose transformation is considerably time consuming. To overcome this drawback, a surface model‐based warpage simulation is presented, in which the part is represented as a perfect bonding of two half‐thickness plates with their reference surfaces at the outer boundary of the part. The plates over the surface mesh are modeled as flat shell elements, and a new triangular flat shell element is developed which combines an Assumed Natural DEviatoric Strain (ANDES) based membrane component and a Refined Nonconforming Element Method (RNEM) based bending component. The bonding is accomplished by multipoint constraints and a Lagrange multiplier based elimination method is proposed for constraint application. The results show that compared with some popular shell elements, ANSYS, Moldflow and the experiments, the presented model exhibits a high performance in computation accuracy. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

TESTS FOR FRACTIONAL INTEGRATION:A MONTE CARLO INVESTIGATION

Abstract. The performance of the Geweke-Porter-Hudak (GPH) test, the modified rescaled range (MRR) test and two Lagrange multiplier (LM) type tests for fractional integration in small samples is examined using Monte Carlo methods. Both the GPH and MRR tests are found to be robust to moderate autoregressive moving-average components, autoregressive conditional heteroskedasticity effects and shifts in the variance. However, these two tests are sensitive to large autoregressive moving-average components and shifts in the mean. It is also found that the LM tests are sensitive to deviations from the null hypothesis. As an illustration, the GPH test is applied to two economic data series.     

Local Asymptotic Distributions of Stationarity Tests

Abstract. In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non‐stationary process in any finite sample which converges to a stationary process as T ↑ ∞. From the asymptotic distributions, we find that the stationarity tests have non‐trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704–709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.     

Powerful Unit Root Tests Free of Nuisance Parameters

We propose a variance ratio‐type unit root test where the nuisance parameter cancels asymptotically under both the null of a unit root and a local‐to‐unity alternative. Critical values and asymptotic power curves can be computed using standard numerical techniques. Our test exhibits higher power compared with tests that share the virtue of being free of tuning parameters. In fact, the local asymptotic power curves of our procedure get close to the power functions of the point optimal test, where the latter suffers from the drawback of having to correct for a nuisance parameter consistently.     

ON THE LAGRANGE MULTIPLIER TEST FOR AUTOREGRESSIVE MOVING-AVERAGE MODELS

Abstract. This paper examines the score or Lagrange multiplier statistic for testing the adequacy of a fitted autoregressive moving-average model and gives a simple closed-form expression for this test statistic. Some singularities arising as the order of the alternative model is increased are examined.     

A FREQUENCY DOMAIN APPROACH TO LAGRANGE MULTIPLIER TEST FOR AUTOREGRESSIVE MOVING AVERAGE MODELS

Abstract. The paper derives a goodness of fit test for autoregressive moving average models using the frequency domain approximation to the log likelihood and the Lagrange multiplier approach. The test statistic is based on the sample autocovariances and can be quickly computed through a recursive procedure.     

最小?损优化方法在椭圆换热管内的应用

在流体对流换热分析的基础上得到局部?损率的表达式,以局部?损率为优化目标,满足能量与质量守恒条件,在流动功耗为定值条件下,根据拉格朗日泛函极值原理得到?损为极值时的控制方程组,发展了最小?损优化方法。将该方法应用到椭圆换热单管中,得到优化后的速度场与温度场。优化结果表明,优化流动结构为纵向旋流,具有较好的传热及流动性能,相比未优化椭圆管综合换热性能（Nu/Nu_s）/（f/f_s）可达3.21,同时得到了纵向涡在流场中的分布情况,这对椭圆管内强化换热发展具有指导意义。