kernel density estimation for linear processes in this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one sided linear processes the conjecture that asymptotic normality for the kernel density estimator holds under short range dependence is proved under minimal assumptions on bandwidths we also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when the process is long range dependent

bogomolov multipliers and retract rationality for semidirect products abstract let g be a finite group the bogomolov multiplier b 0 g is constructed as an obstruction to the rationality of c v g where g g l v is a faithful representation over c we prove that for any finite groups g 1 and g 2 b 0 g 1 g 2 b 0 g 1 b 0 g 2 under the restriction map if g n g 0 with gcd n g 0 1 then b 0 g b 0 n g 0 b 0 g 0 under the restriction map for any integer n we show that there are non direct product p groups g 1 and g 2 such that b 0 g 1 and b 0 g 2 contain subgroups isomorphic to z p z n and z p n z respectively on the other hand if k is an infinite field and g n g 0 where n is an abelian normal subgroup of exponent e satisfying that e k we will prove that if k g 0 is retract k rational then k g is also retract k rational provided that certain local conditions are satisfied this result generalizes previous results of saltman and jambor 18

noether s problem for some semidirect products abstract let k be a field g be a finite group k x g g g be the rational function field with the variables x g where g g the group g acts on k x g g g by k automorphisms where h x g x h g for all h g g let k g be the fixed field defined by k g k x g g g g f k x g g g h f f for all h g noether s problem asks whether the fixed field k g is rational purely transcendental over k let m and n be positive integers and assume that there is an integer t such that t z m z is of order n define a group g m n m n 1 1 t c m c n assume furthermore that i m is an odd integer and ii for any e n the ideal e t m in z e is a principal ideal where e is a primitive e th root of unity theorem if k is a field with m n k then k g m n is rational over k consequently it may be shown that for any positive integer n the set s p p is a prime number such that c g p n is rational over c is of positive dirichlet density in particular s is an infinite set

central limit theorems for quadratic forms with time domain conditions we establish the central limit theorem for quadratic forms t s 1 n b t s p m n x t x s of the bivariate appell polynomials p m n x t x s under time domain conditions these conditions relate the weights b t and the covariances of the sequences p m n x t x s and x t the time domain approach together with the spectral domain approach developed earlier yields a general set of conditions for central limit theorems

some convergence results on quadratic forms for random fields and application to empirical covariances limit theorems are proved for quadratic forms of gaussian random fields in presence of long memory we obtain a non central limit theorem under a minimal integrability condition which allows isotropic and anisotropic models we apply our limit theorems and those of ginovian j contemp math anal 34 2 1 15 to obtain the asymptotic behavior of the empirical covariances of gaussian fields which is a particular example of quadratic forms we show that it is possible to obtain a gaussian limit when the spectral density is not in l 2 therefore the dichotomy observed in dimension d 1 between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in d 1

an application of the seasonal fractionally differenced model to the monetary aggregates abstract in this article three significant variables used by the u s federal reserve as targets to shape monetary policy the monetary aggregates m1 m2 and m3 are examined using a seasonal fractionally differenced model the sample autocorrelation functions of these monetary variables exhibit a decay pattern at the seasonal lags that is typical of a fractional model the seasonal fractionally differenced model is found to remove a great deal of the autocorrelation at the seasonal lags especially when a series is extended by splicing together earlier monetary data some monte carlo evidence as to the efficacy of this technique is presented finally one year ahead out of sample forecasts of m1 are made using both the box jenkins airline model and the seasonal fractionally differenced model

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

bias in the sample autocorrelations of fractional noise summary the autocorrelation function of fractional noise when the difference parameter is positive is quite distinctive however for time series of moderate length this pattern is unlikely to be seen in the sample autocorrelations which are severely biased when the process mean is unknown

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

stable convergence acceleration using laplace transforms we consider the general class of power series where the terms may be expressed as the laplace transforms of known functions the sum of the series can then be evaluated efficiently and accurately by means of quadrature schemes recently published by frank stenger the method works also far outside the region of convergence as will be illustrated by numerical examples

noether s problem on semidirect product groups abstract let k be a field g a finite group let g act on the function field l k x g by x x for any g denote the fixed field of the action by k g l g f g l f g f g g noether s problem asks whether k g is rational purely transcendental over k it is known that if g c m c n is a semidirect product of cyclic groups c m and c n with z n a unique factorization domain and k contains an eth primitive root of unity where e is the exponent of g then k g is rational over k in this paper we give another criteria to determine whether k c m c n is rational over k in particular if p q are prime numbers and there exists x z q such that the norm n q q q x p then c c p c q is rational over c

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

indirect estimation of arfima and varfima models indirect estimation methods are proposed for estimating arfima as well as more complex varfima models a general framework for conducting indirect estimation of fractional models is developed that covers simulation methods choice of auxiliary model and estimation algorithm special attention is given to comparing the finite sampling properties of the indirect estimator with sowell s 1992a exact time domain maximum likelihood estimator the spectral maximum likelihood estimator of fox and taqqu 1986 and the geweke and porter hudak 1983 spectral regression estimator the indirect estimator can be computationally faster than the exact time domain maximum likelihood estimator while generating similar small sample properties the computational gains of the indirect estimator over maximum likelihood increase as the complexity of the data generating process increases

bayesian analysis of long memory and persistence using arfima models abstract this paper provides a bayesian analysis of autoregressive fractionally integrated moving average arfima models we discuss in detail inference on impulse responsens and show how bayesian methods can be used to i test arfima models against arima alternatives and ii take model uncertainty into account when making inferences on quantities of interest our methods are then used to investigate the persistence properties of real u s gnp

differentiating intraday seasonalities through wavelet multi scaling it is well documented that strong intraday seasonalities may induce distortions in the estimation of volatility models these seasonalities are also the dominant source for the underlying misspecifications of the various volatility models therefore an obvious route is to filter out the underlying intraday seasonalities from the data in this paper we propose a simple method for intraday seasonality extraction that is free of model selection parameters which may affect other intraday seasonality filtering methods our methodology is based on a wavelet multi scaling approach which decomposes the data into its low and high frequency components through the application of a non decimated discrete wavelet transform it is simple to calculate does not depend on a particular model selection criterion or model specific parameter choices the proposed filtering method is translation invariant has the ability to decompose an arbitrary length series without boundary adjustments is associated with a zero phase filter and is circular being circular helps to preserve the entire sample unlike other two sided filters where data loss occurs from the beginning and the end of the studied sample

clt and other limit theorems for functionals of gaussian processes conditions for the clt for non linear functionals of stationary gaussian sequences are discussed with special references to the borderline between the clt and the non clt examples of the non clt for such functionals with the norming factor sqrt n are given

on two methods for accelerating convergence of series the euler knopp transformation and a recently considered transformation effective for entire function of order 1 are applied to series involving completely monotonic coefficients some properties of the resulting series are analyzed these include uniform convergence with respect to the index a priori and a posteriori estimates of the remainder for the latter transformation a compact recursive algorithm is established which enables one to make effective use of the transformation to illustrate the effectiveness of the transformations three applications with examples are included

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

noncentral limit theorems for quadratic forms in random variables having long range dependence we study the weak convergence in d lbrack 0 1 rbrack of the quadratic form sum lbrack nt rbrack j 1 sum lbrack nt rbrack k 1 a j k h m x j h m x k adequately normalized here a s infty s infty is a symmetric sequence satisfying sum a s infty h m is the m th hermite polynomial and x j j geq 1 is a normalized gaussian sequence with covariances r k sim k d l k as k rightarrow infty where 0 d 1 and l is slowly varying we prove that for all m geq 1 the limit is brownian motion when 1 2 d 1 and it is the non gaussian rosenblatt process when 0 d 1 2

some actions of symmetrical groups abstract let k be any field v the n dimensional vector space over k on which the symmetric group sn acts by permuting a basis then the fixed fields k skv sn and k k v sn are rational over k where skv and k v are the kth symmetric power and exterior power of v respectively the rationality of some other fixed fields are established also

rationality problem for some meta abelian groups abstract let k be any field g be a finite group theorem assume that i g contains an abelian normal subgroup h so that g h is cyclic of order n ii z n is a unique factorization domain and iii e k where e is the exponent of g i e e lcm ord g g g if g gl v is any finite dimensional linear representation of g over k then k v g is rational purely transcendental over k

a central limit theorem for the kpz equation we consider the kpz equation in one space dimension driven by a stationary centred space time random field which is sufficiently integrable and mixing but not necessarily gaussian we show that in the weakly asymmetric regime the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the hopf cole solution to the kpz equation driven by space time gaussian white noise while the limiting process depends only on the integrated variance of the driving field the diverging constants appearing in the definition of the reference frame also depend on higher order moments

some generalizations of the euler knopp transformation the purpose of this paper is to construct a generalization of the euler knopp transformation using this one may recover previously known transformations derive new transformations useful for numerical calculations and derive generating functions and other formulas of theoretical interest involving well known functions

lattices over cyclic groups and noether settings abstract for each positive integer m let m be a primitive mth root of 1 given a prime p let a be an integer which is a primitive root of 1 mod p let i p m be the ideal in z m generated by p and m a let g be a cyclic group of order n such that the flasque class of any maximal projective ideal in z g contains a maximal ideal u of index p for some prime p such that n divides p 1 and such that i p n is principal it is not known whether the number of groups satisfying this property is finite or infinite we show that if f is a field of characteristic zero containing all nth roots of 1 then for any z g lattice m the fixed subfield of f m is stably rational over f if f also contains primitive mth roots of 1 for all natural numbers m then for any finite g module t the fixed subfield of the noether setting of the group g t g is stably rational over f

asymptotic distributions of the sample mean autocovariances and autocorrelations of long memory time series we derive the asymptotic distributions of the sample mean autocovariances and autocorrelations for a time series whose autocovariance function has the powerlaw decay 0 o 1 as the results differ in important respects from the corresponding results for short memory processes whose autocovariance functions are absolutely summable for long memory processes the variances of the sample mean and of the sample autocovariances and autocorrelations for 0 12 are not of asymptotic order n 1 when 0 12 the asymptotic distributions of the sample autocovariances and autocorrelations are not normal

accelerated polynomial approximation of finite order entire functions by growth reduction let f be an entire function of positive order and finite type the subject of this note is the convergence acceleration of polynomial approximants of f by incorporating information about the growth of f z for z we consider near polynomial approximation on a compact plane set k which should be thought of as a circle or a real interval our aim is to find sequences f n n of functions which are the product of a polynomial of degree n and an easy computable second factor and such that f n n converges essentially faster to f on k than the sequence p n n of best approximating polynomials of degree n the resulting method which we call reduced growth method rg method is introduced in section 2 in section 5 numerical examples of the rg method applied to the complex error function and to bessel functions are given

how much information does dependence between wavelet coefficients contain abstractthis article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short as well as long range dependent time series is assumed we focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic to this end we derive asymptotic distributional properties of the sample variance for a time series that is synthesized ignoring some or all dependence between wavelet coefficients we show that the second order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent gaussian case this holds true even if the dependency is correct within each level and only the dependence between levels is ignored in the case of sample autocovariances and sample autocorrelations at lag one we indicate that first order properties are erroneous in a second step we investigate several nonparametric b

noether s problem for metacyclic p groups abstract let k be any field and g be a finite group let g act on the rational function field k x g g g by k automorphisms defined by g x h x gh for any g h g denote by k g the fixed field k x g g g g noether s problem asks whether k g is rational purely transcendental over k an affirmative answer to noether s problem for metacyclic p groups will be proved provided that k contains enough roots of unity

some simple properties of sums of random variables having long range dependence the higher order moments and cumulants of sums of a special case of random variables having long range dependence are investigated tensor methods are used to simplify the calculations the limiting form of the second and third cumulants as the number of variables added becomes large is studied by analytical and numerical methods the implications are discussed for the existence of non gaussian limits of sums of random quantities of finite variance and long range dependence

empirical study of arfima model based on fractional differencing abstract in this paper we studied the long term memory of hong kong hang sheng index using mrs analysis established arfima model for it and detailed the procedure of fractional differencing furthermore we compared the arfima model built by this means with the one that took first order differencing as an alternative the result showed that if doing so much useful information of time series would be lost the forecast formula of arfima model was corrected according to the method of fractional differencing and was employed in the empirical study it was illustrated that the forecast performance of arfima model was not as good as we expected since the arfima model was ineffective in forecasting hang sheng index the certainty of this conclusion was proposed from two different aspects

power variation for a class of stationary increments levy driven moving averages in this paper we present some new limit theorems for power variation of kkth order increments of stationary increments levy driven moving averages in the infill asymptotic setting where the sampling frequency converges to zero while the time span remains fixed the asymptotic theory gives novel results which partially have no counterpart in the theory of discrete moving averages more specifically we show that the first order limit theory and the mode of convergence strongly depend on the interplay between the given order of the increments k 1k 1 the considered power p 0p 0 the blumenthal getoor index 0 2 0 2 of the driving pure jump levy process ll and the behaviour of the kernel function gg at 00 determined by the power first order asymptotic theory essentially comprises three cases stable convergence towards a certain infinitely divisible distribution an ergodic type limit theorem and convergence in probability towards an integrated random process we also prove a second order limit theorem connected to the ergodic type result when the driving levy process ll is a symmetric stable process we obtain two different limits a central limit theorem and convergence in distribution towards a k k stable totally right skewed random variable

an acceleration method for the power series of entire functions of order 1 when f z is given by a known power series expansion it is possible to construct the power series expansion for f z p e sup p z f z we define p sub opt to be the value of p for which the expansion for f z p converges most rapidly when f z is an entire function of order 1 we show that p sub opt is uniquely defined and may be characterized in terms of the set of singularities z sub i 1 sigma sub i of an associated function h z specifically it is the center of the smallest circle in the complex plane which contains all points sigma sub i