On- and offline detection of structural breaks in thermal spraying processes

We investigate and develop methods for structural break detection, considering time series from thermal spraying process monitoring. Since engineers induce technical malfunctions during the processes, the time series exhibit structural breaks at known time points, giving us valuable information to conduct the investigations. First, we consider a recently developed robust online (also real-time) filtering (i.e. smoothing) procedure that comprises a test for local linearity. This test rejects when jumps and trend changes are present, so that it can also be useful to detect such structural breaks online. Second, based on the filtering procedure we develop a robust method for the online detection of ongoing trends. We investigate these two methods as to the online detection of structural breaks by simulations and applications to the time series from the manipulated spraying processes. Third, we consider a recently developed fluctuation test for constant variances that can be applied offline, i.e. after the whole time series has been observed, to control the spraying results. Since this test is not reliable when jumps are present in the time series, we suggest data transformation based on filtering and demonstrate that this transformation makes the test applicable.     

Further Investigation of the Uncertain Unit Root in GNP

A more powerful version of the augmented Dickey–Fuller test and a test that has trend stationarity as the null are applied to U.S. gross national product. Simulated critical values generated from plausible trend- and difference-stationary models are used to minimize possible finite-sample biases. The discriminatory power of the two tests is evaluated using alternative-specific rejection frequencies. For postwar quarterly data, these two tests do not provide a definite conclusion. When analyzing annual data over the 1869–1986 period, however, the unit-root null is rejected, but the trend-stationary null is not.     

Testing for spurious and cointegrated regressions: A wavelet approach

This paper proposes a wavelet-based approach to analyze spurious and cointegrated regressions in time series. The approach is based on the properties of the wavelet covariance and correlation in Monte Carlo studies of spurious and cointegrated regression. In the case of the spurious regression, the null hypotheses of zero wavelet covariance and correlation for these series across the scales fail to be rejected. Conversely, these null hypotheses across the scales are rejected for the cointegrated bivariate time series. These nonresidual-based tests are then applied to analyze if any relationship exists between the extraterrestrial phenomenon of sunspots and the earthly economic time series of oil prices. Conventional residual-based tests appear sensitive to the specification in both the cointegrating regression and the lag order in the augmented Dickey–Fuller tests on the residuals. In contrast, the wavelet tests, with their bootstrap t-statistics and confidence intervals, detect the spuriousness of this relationship.     

True Versus Spurious Long Memory: Some Theoretical Results and a Monte Carlo Comparison

A common feature of financial time series is their strong persistence. Yet, long memory may just be the spurious effect of either structural breaks or slow switching regimes. We explore the effects of spurious long memory on the elasticity of the stock market price with respect to volatility and show how cross-sectional aggregation may generate spurious persistence in the data. We undertake an extensive Monte Carlo study to compare the performance of five tests, constructed under the null of true long memory versus the alternative of spurious long memory due to level shifts or breaks.     

Detection and correction of artificial shifts in climate series

Summary.  Many long instrumental climate records are available and might provide useful information in climate research. These series are usually affected by artificial shifts, due to changes in the conditions of measurement and various kinds of spurious data. A comparison with surrounding weather-stations by means of a suitable two-factor model allows us to check the reliability of the series. An adapted penalized log-likelihood procedure is used to detect an unknown number of breaks and outliers. An example concerning temperature series from France confirms that a systematic comparison of the series together is valuable and allows us to correct the data even when no reliable series can be taken as a reference.     

结构突变趋势平稳过程与随机趋势过程的虚假回归研究

 内容提要：在已有研究的基础上,本文更为深入的研究含有结构突变的趋势平稳变量与随机趋势变量间的虚假回归问题。本文推导出OLS估计下DW统计量、F统计量以及R2的极限分布,并且将回归模型扩展到动态情形下,推导出用于Granger因果检验的F统计量的极限分布;采用Monte Carlo模拟方法分析了数据生成过程的各项参数对各统计量有限样本分布的影响;最后,本文分析了在有限样本下,数据生成过程的各项参数对虚假回归及虚假Granger因果关系发生概率的影响。     

基于自相关视角的弱平稳过程之间的伪回归分析

随机干扰项之间的未知形式自相关是导致相互独立的弱平稳过程之间伪回归的主要原因.通过理论分析和一系列的蒙特卡罗模拟,揭示了数据过程本身的持久性、样本容量T和随机干扰项自相关之间的内在联系.研究发现随机干扰项往往呈现出与数据过程阶数相同的自相关.进一步研究表明,运用广义差分法和Cochrane- Orcutt迭代法虽然能大大减少伪回归概率,但在有些情况下,即使当样本容量较大时,较高阶的Cochrane- Orcutt迭代法仍然无法避免伪回归的发生.     

Page's sequential procedure for change-point detection in time series regression

In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change and is best under early change scenarios. For later changes their finite sample behavior is rather questionable. We therefore propose modified CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple time series regression models, that show a higher stability with respect to the time of change than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the consistency of the procedures are provided. In a simulation study it is shown that the proposed procedures behave well in finite samples. Finally the procedures are applied to a set of capital asset pricing data related to the Fama–French extension of the CAPM.     

Spurious regression between long memory series due to mis-specified structural breaks

This article examines the spurious regression phenomenon between long memory series if the generating mechanism of individual series is assumed to follow a stationary/nonstationary process with mis-specified breaks. By using least-squares regression, the t-ratio becomes divergent and spurious regression is present. The intuition behind this is that the long memory series with change points can increase persistency in the level of regression errors and cause such spurious relationship. Simulation results indicate that the extent of spurious regression heavily relies on memory index, sample size, and location of break. As a remedy, we employ a four-stage procedure motivated by Maynard, Smallwood and Wohar (2013 Maynard, A., Smallwood, A., Wohar, M. E. (2013). Long memory regressors and predictive testing: a two-stage rebalancing approach. Econometric Reviews 32:318–360.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Econ. Rev., 32, 318–360) to alleviate the size distortions. Finally, an empirical illustration using some stock price data from Shanghai Stock Exchange is reported.     

基于傅里叶变换的含确定性趋势结构突变的协整回归模型和不等方差检验

一般来说,数据结构突变点的位置是未知的或突变点的存在性无法准确预知。Enders和Lee（2009,2011）[1][2]证明低频的傅里叶变换（Fourier transformation）就能较精确地处理单位根检验中的数据结构突变（异质结构突变）问题。本文在协整模型框架下,使用傅里叶变换处理协整模型确定性趋势项下的结构突变,考察了协整模型参数的收敛速度,并重新推导了不等方差检验。傅里叶近似项参数的收敛速度为： 。使用蒙特卡洛模拟表明：在缺乏结构突变的先验知识的情况下,使用低频的傅里叶变换能较好地处理协整回归中的确定性趋势的结构突变的问题,显著提高协整向量的估计效率。使用改进后的方法,重新研究了中国股市和国际股市联动关系的密切程度,实证结果更为强烈地支持：中国投资者投资于澳大利亚市场分散风险的收益显著弱于投资其他国际市场。     

On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

Elliott and Müller (2006) considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-called qL?L test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald (SW) test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the SW test does not show this non-monotonicity and its power is far superior to the qL?L test when the break is not very small. We claim that the optimality of the qL?L test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use fixed-break size asymptotic approximations to assess the relative efficiency or power of the two tests. When doing so, it is shown that the SW test indeed dominates the qL?L test and, in many cases, the latter has zero relative asymptotic efficiency.     

Long memory versus structural breaks: An overview

We discuss the increasing literature on misspecifying structural breaks or more general trends as long-range dependence. We consider tests on structural breaks in the long-memory regression model as well as the behaviour of estimators of the memory parameter when structural breaks or trends are in the data but long memory is not. Methods for distinguishing both of these phenomena are proposed. The financial support of Volkswagenstiftung is gratefully acknowledged.     

Forecasting With Nonspurious Factors in U.S. Macroeconomic Time Series

This study examines the practical implications of the fact that structural changes in factor loadings can produce spurious factors (or irrelevant factors) in forecasting exercises. These spurious factors can induce an overfitting problem in factor-augmented forecasting models. To address this concern, we propose a method to estimate nonspurious factors by identifying the set of response variables that have no structural changes in their factor loadings. Our theoretical results show that the obtained set may include a fraction of unstable response variables. However, the fraction is so small that the original factors are able to be identified and estimated consistently. Moreover, using this approach, we find that a significant portion of 132 U.S. macroeconomic time series have structural changes in their factor loadings. Although traditional principal components provide eight or more factors, there are significantly fewer nonspurious factors. The forecasts using the nonspurious factors can significantly improve out-of-sample performance.     

A note on spurious regression in seasonal time series

This paper considers spurious regression between two different types of seasonal time series: one with a deterministic seasonal component and the other with a stochastic seasonal component. When one type of seasonal time series is regressed on the other type and they are independent of each other, the phenomenon of spurious regression occurs. Asymptotic properties of the regression coefficient estimator and the associated regression ‘t-ratio’ are studied. A Monte Carlo simulation study is conducted to confirm the phenomenon of spurious regression and spurious rejection of seasonal cointegration for finite samples.     

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.     

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.     

Critical values for unit root tests in seasonal time series

SUMMARY In this paper, we present tables with critical values for a variety of tests for seasonal and non-seasonal unit roots in seasonal time series. We consider (extensions of) the Hylleberg et al. and Osborn et al. test procedures. These extensions concern time series with increasing seasonal variation and time series with structural breaks in the seasonal means. For each case, we give the appropriate auxiliary test regression, the test statistics, and the corresponding critical values for a selected set of sample sizes. We also illustrate the practical use of the auxiliary regressions for quarterly new car sales in the Netherlands. Supplementary to this paper, we provide Gauss programs with which one can generate critical values for particular seasonal frequencies and sample sizes.     

HAC法在平稳过程之间伪回归中的适用性研究

通过蒙特卡罗模拟技术揭示各种HAC法在平稳过程伪回归中的适用性.研究发现,与核权函数HAC相比,预白化HAC法具有明显的优势;进一步的研究表明相对于被解释变量的持久性,解释变量的持久性对HAC的影响较大;当数据过程是高阶自回归过程时,在样本容量不是很大的情况下预白化方法的拒绝率会随着阶数增加而增大,只有在样本容量较大和BIC信息准则情况下预白化HAC的拒绝率才接近检验水平.     

Analysis of structural break models based on the evolutionary spectrum: Monte Carlo study and application

We investigate the instability problem of the covariance structure of time series by combining the non-parametric approach based on the evolutionary spectral density theory of Priestley [Evolutionary spectra and non-stationary processes, J. R. Statist. Soc., 27 (1965), pp. 204–237; Wavelets and time-dependent spectral analysis, J. Time Ser. Anal., 17 (1996), pp. 85–103] and the parametric approach based on linear regression models of Bai and Perron [Estimating and testing linear models with multiple structural changes, Econometrica 66 (1998), pp. 47–78]. A Monte Carlo study is presented to evaluate the performance of some parametric testing and estimation procedures for models characterized by breaks in variance. We attempt to see whether these procedures perform in the same way as models characterized by mean-shifts as investigated by Bai and Perron [Multiple structural change models: a simulation analysis, in: Econometric Theory and Practice: Frontiers of Analysis and Applied Research, D. Corbea, S. Durlauf, and B.E. Hansen, eds., Cambridge University Press, 2006, pp. 212–237]. We also provide an analysis of financial data series, of which the stability of the covariance function is doubtful.     

Multivariate temporal disaggregation with cross-sectional constraints

Multivariate temporal disaggregation deals with the historical reconstruction and nowcasting of economic variables subject to temporal and contemporaneous aggregation constraints. The problem involves a system of time series that are related not only by a dynamic model but also by accounting constraints. The paper introduces two fundamental (and realistic) models that implement the multivariate best linear unbiased estimation approach that has potential application to the temporal disaggregation of the national accounts series. The multivariate regression model with random walk disturbances is most suitable to deal with the chained linked volumes (as the nature of the national accounts time series suggests); however, in this case the accounting constraints are not binding and the discrepancy has to be modeled by either a trend-stationary or an integrated process. The tiny, compared with other driving disturbances, size of the discrepancy prevents maximum-likelihood estimation to be carried out, and the parameters have to be estimated separately. The multivariate disaggregation with integrated random walk disturbances is suitable for the national accounts aggregates expressed at current prices, in which case the accounting constraints are binding.