Statistical Inference for Nonstationary Processes

In this chapter, statistical inference for nonstationary processes is discussed. For long-memory, or, more generally, fractional stochastic processes this is of particular interest because long-range dependence often generates sample paths that mimic certain features of nonstationarity. It is therefore often not easy to distinguish between stationary long-memory behaviour and nonstationary structures. For statistical inference, including estimation, testing and forecasting, the distinction between stationary and nonstationary, as well as between stochastic and deterministic components, is essential.

[1]  Yuhong Yang,et al.  Nonparametric Regression with Correlated Errors , 2001 .

[2]  J. Beran,et al.  Volatility of Stock-Market Indexes—An Analysis Based on SEMIFAR Models , 2001 .

[3]  S. Johansen.  Likelihood-Based Inference in Cointegrated Vector Autoregressive Models , 1996 .

[4]  Elias Masry,et al.  Local linear regression estimation under long-range dependence: Strong consistency and rates , 2001, IEEE Trans. Inf. Theory.

[5]  D. Picard.  Testing and estimating change-points in time series , 1985, Advances in Applied Probability.

[6]  S. Lahiri,et al.  On bandwidth choice in nonparametric regression with both short- and long-range dependent errors , 1995 .

[7]  J. Hualde.  Cointegration in Fractional Systems with Unkown Integration Orders , 2003 .

[8]  Yuanhua Feng.  SIMULTANEOUSLY MODELING CONDITIONAL HETEROSKEDASTICITY AND SCALE CHANGE , 2004, Econometric Theory.

[9]  Uffe Andersen,et al.  The δ18O record along the Greenland Ice Core Project deep ice core and the problem of possible Eemian climatic instability , 1997 .

[10]  Clifford M. Hurvich,et al.  Computationally Efficient Methods for Two Multivariate Fractionally Integrated Models , 2009 .

[11]  Jianqing Fan,et al.  Data‐Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation , 1995 .

[12]  H. Künsch.  Discrimination between monotonic trends and long-range dependence , 1986 .

[13]  Richard A. Davis,et al.  Handbook of Financial Time Series , 2009 .

[14]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[15]  THE SMOOTHING DICHOTOMY IN RANDOM-DESIGN REGRESSION WITH LONG-MEMORY ERRORS BASED ON MOVING AVERAGES , 2000 .

[16]  C. Granger.  Some properties of time series data and their use in econometric model specification , 1981 .

[17]  R. Dahlhaus,et al.  On the Optimal Segment Length for Parameter Estimates for Locally Stationary Time Series , 1998 .

[18]  T. Gasser,et al.  A Flexible and Fast Method for Automatic Smoothing , 1991 .

[19]  Mathias Dewatripont,et al.  Special Issue The Econometrics of Financial Markets , 1991 .

[20]  Yimin Xiao,et al.  Mean Integrated Squared Error of Nonlinear Wavelet-based Estimators with Long Memory Data , 2007 .

[21]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[22]  K. Lasak.  Likelihood Based Testing for No Fractional Cointegration , 2008 .

[23]  R. Leipus,et al.  The change-point problem for dependent observations , 1996 .

[24]  P. Phillips.  Understanding spurious regressions in econometrics , 1986 .

[25]  James Davidson,et al.  Generating Schemes for Long Memory Processes: Regimes, Aggregation and Linearity , 2005 .

[26]  H. Müller,et al.  Kernels for Nonparametric Curve Estimation , 1985 .

[27]  Rafal Kulik,et al.  WAVELET REGRESSION IN RANDOM DESIGN WITH HETEROSCEDASTIC DEPENDENT ERRORS , 2009, 0909.0384.

[28]  L. Horváth,et al.  The effect of long-range dependence on change-point estimators , 1997 .

[29]  Mustapha Rachdi,et al.  Consistency of the regression estimator with functional data under long memory conditions , 2008 .

[30]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[31]  Domenico Marinucci,et al.  Weak convergence of multivariate fractional processes , 2000 .

[32]  Søren Johansen,et al.  A REPRESENTATION THEORY FOR A CLASS OF VECTOR AUTOREGRESSIVE MODELS FOR FRACTIONAL PROCESSES , 2008, Econometric Theory.

[33]  S. Johansen.  An Extension of Cointegration to Fractional Autoregressive Processes , 2010 .

[34]  Morten Ørregaard Nielsen,et al.  Local empirical spectral measure of multivariate processes with long range dependence , 2004 .

[35]  Domenico Marinucci,et al.  Alternative forms of fractional Brownian motion , 1998 .

[36]  Dawei Huang,et al.  Testing for a Change in the Parameter Values and Order of an Autoregressive Model , 1995 .

[37]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .

[38]  Wei Biao Wu,et al.  CONFIDENCE BANDS IN NONPARAMETRIC TIME SERIES REGRESSION , 2008, 0808.1010.

[39]  Peter Hall,et al.  Nonparametric regression with long-range dependence , 1990 .

[40]  Edward Carlstein,et al.  Nonparametric Change-Point Estimation for Data from an Ergodic Sequence , 1994 .

[41]  James Davidson,et al.  Econometric Modelling of the Aggregate Time-Series Relationship Between Consumers' Expenditure and Income in the United Kingdom , 1978 .

[42]  J. Beran,et al.  On asymptotically optimal wavelet estimation of trend functions under long-range dependence , 2012, 1203.0392.

[43]  P. Robinson,et al.  Large-Sample Inference for Nonparametric Regression with Dependent Errors - (Now published in 'Annals of Statistics', 28 (1997), pp.2054-2083.) , 1997 .

[44]  E. Nadaraya.  On Estimating Regression , 1964 .

[45]  William F. Rosenberger,et al.  Likelihood‐Based Inference , 2006 .

[46]  J. Mielniczuk,et al.  Density Estimation Under Long-Range Dependence , 1995 .

[47]  C. Velasco.  Gaussian Semi‐parametric Estimation of Fractional Cointegration , 2003 .

[48]  P. Jeganathan.  ON ASYMPTOTIC INFERENCE IN COINTEGRATED TIME SERIES WITH FRACTIONALLY INTEGRATED ERRORS , 1999, Econometric Theory.

[49]  Heri Kuswanto.  A new simple test against spurious long memory using temporal aggregation , 2009 .

[50]  S. Johansen.  The Analysis of Nonstationary Time Series Using Regression, Correlation and Cointegration , 2010 .

[51]  Ulrich Stadtmüller,et al.  Signal Sampling and Recovery Under Dependent Errors , 2007, IEEE Transactions on Information Theory.

[52]  V. Klemeš.  The Hurst Phenomenon: A puzzle? , 1974 .

[53]  Yuanhua Feng.  Kernel- and Locally Weighted Regression -- with Application to Time Series Decomposition , 1999 .

[54]  M. Taqqu,et al.  The Empirical Process of some Long-Range Dependent Sequences with an Application to $U$-Statistics , 1989 .

[55]  Yoshihiro Yajima.  Determination of Cointegrating Rank in Fractional Systems , 2001 .

[56]  DISTRIBUTION-FREE TESTS OF FRACTIONAL COINTEGRATION , 2007, Econometric Theory.

[57]  R. Eubank.  Nonparametric Regression and Spline Smoothing , 1999 .

[58]  T. Mikosch,et al.  Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects , 2004, Review of Economics and Statistics.

[59]  M. Taqqu,et al.  Integration questions related to fractional Brownian motion , 2000 .

[60]  Ching-Fan Chung.  SAMPLE MEANS, SAMPLE AUTOCOVARIANCES, AND LINEAR REGRESSION OF STATIONARY MULTIVARIATE LONG MEMORY PROCESSES , 2002, Econometric Theory.

[61]  A. Ullah.  Non-parametric estimation of econometric functionals , 1988 .

[62]  J. Davidson.  A model of fractional cointegration, and tests for cointegration using the bootstrap☆ , 2002 .

[63]  Second-order behavior of M-estimators in linear regression with long-memory errors , 2000 .

[64]  Henghsiu Tsai.  QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF LONG-MEMORY LIMITING AGGREGATE PROCESSES , 2006 .

[65]  Hans-Georg Müller,et al.  Smooth optimum kernel estimators near endpoints , 1991 .

[66]  Jan Beran,et al.  Nonparametric M-estimation with long-memory errors , 2000 .

[67]  Theo Gasser,et al.  Smoothing Techniques for Curve Estimation , 1979 .

[68]  T. Gasser,et al.  Choice of bandwidth for kernel regression when residuals are correlated , 1992 .

[69]  C. Granger,et al.  Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns , 2004 .

[70]  Jose D. Salas,et al.  Nonstationarity of the mean and the hurst Phenomenon , 1978 .

[71]  Patricia Galván.  Statistical tools for palaeo data , 2009 .

[72]  Erik Hjalmarsson,et al.  What Drives Volatility Persistence in the Foreign Exchange Market , 2006 .

[73]  Lihong Wang.  CHANGE‐POINT DETECTION WITH RANK STATISTICS IN LONG‐MEMORY TIME‐SERIES MODELS , 2008 .

[74]  R. Olea,et al.  AN EFFICIENT ESTIMATOR FOR LOCALLY STATIONARY GAUSSIAN LONG-MEMORY PROCESSES , 2010, 1011.2607.

[75]  Andras Veres,et al.  The chaotic nature of TCP congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[76]  P. Robinson.  Efficient Tests of Nonstationary Hypotheses , 1994 .

[77]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[78]  B. Brodsky,et al.  Nonparametric Methods in Change Point Problems , 1993 .

[79]  Marc Hallin,et al.  Mixed autoregressive-moving average multivariate processes with time-dependent coefficients , 1978 .

[80]  Jan Beran,et al.  Root‐n‐consistent Estimation in Partial Linear Models with Long‐memory Errors , 1998 .

[81]  J. Breitung,et al.  Inference on the cointegration rank in fractionally integrated processes , 2002 .

[82]  L. Gil‐Alana.  Testing of Fractional Cointegration in Macroeconomic Time Series , 2003 .

[83]  M. Wand,et al.  Multivariate Locally Weighted Least Squares Regression , 1994 .

[84]  M. Nielsen.  Multivariate Lagrange Multiplier Tests for Fractional Integration , 2005 .

[85]  Jeffrey R. Russell,et al.  True or Spurious Long Memory? A New Test , 2008 .

[86]  Elias Masry,et al.  Local linear regression estimation for time series with long-range dependence , 1999 .

[87]  U. Hassler,et al.  A RESIDUAL-BASED LM-TYPE TEST AGAINST FRACTIONAL COINTEGRATION , 2006, Econometric Theory.

[88]  Ulrich K. Müller,et al.  Testing Models of Low-Frequency Variability , 2006 .

[89]  J. Simonoff.  Smoothing Methods in Statistics , 1998 .

[90]  Tim Bollerslev,et al.  Cointegration, Fractional Cointegration, and Exchange Rate Dynamics , 1994 .

[91]  Young K. Truong,et al.  On bandwidth choice for density estimation with dependent data , 1995 .

[92]  Hans-Georg Müller,et al.  Smooth Optimum Kernel Estimators of Densities, Regression Curves and Modes , 1984 .

[93]  K. Falconer,et al.  Inference on fractal processes using multiresolution approximation , 2007 .

[94]  H. Müller,et al.  Local Polynomial Modeling and Its Applications , 1998 .

[95]  J. Rice.  Bandwidth Choice for Nonparametric Regression , 1984 .

[96]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[97]  N. Chan,et al.  Residual empirical processes for long and short memory time series , 2008, 0811.0697.

[98]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[99]  Matthew Roughan,et al.  Measuring long-range dependence under changing traffic conditions , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[100]  P. Speckman.  Kernel smoothing in partial linear models , 1988 .

[101]  Christopher A. Sims.  Advances in econometrics : Sixth World Congress , 1994 .

[102]  Alexandre B. Tsybakov,et al.  Introduction to Nonparametric Estimation , 2008, Springer series in statistics.

[103]  Jianqing Fan,et al.  Efficient Estimation of Conditional Variance Functions in Stochastic Regression , 1998 .

[104]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[105]  C. Velasco,et al.  Non-stationary log-periodogram regression , 1999 .

[106]  Semiparametric and nonparametric econometrics , 1988 .

[107]  Q. Shao,et al.  On discriminating between long-range dependence and changes in mean , 2006, math/0607803.

[108]  Jianqing Fan.  Design-adaptive Nonparametric Regression , 1992 .

[109]  Peter Guttorp,et al.  Multiscale detection and location of multiple variance changes in the presence of long memory , 2000 .

[110]  D. Pollard.  Convergence of stochastic processes , 1984 .

[111]  Predicting the distribution function for long-memory processes , 2002 .

[112]  Katsumi Shimotsu,et al.  Simple (but effective) tests of long memory versus structural breaks , 2006 .

[113]  P. Robinson,et al.  Cointegration in fractional systems with deterministic trends , 2005 .

[114]  D. Marinucci.  Spectral Regression For Cointegrated Time Series With Long‐Memory Innovations , 1998 .

[115]  E. Parzen.  Nonparametric Statistical Data Modeling , 1979 .

[116]  Morten Ørregaard Nielsen,et al.  Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence , 2005 .

[117]  A. Ullah.  Nonparametric estimation and hypothesis testing in econometric models , 1988 .

[118]  L. Dümbgen.  The Asymptotic Behavior of Some Nonparametric Change-Point Estimators , 1991 .

[119]  Ignacio N. Lobato.  A semiparametric two-step estimator in a multivariate long memory model , 1999 .

[120]  P. Robinson.  Gaussian Semiparametric Estimation of Long Range Dependence , 1995 .

[121]  Rafal Kulik,et al.  Conditional variance estimation in regression models with long memory , 2012 .

[122]  H. Müller,et al.  Hazard rate estimation under random censoring with varying kernels and bandwidths. , 1994, Biometrics.

[123]  István Berkes,et al.  An almost sure invariance principle for the empirical distribution function of mixing random variables , 1977 .

[124]  R. Dahlhaus,et al.  Semiparametric estimation by model selection for locally stationary processes , 2006 .

[125]  R. J. Bhansali,et al.  On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes , 1998 .

[126]  Holger Dette,et al.  Optimal designs for dose-finding experiments in toxicity studies , 2009, 0902.1426.

[127]  S. Johansen,et al.  Likelihood Inference for a Nonstationary Fractional Autoregressive Model , 2007 .

[128]  Non‐Parametric Change‐Point Tests for Long‐Range Dependent Data , 2013 .

[129]  A. Bowman.  An alternative method of cross-validation for the smoothing of density estimates , 1984 .

[130]  Zhongjun Qu,et al.  A Test Against Spurious Long Memory , 2009 .

[131]  Murad S. Taqqu,et al.  Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator , 1997 .

[132]  Jan Beran,et al.  Local polynomial estimation with a FARIMA-GARCH error process , 2001 .

[133]  Luis A. Gil-Alana,et al.  Fractional Integration and Cointegration: An Overview and an Empirical Application , 2009 .

[134]  P. Robinson.  Nonparametric spectrum estimation for spatial data , 2007 .

[135]  H. Birks,et al.  Quantification of biotic responses to rapid climatic changes around the Younger Dryas — a synthesis , 2000 .

[136]  Fallaw Sowell,et al.  The Fractional Unit Root Distribution , 1990 .

[137]  Ulf Grenander,et al.  On the Estimation of Regression Coefficients in the Case of an Autocorrelated Disturbance , 1954 .

[138]  Walter Krämer,et al.  Testing for structural change in the presence of long memory , 2000 .

[139]  H. Künsch,et al.  On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series , 2013 .

[140]  D. Surgailis,et al.  A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate , 1990 .

[141]  H. Müller,et al.  Kernel estimation of regression functions , 1979 .

[142]  T. Rao.  The Fitting of Non-stationary Time-series Models with Time-dependent Parameters , 1970 .

[143]  Peter Hall,et al.  Convergence rates in density estimation for data from infinite-order moving average processes , 1990 .

[144]  太士 永久保.  Nonparametric Analysis of Longitudinal Data , 2011 .

[145]  W. Härdle.  Smoothing Techniques: With Implementation in S , 1991 .

[146]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[147]  H. Koul,et al.  Asymptotic inference in some heteroscedastic regression models with long memory design and errors , 2008, 0803.2121.

[148]  M. Rosenblatt.  Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[149]  J. Beran,et al.  Modelling financial time series with SEMIFAR–GARCH model , 2007 .

[150]  Francis X. Diebold,et al.  Long Memory and Structural Change , 1999 .

[151]  P. Lorek,et al.  Some results on random design regression with long memory errors and predictors , 2011, 1102.4372.

[152]  V. A. Epanechnikov.  Non-Parametric Estimation of a Multivariate Probability Density , 1969 .

[153]  Stepana Lazarova,et al.  Testing for structural change in regression with long memory processes , 2004 .

[154]  C. Granger,et al.  Spurious regressions in econometrics , 1974 .

[155]  B. Christensen,et al.  Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting , 2006 .

[156]  P. Guttorp,et al.  Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River , 2002 .

[157]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[158]  F. Mármol,et al.  SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES , 1995 .

[159]  Massimo Franchi.  A REPRESENTATION THEORY FOR POLYNOMIAL COFRACTIONALITY IN VECTOR AUTOREGRESSIVE MODELS , 2009, Econometric Theory.

[160]  M. Priestley,et al.  Non‐Parametric Function Fitting , 1972 .

[161]  M. Nielsen.  Spectral Analysis of Fractionally Cointegrated Systems , 2002 .

[162]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[163]  Jan Beran,et al.  Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors , 2002 .

[164]  Michalis Faloutsos,et al.  Long-range dependence ten years of Internet traffic modeling , 2004, IEEE Internet Computing.

[165]  Wenceslao González-Manteiga,et al.  Estimation and testing in a partial linear regression model under long-memory dependence , 2004 .

[166]  H. Müller.  Weighted Local Regression and Kernel Methods for Nonparametric Curve Fitting , 1987 .

[167]  J. Beran,et al.  Nonparametric conditional quantile estimation in the presence of long memory , 1997 .

[168]  W. D. Ray.  Time Series: Theory and Methods , 1990 .

[169]  Lajos Horváth,et al.  Change in autoregressive processes , 1993 .

[170]  C. Velasco,et al.  A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems , 2009 .

[171]  Jushan Bai,et al.  A NOTE ON SPURIOUS BREAK , 1998, Econometric Theory.

[172]  G. Kerkyacharian,et al.  Minimax or maxisets , 2002 .

[173]  Ying-Wong Cheung,et al.  A Fractional Cointegration Analysis of Purchasing Power Parity , 1993 .

[174]  Vladas Pipiras,et al.  Convergence of weighted sums of random variables with long-range dependence ( , 2000 .

[175]  Ying-Wong Cheung,et al.  Long Memory in Foreign-Exchange Rates , 1993 .

[176]  J. Davidson.  Alternative bootstrap procedures for testing cointegration in fractionally integrated processes , 2006 .

[177]  Naomi Altman,et al.  Kernel Smoothing of Data with Correlated Errors , 1990 .

[178]  Clifford M. Hurvich,et al.  Estimating Fractional Cointegration in the Presence of Polynomial Trends , 2002 .

[179]  Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions , 1995 .

[180]  E. Carlstein.  Nonparametric Change-Point Estimation , 1988 .

[181]  P. Robinson,et al.  Semiparametric estimation from time series with long-range dependence , 1994 .

[182]  Jan Mielniczuk,et al.  Random-design regression under long-range dependent errors , 1999 .

[183]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[184]  P. Robinson,et al.  Semiparametric inference in multivariate fractionally cointegrated systems , 2010 .

[185]  Clive W. J. Granger,et al.  Developments in the study of cointegrated economic variables , 2001 .

[186]  Jonathan H. Wright.  Testing for a Structural Break at Unknown Date with Long‐memory Disturbances , 1998 .

[187]  Liudas Giraitis,et al.  Testing and estimating in the change-point problem of the spectral function , 1992 .

[188]  C. Granger,et al.  Varieties of long memory models , 1996 .

[189]  C. Velasco.  Gaussian Semiparametric Estimation of Non‐stationary Time Series , 1999 .

[190]  Hira L. Koul.  M-estimators in linear models with long range dependent errors , 1992 .

[191]  R. Deo.  Asymptotic theory for certain regression models with long memory errors , 1997 .

[192]  L p -WAVELET REGRESSION WITH CORRELATED ERRORS AND INVERSE PROBLEMS , 2008 .

[193]  Minimax estimation via wavelets for indirect long-memory data , 1997 .

[194]  Yoshihiro Yajima,et al.  On Estimation of a Regression Model with Long-Memory Stationary Errors , 1988 .

[195]  M. Nielsen,et al.  Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration , 2011 .

[196]  Yazhen Wang.  Function estimation via wavelet shrinkage for long-memory data , 1996 .

[197]  J. Rice.  Bandwidth choice for differentiation , 1986 .

[198]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[199]  Marc Lavielle,et al.  The Multiple Change-Points Problem for the Spectral Distribution , 2000 .

[200]  R. Baillie,et al.  REGRESSION MODEL FITTING WITH A LONG MEMORY COVARIATE PROCESS , 2004, Econometric Theory.

[201]  D. Marinucci.  Semiparametric Frequency Domain Analysis of Fractional Cointegration - (Revised Version Forthcoming in P M Robinson: Time Series with Long Memory (Oxford University Press). , 1998 .

[202]  R. Dahlhaus.  Fitting time series models to nonstationary processes , 1997 .

[203]  Yi-Ching Yao,et al.  Approximating the Distribution of the Maximum Likelihood Estimate of the Change-Point in a Sequence of Independent Random Variables , 1987 .

[204]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[205]  J. Beran,et al.  On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data , 2013, Sankhya B.

[206]  H. Müller,et al.  Estimating regression functions and their derivatives by the kernel method , 1984 .

[207]  P. Robinson.  Multiple Local Whittle Estimation in Stationary Systems , 2007, 0811.0948.

[208]  M. Wand,et al.  An Effective Bandwidth Selector for Local Least Squares Regression , 1995 .

[209]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[210]  Jan Mielniczuk,et al.  Nonparametric Regression Under Long-Range Dependent Normal Errors , 1995 .

[211]  Kerry Patterson,et al.  Palgrave Handbook of Econometrics , 2009 .

[212]  Changryong Baek,et al.  Statistical tests for a single change in mean against long‐range dependence , 2012 .

[213]  M. Nielsen.  Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics , 2004 .

[214]  Jan Beran,et al.  On spline regression under Gaussian subordination with long memory , 2011, J. Multivar. Anal..

[215]  Patricia Menéndez,et al.  On rapid change points under long memory. , 2010 .

[216]  P. Robinson,et al.  Advances in Econometrics: Time series with strong dependence , 1994 .

[217]  R. Bhattacharya,et al.  THE HURST EFFECT UNDER TRENDS , 1983 .

[218]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[219]  J. Mielniczuk,et al.  ON RANDOM-DESIGN MODEL WITH DEPENDENT ERRORS , 2004 .

[220]  Hira L. Koul,et al.  Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors , 1993 .

[221]  I. Johnstone,et al.  Wavelet Threshold Estimators for Data with Correlated Noise , 1997 .

[222]  C. Velasco.  The Periodogram of fractional processes 1 , 2007 .

[223]  B. Ray,et al.  Bandwidth selection for kernel regression with long-range dependent errors , 1997 .

[224]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[225]  L. Goldstein,et al.  A New Class of Kernels for Nonparametric Curve Estimation , 1993 .

[226]  Jiahui Wang,et al.  Modeling Financial Time Series with S-PLUS® , 2003 .

[227]  Peter C. B. Phillips,et al.  Estimating Long Run Economic Equilibria , 1991 .

[228]  R. K. Adenstedt,et al.  On Large-Sample Estimation for the Mean of a Stationary Random Sequence , 1974 .

[229]  Nonparametric trend estimation in replicated time series , 2001 .

[230]  J. Beran,et al.  Weighted Averages and Local Polynomial Estimation for Fractional Linear ARCH Processes , 2007 .

[231]  Qiang Zhang,et al.  Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences , 2007, 0710.4217.

[232]  Sucharita Ghosh,et al.  A changing world: Challenges for landscape research , 2007 .

[233]  Cornelia Wichelhaus,et al.  Nonparametric conditional variance and error density estimation in regression models with dependent errors and predictors , 2011 .

[234]  Jan Beran,et al.  Contrasts under long-range correlations , 1993 .

[235]  Javier Hidalgo,et al.  Testing for structural change in a long-memory environment☆ , 1996 .

[236]  N. Chan,et al.  Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence , 2007, 0711.3589.

[237]  Yoshihiro Yajima,et al.  Asymptotic Properties of the LSE in a Regression Model with Long-Memory Stationary Errors , 1991 .

[238]  Noël Veraverbeke,et al.  Change-point problem and bootstrap , 1995 .

[239]  T. Mills.  Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends? , 2007 .

[240]  Clifford M. Hurvich,et al.  Semiparametric Estimation of Fractional Cointegrating Subspaces , 2004, 0708.0185.

[241]  L. Giraitis,et al.  Gaussian Estimation of Parametric Spectral Density with Unknown Pole , 2001 .

[242]  Luis A. Gil-Alana,et al.  Fractional integration and structural breaks at unknown periods of time , 2007 .

[243]  N. Terrin,et al.  ESTIMATION OF THE LONG‐MEMORY PARAMETER, BASED ON A MULTIVARIATE CENTRAL LIMIT THEOREM , 1994 .

[244]  A. Banerjee,et al.  Modelling structural breaks, long memory and stock market volatility: an overview , 2005 .

[245]  Herold Dehling,et al.  The functional law of the iterated logarithm for the empirical process of some long-range dependent sequences , 1988 .

[246]  Hira L. Koul,et al.  Asymptotic normality of regression estimators with long memory errors , 1996 .

[247]  W. G. Cochran.  Relative Accuracy of Systematic and Stratified Random Samples for a Certain Class of Populations , 1946 .

[248]  T. Mikosch.  Is it really long memory we see in financial returns , 2004 .

[249]  Murad S. Taqqu,et al.  ON THE EFFICIENCY OF THE SAMPLE MEAN IN LONG‐MEMORY NOISE , 1988 .

[250]  Jan Beran,et al.  On robust local polynomial estimation with long-memory errors , 2002 .

[251]  Masanobu Taniguchi,et al.  Local asymptotic normality for regression models with long-memory disturbance , 1999 .

[252]  Semiparametric Estimation of Multivariate Fractional Cointegration , 2002 .

[253]  A. Zhigljavsky,et al.  Asymptotic optimal designs under long-range dependence error structure , 2009, 1001.1817.

[254]  J. Wylie,et al.  Rates of convergence for the change-point estimator for long-range dependent sequences , 2005 .

[255]  Brandon Whitcher,et al.  Wavelet estimation of a local long memory parameter , 2000 .

[256]  G. Barnard.  Control Charts and Stochastic Processes , 1959 .

[257]  C. Velasco,et al.  Consistent Testing of Cointegrating Relationships , 2004 .

[258]  Richard Startz,et al.  Maximum-Likelihood Estimation of Fractional Cointegration with an Application to U.S. and Canadian Bond Rates , 1998, Review of Economics and Statistics.

[259]  U. Grenander,et al.  Statistical analysis of stationary time series , 1957 .

[260]  Wen-Jen Tsay,et al.  The spurious regression of fractionally integrated processes , 2000 .

[261]  Domenico Marinucci,et al.  Semiparametric frequency domain analysis of fractional cointegration , 1998 .

[262]  Piotr Kokoszka,et al.  Wavelet-domain test for long-range dependence in the presence of a trend , 2008 .

[263]  Weak convergence of two-parameter empirical fields in change-point problems , 1988 .

[264]  J. Beran,et al.  Optimal convergence rates in non‐parametric regression with fractional time series errors , 2013 .

[265]  P. Phillips.  Nonstationary time series and cointegration , 1995 .

[266]  Richard A. Johnson,et al.  The Effect of Serial Correlation on the Performance of CUSUM Tests II , 1974 .

[267]  M. Lejeune,et al.  Smooth estimators of distribution and density functions , 1992 .

[268]  Jan Beran,et al.  Testing for a change of the long-memory parameter , 1996 .

[269]  Jan Beran,et al.  Maximum Likelihood Estimation of the Differencing Parameter for Invertible Short and Long Memory Autoregressive Integrated Moving Average Models , 1995 .

[270]  P. Robinson,et al.  Time series regression with long-range dependence , 1997 .

[271]  W. Härdle,et al.  How Far are Automatically Chosen Regression Smoothing Parameters from their Optimum , 1988 .

[272]  P. Robinson,et al.  Narrow-Band Analysis of Nonstationary Processes , 2001 .

[273]  Jan Beran,et al.  SEMIFAR models|a semiparametric approach to modelling trends , 2002 .

[274]  Paul Embrechts,et al.  Extremes and Integrated Risk Management , 2000 .

[275]  D. Marinucci,et al.  Semiparametric Fractional Cointegration Analysis , 2001 .

[276]  Jesus Gonzalo,et al.  Long-range dependence in Spanish political opinion poll series , 2003 .

[277]  Frank Nielsen.  Local Whittle estimation of multi‐variate fractionally integrated processes , 2011 .

[278]  J. Beran,et al.  Iterative Plug-In Algorithms for SEMIFAR Models—Definition, Convergence, and Asymptotic Properties , 2002 .

[279]  B. Ray,et al.  Bayesian methods for change‐point detection in long‐range dependent processes , 2002 .

[280]  Asymptotic expansion of M-estimators with long-memory errors , 1997 .

[281]  M. C. Jones,et al.  A Brief Survey of Bandwidth Selection for Density Estimation , 1996 .

[282]  R. M. Clark.  A calibration curve for radiocarbon dates , 1975, Antiquity.

[283]  S. Yau.  Mathematics and its applications , 2002 .

[284]  James Davidson,et al.  Type I and type II fractional Brownian motions: A reconsideration , 2009, Comput. Stat. Data Anal..

[285]  Lajos Horváth,et al.  LIMIT THEOREMS FOR QUADRATIC FORMS WITH APPLICATIONS TO WHITTLE'S ESTIMATE , 1999 .

[286]  M. Nielsen.  Nonparametric Cointegration Analysis of Fractional Systems with Unknown Integration Orders , 2009 .

[287]  J. Mielniczuk,et al.  Randomized Fixed Design Regression under Long-Range-Dependent Errors , 2008 .

[288]  Philipp Sibbertsen,et al.  Long memory versus structural breaks: An overview , 2004 .

[289]  J. MacKinnon,et al.  NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS , 2010 .

[290]  R. Dahlhaus.  Efficient Location and Regression Estimation for Long Range Dependent Regression Models , 1995 .

[291]  J. Beran.  On parameter estimation for locally stationary long-memory processes , 2009 .

[292]  Katsumi Shimotsu,et al.  Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach , 2007 .

[293]  J. Beran.  M Estimators of Location for Gaussian and Related Processes With Slowly Decaying Serial Correlations , 1991 .

[294]  Franccois Roueff,et al.  Locally stationary long memory estimation , 2009, 0907.5151.

[295]  James Stephen Marron,et al.  Regression smoothing parameters that are not far from their optimum , 1992 .

[296]  Gennady Samorodnitsky,et al.  Long Range Dependence , 2007, Found. Trends Stoch. Syst..

[297]  I. B. MacNeill,et al.  The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time , 1993 .

[298]  Nalini Ravishanker,et al.  BAYESIAN ANALYSIS OF VECTOR ARFIMA PROCESSES , 1997 .

[299]  Helmut Lütkepohl.  Structural Vector Autoregressive Analysis for Cointegrated Variables , 2006 .

[300]  Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes , 2008 .

[301]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[302]  REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES , 2009, Econometric Theory.

[303]  D. Ferger.  On the rate of almost sure convergence of Dümbgen's change-point estimators , 1994 .

[304]  W. Stute,et al.  Convergence of changepoint estimators , 1992 .

[305]  Empirical process of residuals for regression models with long memory errors , 2011, 1102.4368.

[306]  J. K. Benedetti.  On the Nonparametric Estimation of Regression Functions , 1977 .

[307]  W. Fuller,et al.  Introduction to Statistical Time Series (2nd ed.) , 1997 .

[308]  Stochastic Regression Model with Dependent Disturbances , 2001 .

[309]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[310]  Yuanhua Feng,et al.  A simple root n bandwidth selector for nonparametric regression , 1998 .

[311]  Nalini Ravishanker,et al.  Bayesian prediction for vector ARFIMA processes , 2002 .

[312]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[313]  J. Hart.  Kernel regression estimation with time series errors , 1991 .