Statistical inference on restricted partial linear regression models with partial distortion measurement errors

We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration.     

Reconstruction of previous failure times and records

For the sequences of independent identically distributed random variables with continuous distributions, we provide the optimal upper bounds for the increments of order and record statistics under condition that the values of future order statistics and records are known. The bounds are expressed in terms of quantiles and absolute moments centered about the quantiles of the parent distribution. We also describe the distributions which approach the bounds with arbitrary desired accuracy.The second author was supported by the Polish State Committee for Scientific Research (KBN) under Grant 5 P03A 012 20Received November 2003     

Detecting changes in a multivariate renewal process

Some recent extreme value asymptotics for multivariate renewal processes are used to derive an asymptotic changepoint test. This test is proven to be consistent in the multivariate framework where we assume that at most one change (AMOC) occurrs in any of the component renewal processes. Since the actual covariance structure is often unknown, we also suggest an appropriate estimate. This research was partially supported by an Auckland University Research Grant and by a travel grant of the Deutsche Forschungsgemeinschaft.     

On distribution-free goodness-of-fit testing of exponentiality

There is a need to test the hypothesis of exponentiality against a wide variety of alternative hypotheses, across many areas of economics and finance. Local or contiguous alternatives are the closest alternatives against which it is still possible to have some power. Hence goodness-of-fit tests should have some power against all, or a huge majority, of local alternatives. Such tests are often based on nonlinear statistics, with a complicated asymptotic null distribution. Thus a second desirable property of a goodness-of-fit test is that its statistic will be asymptotically distribution free. We suggest a whole class of goodness-of-fit tests with both of these properties, by constructing a new version of empirical process that weakly converges to a standard Brownian motion under the hypothesis of exponentiality. All statistics based on this process will asymptotically behave as statistics from a standard Brownian motion and so will be asymptotically distribution free. We show the form of transformation is especially simple in the case of exponentiality. Surprisingly there are only two asymptotically distribution free versions of empirical process for this problem, and only this one has a convenient limit distribution. Many tests of exponentiality have been suggested based on asymptotically linear functionals from the empirical process. We illustrate none of these can be used as goodness-of-fit tests, contrary to some previous recommendations. Of considerable interest is that a selection of well-known statistics all lead to the same test asymptotically, with negligible asymptotic power against a great majority of local alternatives. Finally, we present an extension of our approach that solves the problem of multiple testing, both for exponentiality and for other, more general hypotheses.     

Recent and classical tests for exponentiality: a partial review with comparisons

A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramér-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramér-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study.Received: January 2002/Revised: January 2004     

Distribution theory for the studentized mean for long,short, and negative memory time series

We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the first-difference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size, extending known results to the case of flat-top tapers. We adopt the fixed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values—both the subsampling method and a plug-in approach. Simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well–although the subsampling method appears to be better sized–and provide a viable framework for conducting inference for the mean. In summary, we supply a unified asymptotic theory that covers all different types of memory under a single umbrella.     

Testing the Markov property with high frequency data

This paper develops a framework to nonparametrically test whether discrete-valued irregularly spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates the irregular spacing that characterizes transactions data. Under such an observation rule, the current price duration is independent of a previous price duration given the previous price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Monte Carlo simulations suggest that the asymptotic test has huge size distortions, though a bootstrap-based variant entails reasonable size and power properties in finite samples. As for an empirical illustration, we investigate whether bid–ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid–ask spread. We robustly reject the Markov assumption for two out of the five stocks under scrutiny. Finally, it is reassuring that our results are consistent with two alternative measures of asymmetric information.     

分数布朗运动环境下的美式看涨期权的定价方法

在分数布朗运动模拟算法基础上,提出了分数布朗运动环境下标的资产价格过程的一种数值模拟方法。然后应用于欧式和美式看涨期权定价。结果表明,该方法具有很快的收敛速度,而且基于最小二乘方法和偏最小二乘方法的美式看涨期权价格,都与对应的欧式看涨期权价格几乎完全一样。这恰恰验证了不支付红利的条件下,美式看涨期权不应该提前执行的理论论断。     

Heavy tails versus long-range dependence in self-similar network traffic

Empirical studies of the traffic in computer networks suggest that network traffic exhibits self-similarity and long-range dependence. The ON/OFF model considered in this paper gives a simple 'physical explanation' for these observed phenomena. The superposition of a large number of ON/OFF sources, such as workstations in a computer lab, with strictly alternating and heavy-tailed ON- and OFF-periods, can produce a cumulative workload which converges, in a certain sense, to fractional Brownian motion. Fractional Brownian motion exhibits both self-similarity and long-range dependence. However, there are two sequential limits involved in this limiting procedure, and if they are reversed, the limiting process is stable Levy motion, which is self-similar but exhibits no long-range dependence. We study simulations limit regimes and provide conditions under which either fractional Brownian motion or stable Levy motion appears as limiting process.     

Confidence sets for the date of a single break in linear time series regressions

This paper considers the problem of constructing confidence sets for the date of a single break in a linear time series regression. We establish analytically and by small sample simulation that the current standard method in econometrics for constructing such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that breaks of moderate magnitude are a theoretically and empirically relevant phenomenon, we proceed to develop an appropriate alternative. We suggest constructing confidence sets by inverting a sequence of tests. Each of the tests maintains a specific break date under the null hypothesis, and rejects when a break occurs elsewhere. By inverting a certain variant of a locally best invariant test, we ensure that the asymptotic critical value does not depend on the maintained break date. A valid confidence set can hence be obtained by assessing which of the sequence of test statistics exceeds a single number.     

A simple and effective scanning rule for a multi-channel system

We consider a multi-channel system in which one apparatus makes a sequence of observations, one at a time. By means of scanning, i.e. selecting a channel to be analyzed at any instant and deciding to stop at some stage, it is required to determine the channel in which there is the signal with prescribed constraints on error probabilities. A simple scanning rule, based on a cyclic application of a sequential probability ratio test (SPRT) is proposed for this problem. It is proved that in the case of Brownian motion, the expected scanning time of this rule is equal to the one of the optimal scanning rule (which is known only for this case). The simple structure of this rule permits to obtain corrected Brownian approximations for its characteristics in the case of exponential family of distributions. The same procedure is used in multi-channel change point problem.     

Monotonicity of Rank Statistics in some Non–parametric: Testing Problems

For some non–parametric testing problems (one–sided two–sample problem, k –sample trend problem, testing independence against positive dependence) a partial ordering, denoted by ≥, over the alternatives is defined. This partial ordering expresses the strength of the deviation from the null–hypothesis. All familiar rank tests turn out to become more powerful under "increasing" alternatives; that is, all familiar rank statistics preserve the ordering stochastically in samples whenever it is present between underlying distributions. As a tool, the sample equivalence of ≥ is introduced as a partial ordering over pairs of permutations. Functions, defined on pairs of permutations, which preserve this ordering are studied.     

Optimal impulse control for cash management¶with quadratic holding-penalty costs

This paper studies optimal control for an infinite horizon cash management problem where the cash fund fluctuates as a Brownian motion. Holding-penalty costs are assumed to be a quadratic function of the cash level and there are fixed and proportional transaction costs. Using the “impulse technique”, we prove that optimal control exists and takes the form of a control band policy. Received: 4 January 2001 / Accepted: 5 June 2001     

The risk spillover between China’s economic policy uncertainty and commodity markets: Evidence from frequency spillover and quantile connectedness approaches

Based on the frequency spillover method extended by Baruník and Křehlík (2018), we explore the risk spillover relationship between China’s economic policy uncertainty (CNEPU) and commodity futures in different frequency domains with daily settlement price data of 14 commodity futures in China. The results show that the risk spillover relationship between CNEPU and the commodity market mainly occurs in the short term. Quantile connectedness results show that economic policy uncertainty, which mainly plays the role of risk transmitter, is more closely related to the commodity market during the market boom and recession. Soybeans, soybean meal, and corn have shown high investment value in the process of market recovery, which is exposed to less risk spillover from policy uncertainty. Finally, the economic crisis with different characteristics will have specific impacts on asymmetric risk spillovers based on certain impact mechanisms.     

Pricing perpetual options with stochastic discount interest rates

The aim of this study is to investigate the prices and optimal exercise strategies of certain perpetual American options on the asset under stochastic discount interest model. This is different from Gerber and Shiu (N Am Actuar J 2(3):101–112, 1998), in which the interest force was a constant; here we suppose that the accumulated interest function is perturbed by the standard Brownian motion and Poisson process. We obtain an explicit expression of optimal option-exercise boundary in the case of perpetual put option. Moreover, we get a corresponding result when the individual claim is described by an exponential distribution. Finally, we analyze the influence of certain coefficients in stochastic interest model on the optimal option-exercise boundary.     

Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

Perron [Perron, P., 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361–1401] introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and Andrews [Zivot, E., Andrews, D.W.K., 1992. Further evidence on the great crash, the oil price shock and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251–270], assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable since (a) it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing; (b) if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples.     

The one-sided Kolmogorov-Smirnov test in signal detection problems with Gaussian white noise

In this paper, we investigate the power of the Kolmogorov-Smirnov test for negativity of signals in signal detection problems with Brownian motion noise. Strict unbiasedness and admissibility are established. Moreover, taking up an approach of Häjek and Sidäk (1967) for the classical Brownian bridge case, we compute the directional derivative of the power function at the hypothesis, thus obtaining the principal direction of alternatives of the test. As an application, in a hazard rates set-up, one-sided Rényi-tests may be adjusted by choosing their weight function such that they are most sensitive against a prescribed type of alternatives. Finally, we give some numerical and simulation results.     

Een algemene methode tot leemtevulling

An exposition of the missing plot technique often applied in analysis of variance is given in very general terms.
Non-orthogonality mostly implies heavy computations. If the scheme of observations is almost orthogonal this technique, however, supplies in a simple way unbiassed and efficient estimates of the expectation values which occur in a linear hypothesis underlying an analysis of variance. Moreover the correct residual sum of squares required for a test or a confidence interval estimation is obtained without difficulty.
A correct test of an effect or an interaction will be provided by two estimates, the first under the null-hypothesis, the second under the alternative hypothesis. In the case of non-orthogonality this may imply two separate applications of the discussed technique. The difference between the two residual sums of squares will be used for the numerator of a valid F-criterion.
The technique is illustrated by an example.     

后现代组织理论与作业成本法的整合研究

后现代组织是20世纪80年代开始由变革浪潮催生的新型组织,这种新型组织突破了20世纪初设计成本系统的关键假设,制造成本法所产生的成本信息相关性消失,作业成本法作为备选方案被运用。本文认为,后现代组织理论与作业成本法之间存在理论上的逻辑关系,对其进行整合研究不仅具有理论价值,也具有现实意义。     

Tests for Stationarity in Series with Endogenously Determined Structural Change*

We consider tests of the null hypothesis of stationarity against a unit root alternative, when the series is subject to structural change at an unknown point in time. Three extant tests are reviewed which allow for an endogenously determined instantaneous structural break, and a related fourth procedure is introduced. We further propose tests which permit the structural change to be gradual rather than instantaneous, allowing the null hypothesis to be stationarity about a smooth transition in linear trend. The size and power properties of the tests are investigated, and the tests are applied to four economic time series.