The impact of GARCH on asymmetric unit root tests

Using Monte Carlo simulation, threshold autoregressive (TAR) and momentum-threshold autoregressive (MTAR) asymmetric unit root tests are examined in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). It is shown that TAR and MTAR unit root tests exhibit greater size distortion than the original (implicitly symmetric) Dickey–Fuller unit root test when applied to series exhibiting GARCH. Importantly, it is found that the use of consistent-threshold estimation increases the oversizing of the resulting asymmetric unit root test whether based upon the TAR or the MTAR model. The extent of oversizing of all tests considered is shown to be positively dependent upon the size of the volatility parameter of the GARCH model. The relevance of the simulation analysis conducted is supported by GARCH modelling of the term structure of US interest rates. The results of the current analysis indicate that if GARCH behaviour is suspected in economic or financial data, practitioners should interpret the results of asymmetric unit root tests with care to avoid drawing a spurious inference of stationarity. The paper concludes by suggesting future areas of research prompted by the present findings.     

Will the leading firm continue to dominate the market in the Taiwan notebook industry?

This study investigates whether the market share leader in the notebook industry in Taiwan is likely to maintain its dominant position. Market share data are used to investigate the intensity of competitiveness in the industry, and data on the gap in market shares are employed to elucidate the dominance of the leading firm in Taiwan's notebook industry during the 1998-2004 period. The newly developed Panel SURADF tests advanced by Breuer et al. [Misleading inferences from panel unit root tests with an illustration from purchasing power parity, Rev. Int. Econ. 9 (3) (2001) 482-493] are employed to determine whether the market share gap is stationary or not. Unlike other panel-based unit root tests which are joint tests of a unit root for all members of a panel and are incapable of determining the mix of I(0) and I(1) series in a panel setting, the Panel SURADF tests have the advantage of being able to investigate a separate unit root null hypothesis for each individual panel member and are, therefore, able to identify how many and which series in a panel are stationary processes. The empirical results from several panel-based unit root tests substantiate that the market shares of the firms studied here are non-stationary, indicating that Taiwan's notebook industry is highly competitive; however, Breuer et al.'s [12] Panel SURADF tests unequivocally show that only Compal is stationary with respect to market share gap. In terms of sales volume, Compal is the second largest firm in the notebook industry in Taiwan, and the results indicate that it alone has the opportunity to become the market share leader in the notebook industry.     

Asymptotic Properties of Estimators for Seasonally Cointegrated State Space Models Obtained Using the CVA Subspace Method

This paper investigates the asymptotic properties of estimators obtained from the so called CVA (canonical variate analysis) subspace algorithm proposed by Larimore (1983) in the case when the data is generated using a minimal state space system containing unit roots at the seasonal frequencies such that the yearly difference is a stationary vector autoregressive moving average (VARMA) process. The empirically most important special cases of such data generating processes are the I(1) case as well as the case of seasonally integrated quarterly or monthly data. However, increasingly also datasets with a higher sampling rate such as hourly, daily or weekly observations are available, for example for electricity consumption. In these cases the vector error correction representation (VECM) of the vector autoregressive (VAR) model is not very helpful as it demands the parameterization of one matrix per seasonal unit root. Even for weekly series this amounts to 52 matrices using yearly periodicity, for hourly data this is prohibitive. For such processes estimation using quasi-maximum likelihood maximization is extremely hard since the Gaussian likelihood typically has many local maxima while the parameter space often is high-dimensional. Additionally estimating a large number of models to test hypotheses on the cointegrating rank at the various unit roots becomes practically impossible for weekly data, for example. This paper shows that in this setting CVA provides consistent estimators of the transfer function generating the data, making it a valuable initial estimator for subsequent quasi-likelihood maximization. Furthermore, the paper proposes new tests for the cointegrating rank at the seasonal frequencies, which are easy to compute and numerically robust, making the method suitable for automatic modeling. A simulation study demonstrates by example that for processes of moderate to large dimension the new tests may outperform traditional tests based on long VAR approximations in sample sizes typically found in quarterly macroeconomic data. Further simulations show that the unit root tests are robust with respect to different distributions for the innovations as well as with respect to GARCH-type conditional heteroskedasticity. Moreover, an application to Kaggle data on hourly electricity consumption by different American providers demonstrates the usefulness of the method for applications. Therefore the CVA algorithm provides a very useful initial guess for subsequent quasi maximum likelihood estimation and also delivers relevant information on the cointegrating ranks at the different unit root frequencies. It is thus a useful tool for example in (but not limited to) automatic modeling applications where a large number of time series involving a substantial number of variables need to be modelled in parallel.     

高炉铁水含硅量序列的动力学结构分析

以邯郸钢铁公司7号高炉在线采集的2000炉铁水含硅量［Si］数据为样本,对［Si］时间序列作了基于逆序数的平稳性检验.然后,在关联积分的基础上,定义了衡量不同时间序列间动力学相似性的“距离”,通过等分采集得到的［Si］序列,计算子序列间的“距离”,发现了高炉冶炼过程中存在显著的动力学结构突变性,最后应用DVV算法分析动力学性质变动下,高炉铁水含硅量［Si］的可预测性. 关键词： 高炉冶炼 平稳性 动力学相似性 可预测性     

Estimation of time to stationarity in geometrically nonlinear structural responses

The determination of the time to stationarity is defined here through the convergence, to its stationary limit, of the nonstationary variance. This function is estimated through Monte Carlo simulations and a two-step, autoregressive-based modeling approach is employed to minimize the effects of randomness introduced by the limited number of simulations that can be carried out. The methodology is applied extensively to nonlinear single-degree-of-freedom models but is also demonstrated on 8-mode reduced order models of clamped–clamped straight and curved beams. In the latter case, it is found that the time to stationarity is strongly dependent on the excitation level, i.e. varying from one case to another by a factor at least larger than 4, thereby emphasizing the interest in estimating it beforehand. It is finally shown that the single-degree-of-freedom results tabulated here may be used for these reduced order models to obtain a first estimate of the time to stationarity.     

Correlation theory of quantized electromagnetic field II

Some general properties of a correlation matrix which has been defined in recent paper are investigated. The cross-symmetry condition and the non-negative-definiteness condition for the arbitrary order correlation matrix of an electromagnetic field are derived. Further, the stationarity condition in terms of time derivatives of the correlation matrix as well as a necessary condition of the stationarity of the electromagnetic field by means of the generalized Wiener-Khinchin theorem are obtained. With the help of the new form of the stationarity condition a connection between this condition and monochromacity of a coherent field is shown.The author wishes to thank Dr. J. Peina for discussions.     

Dimension and entropy analysis of MEG time series from human α-rhythm

Magnetoencephalograms (MEG) from human brain were measured by means of a 37 channel SQUID magnetometer (KRENIKON). Correlation integrals were calculated from time series exhibiting strong -rhythm in order to give estimates of correlation dimension andK ₂ entropy. The results are discussed regarding the length and the stationarity of the data. It is shown that low spurious correlation dimensions andK ₂-entropies may easily be obtained as artefacts due to time correlations in phase space and data length. When time correlations are avoided and the length of time series is taken into account, estimates of correlation dimension andK ₂ entropy indicate no evidence of the existence of low dimensionality.     

A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground

A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton’s square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution. Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.     

Investigation of determinism in heart rate variability

The article searches for the possible presence of determinism in heart rate variability (HRV) signals by using a new approach based on NARMA (nonlinear autoregressive moving average) modeling and free-run prediction. Thirty-three 256-point HRV time series obtained from Wistar rats submitted to different autonomic blockade protocols are considered, and a collection of surrogate data sets are generated from each one of them. These surrogate sequences are assumed to be nondeterministic and therefore they may not be predictable. The original HRV time series and related surrogates are submitted to NARMA modeling and prediction. Special attention has been paid to the problem of stationarity. The results consistently show that the surrogate data sets cannot be predicted better than the trivial predictor-the mean-while most of the HRV control sequences are predictable to a certain degree. This suggests that the normal HRV signals have a deterministic signature. The HRV time series derived from the autonomic blockade segments of the experimental protocols do not show the same predictability performance, albeit the physiological interpretation is not obvious. These results have important implications to the methodology of HRV analysis, indicating that techniques from nonlinear dynamics and deterministic chaos may be applied to elicit more information about the autonomic modulation of the cardiovascular activity. (c) 2000 American Institute of Physics.     

Research on the relationship between the multifractality and long memory of realized volatility in the SSECI

We examine the multifractal properties of the realized volatility (RV) and realized bipower variation (RBV) series in the Shanghai Stock Exchange Composite Index (SSECI) by using the multifractal detrended fluctuation analysis (MF-DFA) method. We find that there exist distinct multifractal characteristics in the volatility series. The contributions of two different types of source of multifractality, namely, fat-tailed probability distributions and nonlinear temporal correlations, are studied. By using the unit root test, we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive.     

Mean reversion in the current account of forty-eight african countries: Evidence from the Panel SURADF test

Here, the Panel seemingly unrelated regressions augmented Dickey-Fuller test (SURADF) test, first introduced and advanced by Breuer et al. [Misleading inferences from panel unit-root tests with an illustration from purchasing power parity, Rev. Int. Econ. 9(3) (2001) 482-493], is used to investigate the mean-reverting behavior of the current account of 48 African countries during the 1980-2004 periods. The empirical results from numerous panel-based unit root tests, conducted earlier, indicated that the current account of each of these countries is stationary; however, when Breuer et al.'s (2001) Panel SURADF test is conducted, it is found that a unit root exists in the current account of 11 of the countries studied. These results have one extremely important policy implication for the 48 African countries studied: the current account deficit of most is sustainable, and thus signifying that those nations should have no incentive to default on their international debt.     

Testing for unit root bilinearity in the Brazilian stock market

In this paper a simple test for detecting bilinearity in a stochastic unit root process is used to test for the presence of nonlinear unit roots in Brazilian equity shares. The empirical evidence for a set of 53 individual stocks, after adjusting for GARCH effects, suggests that for more than 66%, the hypothesis of unit root bilinearity is accepted. Therefore, the dynamics of Brazilian share prices is in conformity with this type of nonlinearity. These nonlinearities in spot prices may emerge due to the sophistication of the derivatives market.     

Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics

In a pair of earlier papers the author showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD. Second order accurate divergence-free schemes for MHD have shown themselves to be very useful in several areas of science and engineering. However, certain computational MHD problems would be much benefited if the schemes had third and higher orders of accuracy. In this paper we show that the reconstruction of divergence-free vector fields can be carried out with better than second order accuracy. As a result, we design divergence-free weighted essentially non-oscillatory (WENO) schemes for MHD that have order of accuracy better than second. A multi-stage Runge–Kutta time integration is used to ensure that the temporal accuracy matches the spatial accuracy. While this is achieved quite simply up to third order in time, going beyond third order is most simply achieved by using the ADER-WENO schemes that are detailed in a companion paper. (ADER stands for Arbitrary Derivative Riemann Problem.) Accuracy analysis is carried out and it is shown that the schemes meet their design accuracy for smooth problems. Stringent tests are also presented showing that the schemes perform well on those tests.     

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.     

Minimum entropy density method for the time series analysis

The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the pattern is revealed most. The MEDM is applied to the financial time series of Standard and Poor’s 500 index from February 1983 to April 2006. Then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis.     

Searching threshold effects in the interest rate: An application to Turkey case

This paper investigates the behaviour of interest rates in Turkey using a two-regime TAR model with an autoregressive unit root. This method recently developed by Caner and Hansen [Threshold autoregression with a unit roots, Econometrica 69 (6) (2001) 1555–1596] allows to simultaneously consider non-stationarity and non-linearity. Our finding indicates that the interest rate is a non-linear series and is characterized by a unit root process over the period 1990:1–2006:5.     

Measures of auditory-visual integration in nonsense syllables and sentences.

For all but the most profoundly hearing-impaired (HI) individuals, auditory-visual (AV) speech has been shown consistently to afford more accurate recognition than auditory (A) or visual (V) speech. However, the amount of AV benefit achieved (i.e., the superiority of AV performance in relation to unimodal performance) can differ widely across HI individuals. To begin to explain these individual differences, several factors need to be considered. The most obvious of these are deficient A and V speech recognition skills. However, large differences in individuals' AV recognition scores persist even when unimodal skill levels are taken into account. These remaining differences might be attributable to differing efficiency in the operation of a perceptual process that integrates A and V speech information. There is at present no accepted measure of the putative integration process. In this study, several possible integration measures are compared using both congruent and discrepant AV nonsense syllable and sentence recognition tasks. Correlations were tested among the integration measures, and between each integration measure and independent measures of AV benefit for nonsense syllables and sentences in noise. Integration measures derived from tests using nonsense syllables were significantly correlated with each other; on these measures, HI subjects show generally high levels of integration ability. Integration measures derived from sentence recognition tests were also significantly correlated with each other, but were not significantly correlated with the measures derived from nonsense syllable tests. Similarly, the measures of AV benefit based on nonsense syllable recognition tests were found not to be significantly correlated with the benefit measures based on tests involving sentence materials. Finally, there were significant correlations between AV integration and benefit measures derived from the same class of speech materials, but nonsignificant correlations between integration and benefit measures derived from different classes of materials. These results suggest that the perceptual processes underlying AV benefit and the integration of A and V speech information might not operate in the same way on nonsense syllable and sentence input.     

A numerical scheme for the integration of the Vlasov–Poisson system of equations, in the magnetized case

We present a numerical algorithm for the solution of the Vlasov–Poisson system of equations, in the magnetized case. The numerical integration is performed using the well-known “splitting” method in the electrostatic approximation, coupled with a finite difference upwind scheme; finally the algorithm provides second order accuracy in space and time. The cylindrical geometry is used in the velocity space, in order to describe the rotation of the particles around the direction of the external uniform magnetic field.Using polar coordinates, the integration of the Vlasov equation is very simplified in the velocity space with respect to the cartesian geometry, because the rotation in the velocity cartesian space corresponds to a translation along the azimuthal angle in the cylindrical reference frame. The scheme is intrinsically symplectic and significatively simpler to implement, with respect to a cartesian one. The numerical integration is shown in detail and several conservation tests are presented, in order to control the numerical accuracy of the code and the time evolution of the entropy, strictly related to the filamentation problem for a kinetic model, is discussed.     

Entropy correlation distance method. The Euro introduction effect on the Consumer Price Index

The idea of entropy was introduced in thermodynamics, but it can be used in time series analysis. There are various ways to define and measure the entropy of a system. Here the so called Theil index, which is often used in economy and finance, is applied as it were an entropy measure. In this study the time series are remapped through the Theil index. Then the linear correlation coefficient between the remapped time series is evaluated as a function of time and time window size and the corresponding statistical distance is defined. The results are compared with the the usual correlation distance measure for the time series themselves. As an example this entropy correlation distance method (ECDM) is applied to several series, as those of the Consumer Price Index (CPI) in order to test some so called globalisation processes. Distance matrices are calculated in order to construct two network structures which are next analysed. The role of two different time scales introduced by the Theil index and a correlation coefficient is also discussed. The evolution of the mean distance between the most developed countries is presented and the globalisation periods of the prices discussed. It is finally shown that the evolution of mean distance between the most developed countries on several networks follows the process of introducing the European currency — the Euro. It is contrasted to the GDP based analysis. It is stressed that the entropy correlation distance measure is more suitable in detecting significant changes, like a globalisation process than the usual statistical (correlation based) measure.     

Virtual pitch integration for asynchronous harmonics

This experiment examined the generation of virtual pitch for harmonically related tones that do not overlap in time. The interval between successive tones was systematically varied in order to gauge the integration period for virtual pitch. A pitch discrimination task was employed, and both harmonic and nonharmonic tone series were tested. The results confirmed that a virtual pitch can be generated by a series of brief, harmonically related tones that are separated in time. Robust virtual pitch information can be derived for intervals between successive 40-ms tones of up to about 45 ms, consistent with a minimum estimate of integration period of about 210 ms. Beyond intertone intervals of 45 ms, performance becomes more variable and approaches an upper limit where discrimination of tone sequences can be undertaken on the basis of the individual frequency components. The individual differences observed in this experiment suggest that the ability to derive a salient virtual pitch varies across listeners.