a causality in variance test and its application to financial market prices abstract this paper develops a test for causality in variance the test is based on the residual cross correlation function ccf and is robust to distributional assumptions asymptotic normal and asymptotic 2 statistics are derived under the null hypothesis of no causality in variance monte carlo results indicate that the proposed ccf test has good empirical size and power properties two empirical examples illustrate that the causality test yields useful information on the temporal dynamics and the interaction between two time series

configurational properties of dilute polymer solutions dimensionality and perturbation theory by using second order perturbation theory in the small parameter epsilon 4 d to 0 the author determines a specific value of the excluded volume parameter u equivalent to the fixed point value given by renormalisation group theory for this value of the excluded volume parameter each expansion series in epsilon can be summed to an exponential function the author thus studies the total number of configurations c the number of configurations returning to the origin u and the mean square end to end distance r2 of the polymer coil an interdimensional relationship developed by kosmas and freed 1978 is used to extrapolate the authors results to lower dimensions finally the author compares his results with those of previous theories and lattice enumerations discussing possible differences between the gaussian excluded volume model used by him and the self avoiding walk model close to dimensionality d 1

the predictive ability of several models of exchange rate volatility abstract we compare the out of sample forecasting performance of univariate homoskedastic garch autoregressive and nonparametric models for conditional variances using five bilateral weekly exchange rates for the dollar 1973 1989 for a one week horizon garch models tend to make slightly more accurate forecasts for longer horizons it is difficult to find grounds for choosing between the various models none of the models perform well in a conventional test of forecast efficiency

the radius of gyration of a branch of a uniform star polymer the authors use monte carlo methods and perturbation calculations to study the mean square radius of gyration of a branch of a uniform star with excluded volume as a function of the number f of branches and of the number n of monomers per branch they show that the mean square radius of gyration s n f 2 scales like a f n2v f fixed n to infinity where the exponent is independent of f they estimate the amplitude ratios a f a 1 for various values of f and show that these ratios are lattice independent the amplitude ratio increases as f increases but the effect is small the numerical agreement between the two methods is good especially for small values of f

lattice models of branched polymers statistics of uniform stars the authors investigate the statistical properties of uniform star polymers with f branches modelled on lattices in two and three dimensions it is shown that the growth constant exists and is equal to mu f where mu is the self avoiding walk limit the f dependence of the corresponding critical exponent gamma f is studied using exact enumeration and monte carlo techniques and the results are compared with the predictions of miyake and freed 1983 obtained using chain conformation space renormalisation group method

when is a symmetric pin jointed framework isostatic maxwell s rule from 1864 gives a necessary condition for a framework to be isostatic in 2d or in 3d given a framework with point group symmetry group representation theory is exploited to provide further necessary conditions this paper shows how for an isostatic framework these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework in particular it turns out that an isostatic framework in 2d can belong to one of only six point groups some conjectures and initial results are presented that would give sufficient conditions in both 2d and 3d for a framework that is realized generically for a given symmetry group to be an isostatic framework

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

a symmetry extension of maxwell s rule for rigidity of frames a symmetry extension of maxwell s rule for rigidity of frames is found this rule subsumes and strengthens maxwell s 1864 rule by requiring that the internal and external degrees of freedom of a pin jointed structure are not only numerically equal but are also equisymmetric a number of special cases of maxwell s original rule are studied to show the improved insight that the symmetry adapted version can give

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

dimensions of the branches of a uniform brush polymer excluded volume effects increase the dimensions of the various branches of a uniform brush polymer to different extents the authors use monte carlo methods and perturbation calculations to study the mean square end to end branch lengths of a uniform brush with two branch points as a function of the number n of monomers in a branch and the functionalities f1 and f2 of the branch points the mean square end to end length rn2 of a branch scales like bn2v and they investigate how the amplitude b varies for the different types of branch as f1 and f2 vary the amplitude ratios are expected to be lattice independent and they find good agreement between their numerical estimates of these ratios from perturbation and monte carlo calculations they have extended the perturbation calculations to make predictions for the corresponding amplitude ratios for the mean square radii of gyration of the various branches

testing for independence between two covariance stationary time series summary a one sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross correlation function the test statistic is a properly standardised version of the sum of weighted squares of residual cross correlations with weights depending on a kernel function haugh s 1976 test can be viewed as a special case of our approach in the sense that it corresponds to the use of the truncated kernel many kernels deliver better power than haugh s test a simulation study shows that the new test has good power against short and long cross correlations

testing conditional independence via empirical likelihood we construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter one class is based on the cdf another is based on smoother functions we show that the test statistics are asymptotically normal under the null hypothesis and a sequence of pitman local alternatives we also show that the tests possess an asymptotic optimality property in terms of average power simulations suggest that the tests are well behaved in finite samples applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear granger causality test fails to detect

a test for volatility spillover with application to exchange rates abstract this paper proposes a class of asymptotic n 0 1 tests for volatility spillover between two time series that exhibit conditional heteroskedasticity and may have infinite unconditional variances the tests are based on a weighted sum of squared sample cross correlations between two squared standardized residuals we allow to use all the sample cross correlations and introduce a flexible weighting scheme for the sample cross correlation at each lag cheung and ng 1996 test and granger 1969 type regression based test can be viewed as uniform weighting because they give equal weighting to each lag non uniform weighting often gives better power than uniform weighting as is illustrated in a simulation study we apply the new tests to study granger causalities between two weekly nominal u s dollar exchange rates deutschemark and japanese yen it is found that for causality in mean there exists only simultaneous interaction between the two exchange rates for causality in variance there also exists strong simultaneous interaction between them moreover a change in past deutschemark volatility granger causes a change in current japanese yen volatility but a change in past japanese yen volatility does not granger cause a change in current deutschemark volatility

branched polymers in a wedge geometry in three dimensions we investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and we show that the growth constant is equal to f where is the self avoiding walk limit thef and dependences of the corresponding critical exponent f are studied using monte carlo techniques in the casef 1 our results are compared with existing predictions obtained from series expansion and renormalization group methods we have also estimated the amplitudes for the mean square radius of gyration and the mean square end to end branch length our results for the ratio of the mean square radius of gyration of anf star to that of a linear polymer of the same degree of polymerization attached in a similar wedge and the analogous ratio for the mean square end to end branch length are consistent with these ratios being lattice independent quantities

testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression abstract broad classes of diagnostics for serial correlation and or dynamic conditional heteroskedasticity of regression disturbances are considered the classes include statistics with good power against strongly dependent alternatives along with the usual ones that test against weak dependence and many others limiting null distributions are obtained under mild conditions on the dependence structure of the alternative against which the test is derived on moments of the disturbances and on the regressors the various test statistics have a similar overall structure and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives the difference can be slight if the fast fourier transform is used

modeling and estimating the jump risk of exchange rates applications to rmb abstract in this paper we propose a new type of continuous time stochastic volatility model svdj for the spot exchange rate of rmb and other foreign currencies in the model we assume that the change of exchange rate can be decomposed into two components one is the normally small cope innovation driven by the diffusion motion the other is a large drop or rise engendered by the poisson counting process furthermore we develop a mcmc method to estimate our model empirical results indicate the significant existence of jumps in the exchange rate jump components explain a large proportion of the exchange rate change

periodic frameworks and flexibility we formulate a concise deformation theory for periodic bar and joint frameworks in r d and illustrate our algebraic geometric approach on frameworks related to various crystalline structures particular attention is given to periodic frameworks modelled on silica zeolites and perovskites for frameworks akin to tectosilicates which are made of one skeleta of d dimensional simplices with each vertex common to exactly two simplices we prove the existence of a space of periodicity preserving infinitesimal flexes of dimension at least graphic 1 however these infinitesimal flexes need not come from genuine flexibility as shown by rigid examples the changes implicated in passing from a given lattice of periods to a sublattice of periods are illustrated with frameworks modelled on perovskites 1 embed inline graphic 1 gif

a consistent bootstrap test for conditional density functions with time series data this paper presents a new test for evaluating conditional density functions for time series data thereby being applicable to forecasting problems we show that the test statistic is asymptotically distributed standard normal under the null hypothesis and diverges to infinity when the null hypothesis is false we use a bootstrap algorithm to approximate the distribution of the test statistic and show that the bootstrap distribution converges to the asymptotic distribution of the test statistic in probability an application to inflation forecasting is also presented to demonstrate the usefulness of the test

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

moment condition tests for heavy tailed time series abstract we develop an asymptotically chi squared statistic for testing moment conditions e m t 0 0 where m t 0 may be weakly dependent scalar components of m t 0 may have an infinite variance and e m t need not exist for any under the alternative score tests are a natural application and in general a variety of tests can be heavy tail robustified by our method including white noise garch affects omitted variables distribution functional form causation volatility spillover and over identification the test statistic is derived from a tail trimmed sample version of the moments evaluated at a consistent plug in t for 0 depending on the test in question and heaviness of tails t may be any consistent estimator including sub t 1 2 convergent and or asymptotically non gaussian ones since t can be assured not to affect the test statistic asymptotically we adapt bootstrap p value occupation time and covariance determinant methods for selecting the trimming fractile in any sample and apply our statistic to tests of white noise omitted variables and volatility spillover we find it obtains sharp empirical size and strong power while conventional tests exhibit size distortions

sampling rate reduction in multichannel processing of bandpass signals the uniform sampling rate required to reconstruct a deterministic bandpass signal x t having spectrum confined to i1 i2 where i1 0 2 0 2 i2 0 2 0 2 with 0 2 0 depends critically on the positioning of the band and varies from to 2 samples per second the minimum rate of being attained if and only if 0 2 is an integer multiple of if the bandpass signal x is now used as a common input to an even number m of linear time invariant filters to produce m outputs z1 t zm t then it is proved that under a certain independence requirement on the filters a matrix function condition the input x may be reconstructed from samples of the outputs zk t each output being sampled at the uniform rate of m samples second or 1 m th the minimum sampling rate associated with the input the dependence on band position is removed by a partitioning of the set i1 i2 into m disjoint subsets j1 jm of equal length and a subsequent mapping procedure which allows j1

generic combinatorial rigidity of periodic frameworks abstract we give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks the characterization is a true analogue of the maxwell laman theorem from rigidity theory it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms to prove our rigidity theorem we introduce and develop periodic direction networks and z 2 graded sparse colored graphs

finite time and asymptotic behaviour of the maximal excursion of a random walk we evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self similar supports under the assumption of spherical symmetry this distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods we then focus on the early time behaviour of this quantity the instantaneous diffusion exponent n exhibits a systematic overshooting of the long time exponent exact results are obtained in one dimension up to third order in n 1 2 in two dimensions on a regular lattice and on the sierpinski gasket we find numerically that the analytic scaling n an holds