中国居民消费的数据生成过程研究

如果非平稳总量时序列存在结构变化，那么传统的单位根检验往往会得出错误的统计推断。在考虑经济结构变化的基础上，对中国居民消费时序列是具有单位根的非平稳还是分段趋势平稳进行研究，结果发现该时序列是围绕着1个结构断点的分段趋势平稳。分段趋势平稳的结论说明政策主导下的长期经济发展战略能够改变居民消费总量的增长路径；短期消费政策也是值得应用的。     

STAR模型中的递归退势单位根检验研究

在STAR模型框架下,考虑时间序列具有线性确定性趋势成分,本文建立了一个递归退势单位根检验统计量,推导了其渐近分布;并在考虑初始条件情形下,对递归退势、OLS和GLS退势单位根检验统计量的有限样本性质进行了细致的比较研究。若忽略初始条件的影响,GLS退势和递归退势单位根检验统计量的检验势都显著高于OLS退势。随着初始条件的增大,GLS退势单位根检验统计量的检验势下降得比较厉害,递归退势单位根检验统计量的检验势较为稳定,且在样本量较大情形下更具优势。     

Some partially sequential nonparametric tests for detecting linear trend

In the present study, we develop two nonparametric partially sequential tests for detecting possible presence of linear trend among the incoming series of observations. We assume that a sample of fixed size is available a priori from some unknown univariate continuous population and there is no sign of trend among these historical observations. Our proposed tests can be viewed as the sequential type tests for monitoring structural changes. We use partial sequential sampling schemes based on usual ranks as well as on sequential ranks. We provide detailed discussion on asymptotic studies related to the proposed tests. We compare the two tests under various situations. We also present some numerical results based on simulation studies. Proposed tests are extremely important in profit making in volatile market through Margin Trading. We illustrate the mechanism with a detailed analysis of a stock price data.     

Nonparametric Nonlinear Cotrending Analysis,With an Application to Interest and Inflation in the United States

Given the assumption that the components of a vector time series are stationary around nonlinear deterministic time trends, nonlinear cotrending is the phenomenon that one or more linear combinations of the time series are stationary around a linear trend or a constant; hence, the series have common nonlinear deterministic time trends. In this article, I develop nonparametric tests for nonlinear cotrending, and I derive nonparametric estimators of the cotrending vectors. I apply this approach to the federal funds rate and the consumer price index inflation rate in the United States, using monthly data, to analyze the price puzzle.     

Testing nested and non-nested periodically integrated autoregressive models

Periodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing sea- sonal fluctuations for the non-periodic integrated series can be described by seasonal dummy variables for which the corresponding parameters are not constant within the sampie, such a series may not be easily & stinguished from a periodically integrated time series. In this paper, nested and non-nested testing procedures are proposed to distinguish between these two alternative stochastic and non-stochastic seasonal processes, When it is assumed there is a single unknown structural break in the seasonal dummy parameters. Several empirical examples using quarterly real macroeconomic time series for the United Kingdom illustrate the nested and non-nested approaches.     

Nonparametric Phase-II monitoring for detecting monotone trend based on inverse sampling

Recently, Mukherjee and Bandyopadhyay (J Stat Plan Inference, 2011, doi:10.1016/j.jspi.2011.02.017) introduced some partially sequential tests for detecting liner trend among the incoming series of observations when a training sample is available a-priori. Their work is very useful in econometric or environmental monitoring under certain situations. The present work is intended for generalization of their tests for any monotone trend. We develop two nonparametric tests for the identity of some unknown univariate continuous distribution functions against monotone or unidirectional trend in location. One of these two tests is based on usual ranks and the other is based on sequential ranks. These are typical nonparametric tests for monitoring structural changes. Performance of the two tests are compared using asymptotic studies as well as through some numerical results based on Monte-Carlo simulations. An illustration is offered using a real data on monthly production of certain beverage.     

THE BEHAVIOR OF HEGY TESTS FOR QUARTERLY TIME SERIES WITH SEASONAL MEAN SHIFTS

ABSTRACT

This paper studies the behavior of the HEGY statistics for quarterly data, for seasonal autoregressive unit roots, when the analyzed time series is deterministic seasonal stationary but exhibits a change in the seasonal pattern. We analyze also the HEGY test for the nonseasonal unit root. the data generation process being trend stationary too. Our results show that when the break magnitudes are finite, the HEGY test statistics are not asymptotically biased toward the nonrejection of the seasonal and nonseasonal unit root hypotheses. However, the finite sample power properties may be substantially affected, the behavior of the tests depending on the type of the break.     

A multivariate long-memory model with structural breaks

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, the time series exhibits possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure that minimizes the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break, our findings are similar to those of earlier studies based on a standard VAR approach in both the countries, such that the variables exhibit integer degrees of integration. On the contrary, the series is found to be fractionally integrated after the break, with the fractional differencing parameters being higher than one in the case of Mexico.     

Further Evidence on the Great Crash,the Oil-Price Shock,and the Unit-Root Hypothesis

Recently, Perron has carried out tests of the unit-root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil-price shock. His analysis covers the Nelson–Plosser macroeconomic data series as well as a postwar quarterly real gross national product (GNP) series. His tests reject the unit-root null hypothesis for most of the series. This article takes issue with the assumption used by Perron that the Great Crash and the oil-price shock can be treated as exogenous events. A variation of Perron's test is considered in which the breakpoint is estimated rather than fixed. We argue that this test is more appropriate than Perron's because it circumvents the problem of data-mining. The asymptotic distribution of the estimated breakpoint test statistic is determined. The data series considered by Perron are reanalyzed using this test statistic. The empirical results make use of the asymptotics developed for the test statistic as well as extensive finite-sample corrections obtained by simulation. The effect on the empirical results of fat-tailed and temporally dependent innovations is investigated, in brief, by treating the breakpoint as endogenous, we find that there is less evidence against the unit-root hypothesis than Perron finds for many of the data series but stronger evidence against it for several of the series, including the Nelson-Plosser industrial-production, nominal-GNP, and real-GNP series.     

Markov Regime Switching and Unit-Root Tests

We investigate the power and size performance of unit-root tests when the data undergo Markov regime switching. All tests, including those robust to a single break in trend growth rate, have low power against a process with a Markov-switching trend. Under the null hypothesis, we find that previously documented size distortions in Dickey–Fuller-type tests caused by a single break in trend growth rate or variance do not generalize to most parameterizations of Markov switching in trend or variance. However, Markov switching in variance can lead to overrejection in tests allowing for a single break the level of trend.     

Evaluation of Recursive Detection Methods for Turning Points in Financial Time Series

Timely identification of turning points in economic time series is important for planning control actions and achieving profitability. This paper compares sequential methods for detecting peaks and troughs in stock values and deciding the time to trade. Three semi‐parametric methods are considered: double exponential smoothing, time‐varying parameters and prediction error statistics. These methods are widely used in monitoring, forecasting and control, and their common features are recursive computation and exponential weighting of observations. The novelty of this paper is the selection of smoothing and alarm coefficients for maximisation of the gain (the difference in level between subsequent peaks and troughs) of sample data. The methods are compared on applications to leading financial series and with simulation experiments.     

A recursive approach to parameter estimation in regression and time series models

In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated with an example.     

Unit roots and double smooth transitions

Techniques for testing the null hypothesis of difference stationarity against stationarity around some deterministic function have received much attention. In particular, unit root tests where the alternative is stationarity around a smooth transition in a linear trend have recently been proposed to permit the possibility of non-instantaneous structural change. In this paper we develop tests extending such an approach in order to admit more than one structural change. The analysis is motivated by time series that appear to undergo two smooth transitions in the linear trend, and the application of the new tests to two such series (average global temperature and US consumer prices) highlights the benefits of this double transition extension.     

2005年汇改后人民币汇率多次结构突变检验分析——基于循序检验方法

采用最新的多次结构突变循序检验方法,对2005年7月21日汇改后人民币汇率时间序列趋势项是否具有多次结构突变进行研究,并在多次结构突变检验结果的基础上对消除趋势后的人民币汇率数据进行分析,结果发现：人民币汇率时间序列是围绕着4个结构断点的分段趋势平稳的;人民币汇率服从分段趋势平稳的结论对汇率政策有效性、汇率与其他经济总量关系研究及汇率预测具有重要意义。     

Variance Shifts,Structural Breaks,and Stationarity Tests

This article considers the problem of testing the null hypothesis of stochastic stationarity in time series characterized by variance shifts at some (known or unknown) point in the sample. It is shown that existing stationarity tests can be severely biased in the presence of such shifts, either oversized or undersized, with associated spurious power gains or losses, depending on the values of the breakpoint parameter and on the ratio of the prebreak to postbreak variance. Under the assumption of a serially independent Gaussian error term with known break date and known variance ratio, a locally best invariant (LBI) test of the null hypothesis of stationarity in the presence of variance shifts is then derived. Both the test statistic and its asymptotic null distribution depend on the breakpoint parameter and also, in general, on the variance ratio. Modifications of the LBI test statistic are proposed for which the limiting distribution is independent of such nuisance parameters and belongs to the family of Cramér–von Mises distributions. One such modification is particularly appealing in that it is simultaneously exact invariant to variance shifts and to structural breaks in the slope and/or level of the series. Monte Carlo simulations demonstrate that the power loss from using our modified statistics in place of the LBI statistic is not large, even in the neighborhood of the null hypothesis, and particularly for series with shifts in the slope and/or level. The tests are extended to cover the cases of weakly dependent error processes and unknown breakpoints. The implementation of the tests are illustrated using output, inflation, and exchange rate data series.     

Recursive Estimation of GARCH Models

This article develops three recursive on-line algorithms, based on a two-stage least squares scheme for estimating generalized autoregressive conditionally heteroskedastic (GARCH) models. The first one, denoted by 2S-RLS, is an adaptation of the recursive least squares method for estimating autoregressive conditionally heteroskedastic (ARCH) models. The second and the third ones (denoted, respectively, by 2S-PLR and 2S-RML) are adapted versions of the pseudolinear regression (PLR) and the recursive maximum likelihood (RML) methods to the GARCH case. We show that the proposed algorithms give consistent estimators and that the 2S-RLS and the 2S-RML estimators are asymptotically Gaussian. These methods seem very adequate for modeling the sequential feature of financial time series, which are observed on a high-frequency basis. The performance of these algorithms is shown via a simulation study.     

Bayesian tests for unit root and multiple breaks

A Bayesian approach is considered for identifying sources of nonstationarity for models with a unit root and breaks. Different types of multiple breaks are allowed through crash models, changing growth models, and mixed models. All possible nonstationary models are represented by combinations of zero or nonzero parameters associated with time trends, dummy for breaks, or previous levels, for which Bayesian posterior probabilities are computed. Multiple tests based on Markov chain Monte Carlo procedures are implemented. The proposed method is applied to a real data set, the Korean GDP data set, showing a strong evidence for two breaks rather than the usual unit root or one break.     

Small-Sample Improved Seasonal Unit Root Tests for Trending and Breaking Series

In this article three unit root tests that allow for a break in both the seasonal mean and linear trend of the data are proposed. The tests, which can be seen as small-sample corrected versions of already known asymptotic tests, are shown to perform very well in simulations, and much better than their asymptotic counterparts.     

F-tests for seasonal differencing with a break-point

The classification between stochastic trend stationarity and deterministic broken trend stationarity is important because incorrect inferences can follow if a stationary series with a broken trend is incorrectly classified as integrated. In this paper, we consider joint tests for regular and seasonal unit roots null hypothesis against broken trend stationarity alternatives where the location of the break is known or unknown. Based on the F-test proposed by Hasza and Fuller (1982, Ann. Statist. 10, 1209–1216), we develop testing procedures for distinguishing these two types of process. The asymptotic distributions of test statistics are derived as functions of Wiener processes. A response surface regression analysis directed to relating the finite sample distributions and the breaking position is studied. Simulation experiments suggest that the power of the test is reasonable. The testing procedure is illustrated by the Canadian consumer price index series.     

Testing and dating structural changes in copula-based dependence measures

This paper is concerned with testing and dating structural breaks in the dependence structure of multivariate time series. We consider a cumulative sum (CUSUM) type test for constant copula-based dependence measures, such as Spearman''s rank correlation and quantile dependencies. The asymptotic null distribution is not known in closed form and critical values are estimated by an i.i.d. bootstrap procedure. We analyze size and power properties in a simulation study under different dependence measure settings, such as skewed and fat-tailed distributions. To date breakpoints and to decide whether two estimated break locations belong to the same break event, we propose a pivot confidence interval procedure. Finally, we apply the test to the historical data of 10 large financial firms during the last financial crisis from 2002 to mid-2013.