Modelling structural breaks, long memory and stock market volatility: An overview

Journal of Econometrics

Volumn 129, Issue 1-2, 2005, Pages 1-34

  Banerjee, Anindya ^a   Urga, Giovanni ^b  

^a EUROPEAN UNIVERSITY INSTITUTE   (Italy)

^b CITY UNIVERSITY   (United Kingdom)

Author keywords

Long memory; Structural breaks; Volatility

Indexed keywords

COMPUTER SIMULATION; STATISTICAL METHODS;

LONG MEMORY; STOCK MARKETS; STRUCTURAL BREAKS; VOLATILITY;

FINANCE;

EID: 26844499204     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2004.09.001     Document Type: Article

References (178)

1. I. Adelman Long cycles - fact or artifact? American Economic Review 55 1965 444 463
2. C. Agiakloglou, P. Newbold, and M. Wohar Bias in an estimator of the fractional difference parameter Journal of Time Series Analysis 14 1992 235 246
3. J. Andel Long memory time series models Kybernetika 22 1986 105 123
4. R.K. Adenstedt On large sample estimation for the mean of a stationary random sequence Annals of Mathematical Statistics 2 1974 1095 1107
5. E. Andreou, and E. Ghysels Detecting multiple breaks in financial market volatility dynamics Journal of Applied Econometrics 17 2002 579 600
6. D.W.K. Andrews Tests for parameter instability and structural change with unknown change point Econometrica 61 1993 821 856
7. Andrews, D.W.K., Lieberman, O., 2002. Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes. Cowles Foundation, Discussion Paper No. 1378, Yale University.
8. D.W.K. Andrews, and W. Ploberger Optimal tests when a nuisance parameter is present only under the alternative Econometrica 62 1994 1383 1414
9. J. Arteche Semiparametric robust tests on seasonal or cyclical long memory time series Journal of Time Series Analysis 23 2002 251 285
10. K. Aydogan, and G.G. Booth Are there long cycles in common stock returns? Southern Economic Journal 55 1988 141 149
11. J. Bai Likelihood ratio tests for multiple structural change Journal of Econometrics 91 1999 299 323
12. J. Bai, and P. Perron Estimating and testing linear models with multiple structural changes Econometrica 66 1998 47 78
13. J. Bai, and P. Perron Computation and analysis of multiple structural change models Journal of Applied Econometrics 18 2003 1 22
14. J. Bai, and P. Perron Critical values for multiple structural change tests The Econometrics Journal 6 2003 72 78
15. R.T. Baillie Long memory processes and fractional integration in econometrics Journal of Econometrics 73 1996 5 59
16. R.T. Baillie, and C.F. Chung Small sample bias in conditional sum of squares estimators of fractionally integrated ARMA models Empirical Economics 18 1993 791 806
17. A. Banerjee, R.L. Lumsdaine, and J.H. Stock Recursive and sequential tests of the unit root and trend break hypotheses theory and international evidence Journal of Business and Economic Statistics 10 1992 271 287
18. Banerjee, A., Lazarova, S., Urga, G., 1998. Bootstrapping sequential tests for multiple structural breaks, Discussion Paper No.17-98, London Business School.
19. J.M. Bardet, G. Lang, E. Moulines, and P. Soulier Wavelet estimator of long-range dependence processes Statistical Inference for Stochastic Processes 3 2000 85 99
20. J.T. Barkoulas, C.B. Baum, and M. Caglayan Long memory or structural breaks can either explain nonstationary real exchange rates under the current float? Journal of International Financial Markets, Institutions and Money 9 1999 359 376
21. J. Beran Statistics for Long Memory Processes 1994 Chapman and Hall New York
22. J. Beran On a class of M-estimators for Gaussian long-memory models Biometrika 81 1994 755 766
23. J. Beran, and N. Terrin Testing for a change of the long-memory parameter Biometrika 83 1996 627 638
24. R.J. Bhansali, and P.S. Kokoszka Estimation of the long-memory parameters a review of recent developments and an extension I.V. Basawa C.C. Heyde R.L. Taylor Proceedings of the Symposium on Inference for Stochastic Processes 2001 125 150
25. T. Bollerslev, and J.W. Wright Semiparametric estimation of long-memory volatility dependencies the role of high-frequency data Journal of Econometrics 98 2000 81 106
26. C. Bos, S.P.H. Franses, and M. Ooms Long-memory and level shifts re-analyzing inflation rates Empirical Economics 24 1999 427 449
27. F.J. Breidt, N. Crato, and P. de Lima The detection and estimation of long memory in stochastic volatility Journal of Econometrics 83 1998 248 325
28. F. Busetti, and A. Harvey Testing for the presence of a random walk in series with structural breaks Journal of Time Series Analysis 22 2001 127 150
29. F. Busetti, and A. Harvey Further comments on stationarity tests in series with structural breaks Journal of Time Series Analysis 24 2003 137 140
30. N.H. Chan, and N. Terrin Inference for unstable long-memory processes with applications to fractional unit root autoregression Annals of Statistics 23 1995 1662 1683
31. W.W. Chen, and C.M. Hurvich Estimating fractional cointegration in the presence of polynomial trends Journal of Econometrics 117 2003 95 121
32. B.J. Christensen, and M.O. Nielsen Semiparametric analysis of stationary fractional cointegration and the implied-realized volatility relation University of Aarhus Working Paper No. 2001-4 2002
33. C. Chung Estimating a generalized long memory process Journal of Econometrics 73 1996 237 259
34. C. Chung A generalized fractionally integrated autoregressive moving-average process Journal of Time Series Analysis 17 1996 111 140
35. M.P. Clements, and D.F. Hendry Intercept corrections and structural change Journal of Applied Econometrics 11 1996 475 494
36. M.P. Clements, and D.F. Hendry Forecasting Economic Time Series 1998 Cambridge University Press Cambridge
37. F. Comte, and E.G. Renault Long memory continuous time models Journal of Econometrics 73 1996 101 149
38. F. Comte, and E.G. Renault Long memory in continuous-time stochastic volatility models Mathematical Finance 8 1998 291 323
39. Comte, F., Coutin, L., Renault, E.E., 2003. Affine fractional stochastic volatility models with application to option pricing, Discussion paper n. 2003-10, Université de Montreal.
40. Dalla, V., Hidalgo, J., 2004. A parametric bootstrap test for cycles. Journal of Econometrics, 10.1016/j.jeconom.2004.09.008.
41. J. Davidson A model of fractional cointegration, and tests for cointegration using the bootstrap Journal of Econometrics 110 2002 187 212
42. Davidson, J., Terasvirta, T.T. (Eds.), 2002. Long memory and nonlinear time series. Journal of Econometrics 110 (2) 105-437.
43. R.B. Davies, and D.S. Harte Tests for the Hurst effect Biometrika 74 1987 95 102
44. C. de Peretti Bilateral bootstrap tests for long memory an application to the silver market Computational Economics 22 2003 187 212
45. de Peretti, C., Urga, G., 2004. Stopping tests in the sequential estimation for multiple structural breaks. Working Paper CEA-06-2004, Centre for Econometric Analysis, Cass Business School, London.
46. F.X. Diebold, and A. Inoue Long memory and regime switching Journal of Econometrics 105 2001 131 159
47. F.X. Diebold, and G.D. Rudebusch On the power of Dickey-Fuller tests against fractional alternatives Economics Letters 35 1991 155 160
48. I. Dittmann Residual-based tests for fractional cointegration a Monte Carlo study Journal of Time Series Analysis 21 2000 614 647
49. I. Dittmann Error correction models for fractionally cointegrated time series Journal of Time Series Analysis 25 2004 27 32
50. J.J. Dolado, J. Gonzalo, and L. Mayoral A fractional Dickey-Fuller tests for unit toots Econometrica 70 2002 1963 2006
51. Doornik, J.A., Hendry, D.F., 2001. Econometric Modelling Using PcGive, vol. III. Timberlake Consultants Press, London.
52. J.A. Doornik, and M. Ooms Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models Computational Statistics and Data Analysis 41 2003 333 348
53. Doornik, J.A., Ooms, M., 2004. Inference and forecasting for ARFIMA models with an application to US and UK inflation. Studies in Nonlinear Dynamics and Econometrics 8, No. 2, Article 14. http://www.bepress.com/snde/vol8/iss2/ art14.
54. Doukhan, P., Oppenheim, G., Taqqu, M.S. (Eds.), 2003. Theory and Applications of Long-range Dependence. Birkhauser, Berlin.
55. M. Dueker, and R. Startz Maximum-likelihood estimation of fractional cointegration with an application to US and Canadian bond rates Review of Economics and Statistics 83 1998 420 426
56. Dufour, J-M., Ghysels, E. (Eds.), 1996. Recent developments in the econometrics of structural change. Journal of Econometrics 70, 1-316.
57. R.F. Engle, and C.W.J. Granger Co-integration and error correction representation, estimation and testing Econometrica 55 1987 251 276
58. R.F. Engle, and A.D. Smith Stochastic permanent breaks Review of Economics and Statistics 81 1999 553 574
59. R. Fox, and M.S. Taqqu Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series Annals of Statistics 14 1986 517 532
60. P.H. Franses, M. van der Leij, and R. Paap Modelling and forecasting level shifts in absolute returns Journal of Applied Econometrics 17 2002 601 616
61. Gagliardini, P., Trojani, F., Urga, G., 2004, Robust GMM tests for structural breaks. Journal of Econometrics, 10.1016/j.jeconom.2004.09.006.
62. J. Geweke, and S. Porter-Hudak The estimation and application of long memory time series models Journal of Time Series Analysis 4 1983 221 238
63. L.A. Gil-Alana Testing of fractional cointegration in macroeconomic time series Oxford Bulletin of Economics and Statistics 65 2003 517 529
64. L.A. Gil-Alana A joint test of fractional integration and structural breaks at a known period of time Journal of Times Series Analysis 25 2004 681 700
65. L. Giraitis, and P.M. Robinson Whittle estimation of ARCH models Econometric Theory 17 2001 608 631
66. L. Giraitis, P. Kokoszka, R. Leipus, and G. Teyssiere Rescaled variance and related tests for long memory in volatility and levels Journal of Econometrics 112 2003 265 294
67. C. Gourieroux, and J. Jasiak Memory and infrequent breaks Economics Letters 70 2001 29 41
68. C.W.J. Granger Long memory relationships and the aggregation of dynamic models Journal of Econometrics 14 1980 227 238
69. C.W.J. Granger Some properties of time series data and their use in econometric specification Journal of Econometrics 16 1981 121 130
70. Granger, C.W.J., 1983. Cointegrated variables and error correction models. Unpublished Manuscript, University of California, San Diego.
71. C.W.J. Granger Developments in the study of cointegrated economic variables Oxford Bulletin of Economics and Statistics 48 1986 213 228
72. C.W.J. Granger, and N. Hyung Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns Journal of Empirical Finance 11 2004 399 421
73. C.W.J. Granger, and R. Joyeux An introduction to long-memory time series models and fractional differencing Journal of Time Series Analysis 1 1980 15 29
74. C.W.J. Granger, and T. Terasvirta A simple nonlinear time series model with misleading linear properties Economics Letters 62 1999 161 165
75. H.L. Gray, W. Woodward, and N. Zhang On generalized fractional processes Journal of Time Series Analysis 10 1989 233 257
76. H.L. Gray, W. Woodward, and N. Zhang On generalized fractional processes a correction Journal of Time Series Analysis 15 1994 561 562
77. R.E. Hall Stochastic implication of the life cycle-permanent income hypothesis theory and evidence Journal of Political Economy 86 1979 971 987
78. B.E. Hansen Tests for parameter instability in regressions with I(1) processes Journal of Business and Economic Statistics 10 1992 321 335
79. B.E. Hansen Testing for structural change in conditional models Journal of Econometrics 97 2000 93 115
80. P.R. Hansen Structural breaks in the cointegrated vector autoregressive model Journal of Econometrics 114 2003 261 295
81. H. Hansen, and S. Johansen Some tests for parameter constancy in cointegrated VAR-models Econometrics Journal 2 1999 306 333
82. D.I. Harvey, S.J. Leybourne, and P. Newbold Innovational outlier unit root tests with an endogenously determined break in level Oxford Bulletin of Economics and Statistics 63 2001 559 575
83. J. Haslett, and A.E. Raftery Space-time modelling with long-memory dependence assessing Ireland's wind power resource Journal of the Royal Statistical Society 38 Series C 1989 1 50
84. U. Hassler, and J. Wolters On the power of unit roots against fractional alternatives Economics Letters 45 1994 1 5
85. M.A. Hauser, and E. Reschenhofer Estimation of the fractionally differencing parameter with the R/S method Computational Statistics and Data Analysis 20 1995 569 579
86. J. Helson, and Y. Sarason Past and future Mathematica Scandanavia 21 1967 5 16
87. M. Henry Averaged periodogram spectral estimation with long memory conditional heteroscedasticity Journal of Time Series Analysis 22 2001 431 459
88. J. Hidalgo, and P.M. Robinson Testing for structural change in a long-memory environment Journal of Econometrics 70 1996 159 174
89. T. Higuchi Approach to an irregular time series on the basis of the fractal theory Physica D 31 1988 277 283
90. Hillebrand, E., 2004. Neglecting parameter changes in GARCH models. Journal of Econometrics, 10.1016/j.jeconom.2004.09.005.
91. J.R.M. Hosking Fractional differencing Biometrika 68 1981 165 176
92. H.E. Hurst Long-term storage capacity of reservoirs Transactions of the American Society of Civil Engineers 116 1951 770 799
93. H.E. Hurst A suggested statistical model of some time series that occur in nature Nature 180 1957 494
94. C.M. Hurvich, and W.W. Chen An efficient taper for potentially overdifferenced long-memory time series Journal of Time Series Analysis 21 2000 155 180
95. Hyung, N., Franses, P.H., 2001. Structural breaks and long memory in US inflation rates: do they matters for forecasting? Erasmus University Rotterdam, Econometric Institute Research Report EI2001-13.
96. Hyung, N., Franses, P.H., 2002. Inflation rates long-memory, level, shifts, or both? Econometric Institute Report 2002-08, Erasmus University.
97. P. Jeganathan On asymptotic inference in cointegration time series with fractionally integrated errors Econometric Theory 15 1999 583 621
98. M.J. Jensen Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter Journal of Forecasting 18 1999 17 32
99. S. Johansen, R. Mosconi, and B. Nielsen Cointegration analysis in the presence of structural breaks in the deterministic trend The Econometrics Journal 3 2000 216 249
100. T-H. Kim, S.J. Leybourne, and P. Newbold Spurious rejections by Perron tests in the presence of a break Oxford Bulletin of Economics and Statistics 62 2000 433 444
101. W. Kramer, and P. Sibbertsen Testing for structural change in the presence of long memory International Journal of Business and Economics 1 2002 235 242
102. C.M. Kuan, and C.C. Hsu Change point estimation of fractionally Integrated Processes Journal of Time Series Analysis 19 1998 693 708
103. D. Kwiatkowski, P.C.B. Phillips, P. Schmidt, and Y. Shin Testing the null hypothesis of stationarity against the alternative of a unit root how sure are we that economic time series have a unit root? Journal of Econometrics 54 1992 159 178
104. M. Lavielle, and E. Moulines Least-squares estimation of an unknown number of shifts in a time series Journal of Time Series Analysis 21 2000 33 59
105. Lazarova, S., 2004. Testing for structural change in regression with long memory processes. Journal of Econometrics. 10.1016/j.jeconom.2004.09.011.
106. D. Lee, and P. Schmidt On the power of the KPSS Test of stationarity against fractionally integrated alternatives Journal of Econometrics 73 1996 285 302
107. J. Lee, and M. Strazicich Break point estimation and spurious rejections with endogenous unit root tests Oxford Bulletin of Economics and Statistics 62 2001 535 558
108. R. Leipus, and D. Surgailis Random coefficient autoregression, regime switching and long memory Advances in Applied Probability 35 2003 737 754
109. R. Leipus, and M.C. Viano Long memory and stochastic trend Statistics and Probability Letters 61 2003 177 190
110. Leipus, R., Paulauskas, V., Surgailis, D., 2004. Renewal regime switching and stable limit laws. Journal of Econometrics, 10.1016/j.jeconom.2004.09.010.
111. S.J. Leybourne, T.C. Mills, and P. Newbold Spurious rejections by Dickey-Fuller tests in the presence of a break under the null Journal of Econometrics 87 1998 191 203
112. C.-F. Lin, and T. Terasvirta Testing the constancy of regression parameters against continuous structural change Journal of Econometrics 62 1994 211 228
113. C.-F. Lin, and T. Terasvirta Testing parameter constancy in linear models against stochastic stationary parameters Journal of Econometrics 90 1999 193 213
114. M. Liu Modelling long memory in stock market volatility Journal of Econometrics 99 2000 139 171
115. A.W. Lo Long term memory in stock market prices Econometrica 59 1991 1279 1313
116. I.N. Lobato A semiparametric two-step estimator in a multivariate long memory model Journal of Econometrics 90 1999 29 153
117. I.N. Lobato, and P.M. Robinson Averaged periodogram estimation of long memory Journal of Econometrics 73 1996 303 324
118. I.N. Lobato, and P. Robinson A nonparametric test for I(0) Review of Economic Studies 68 1998 475 495
119. B.B. Mandelbrot Statistical methodology for non periodic cycles from the covariance to R/S analysis Annals of Economic and Social Measurement 1 1972 259 290
120. B.B. Mandelbrot A fast fractional Gaussian noise generator Water Resources Research 7 1975 543 553
121. B.B. Mandelbrot, and J. Wallis N. Joseph and operational hydrology Water Resources Research 4 1968 909 918
122. D. Marinucci Spectral regression for cointegrated time series with long-memory innovations Journal of Time Series Analysis 21 2000 685 706
123. A.I. McLeod, and K.W. Hipel Preservation of the rescaled adjusted range, 1. A reassessment of the Hurst phenomenon Water Resources Research 14 1978 159 178
124. T. Mikosch, and C. Starica Nonstationarities in financial time series the long, range dependence and the IGARCH effects Review of Economics and Statistics 86 2004 378 390
125. Montanes, A., Olloqui, I., Calvo, E., 2004. Selection of the break in Perron-type tests. Journal of Econometrics, 10.1016/j.jeconom.2004.09.003.
126. C.R. Nelson, and C.I. Plosser Trends and random walks in macroeconomic time series Journal of Monetary Economics 10 1982 139 162
127. M.O. Nielsen Optimal residual based tests for fractional cointegration and exchange rate dynamics Journal of Business and Economic Statistics 22 2004 331 345
128. J. Nyblom Testing for the constancy of parameters over time Journal of the American Statistical Association 84 1989 223 230
129. A. Ohanissian, J.R. Russell, and R.S. Tsay Using temporal disaggregation to distinguish between true and spurious long memory 2003 Mimeo University of Chicago
130. J. Pai, and S.N. Ravishanker Bayesian analysis of autoregressive fractionally integrated moving average processes Journal of Time Series Analysis 19 1998 99 112
131. W.R. Parke What is fractional integration? The Review of Economics and Statistics 81 1999 632 638
132. P. Perron The great crash, the oil price shock and the unit root hypothesis Econometrica 57 1989 1361 1401
133. P. Perron Further evidence from breaking trend functions in macroeconomic variables Journal of Econometrics 80 1997 355 385
134. P. Perron, and T.J. Vogelsang Testing for a unit root in a time series with a shift in mean, corrections and extensions Journal of Business and Economic Statistics 10 1992 467 470
135. Perron, P., Zhu, X., 2004. Structural breaks with deterministic and stochastic trends. Journal of Econometrics, 10.1016/j.jeconom.2004.09.004.
136. Peters, A., Sibbertsen, P., 2001. Robust tests on fractional cointegration. SFB 475 Technical Report 29/2001, University of Dortmund.
137. Pesaran, H., Timmerman, A., 2004. Small sample properties of forecasts from autoregressive models under structural breaks. Journal of Econometrics, 10.1016/j.jeconom.2004.09.007.
138. P.C.B. Phillips, and S.J. Durlauf Multiple time series regression with integrated processes Review of Economic Studies 53 1986 473 495
139. P.C.B. Phillips, and K. Shimotsu Local Whittle estimation in nonstationary and unit root cases Annals of Statistics 32 2004 656 692
140. Phillips, P.C.B., Shimotsu, K., 2004b. Exact local Whittle estimation of fractional integration. Cowles Foundation Discussion Paper N. 1367 (Revised).
141. R.E. Quandt Tests of the hypothesis that a linear regression obeys two separate regimes Journal of American Statistical Association 55 1960 320 330
142. P. Rappoport, and L. Reichlin Segmented trends and nonstationary time series The Economic Journal 99 Conference Volume 1989 168 177
143. S.I. Resnick Extreme Values, Regular Variation and Point Processes 1987 Springer Berlin
144. P.M. Robinson Statistical inference for a random coefficient autoregressive model Scandinavian Journal of Statistics 5 1978 163 168
145. P.M. Robinson Testing for strong serial correlation and dynamic conditional heteroscedasticity in multiple regression Journal of Econometrics 47 1991 67 84
146. P.M. Robinson Time series with strong dependence C.A. Sims Advances in Econometrics, Sixth World Congress vol. 1 1994 Cambridge University Press Cambridge
147. P.M. Robinson Semiparametric analysis of long-memory time series The Annals of Statistics 22 1994 515 539
148. P.M. Robinson Efficient tests of nonstationary hypotheses Journal of the American Statistical Association 89 1994 1420 1437
149. P.M. Robinson Log-periodogram regression of time series with long range dependence The Annals of Statistics 23 1995 1048 1072
150. P.M. Robinson Gaussian semiparametric estimation of long range dependence The Annals of Statistics 23 1995 1630 1661
151. P.M. Robinson Long memory time series P.M. Robinson Time Series with Long Memory 2003 Oxford University Press Oxford
152. Robinson, P.M., Hualde, J., 2003. Cointegration in fractional systems with unknown integration orders. Econometrica 71, 1727, 1766.
153. Robinson, P.M., Iacone, F., 2004. Cointegration in fractional systems with deterministic trends. Journal of Econometrics, 10.1016/j.jeconom.2004.09. 009.
154. P.M. Robinson, and D. Marinucci The averaged periodogram for nonstationary vector time series Statistical Inference for Stochastic Processes 3 2000 149 160
155. P.M. Robinson, and D. Marinucci Narrow-band analysis of nonstationary processes The Annals of Statistics 29 2001 947 986
156. P.M. Robinson, and Y. Yajima Determination of cointegrating rank in fractional systems Journal of Econometrics 106 2002 217 241
157. P.M. Robinson, and P. Zaffaroni Modelling nonlinearity and long memory in time series Fields Institute Communications 11 1997 161 170
158. P.M. Robinson, and P. Zaffaroni Nonlinear time series with long memory a model for stochastic volatility Journal of Statistical Planning and Inference 68 1998 359 371
159. M. Rosenblatt A central limit theorem and a strong mixing condition Proceedings of the National Academy of Sciences 42 1956 43 47
160. P.A. Samuelson Proof that properly discounted present values of assets vibrate randomly The Bell Journal of Economics and Management Science 4 1973 369 374
161. F.B. Sowell The fractional unit root distribution Econometrica 58 1990 495 505
162. F.B. Sowell Maximum likelihood estimation of stationary univariate fractionally integrated time series models Journal of Econometrics 53 1992 165 188
163. J.H. Stock, and M.W. Watson Testing for common trends Journal of the American Statistical Association (Theory and Methods) 83 1988 1097 1107
164. J.H. Stock, and M.W. Watson Macroeconomic forecasting using diffusion indexes Journal of Business and Economic Statistics 20 2002 147 162
165. Szego, G. 1975. Orthogonal polynomials, 4th Edition, Colloquium Publications, vol. XXIII, American Mathematical Society, Rhode Island.
166. M.S. Taqqu Weak convergence to fractional Brownian motion and to the Rosenblatt process Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 31 1975 287 302
167. M.S. Taqqu, V. Teverovsky, and W. Willinger Estimators for long range dependence an empirical study Fractals 3 1995 785 798
168. C. Velasco Gaussian semiparametric estimation of non-stationary time series Journal of Time Series Analysis 20 1999 87 127
169. Velasco, C., 2003. Gaussian semi-parametric estimation of fractional cointegration. Journal of Time Series Analysis 24, 345-378.
170. C. Velasco, and P.M. Robinson Whittle pseudo-maximum likelihood estimation for nonstationary time series Journal of the American Statistical Association 95 2000 1229 1243
171. T.J. Vogelsang, and P. Perron Additional tests for unit root allowing the possibility of breaks in the trend function International Economic Review 39 1998 1073 1110
172. B. Whitcher Wavelet-based estimation for seasonal long-memory processes Technometrics 46 2004 225 238
173. P. Whittle Hypothesis Testing in Time Series Analysis 1951 Almquist and Wiksells Uppsala
174. J.H. Wright Testing for a structural break at unknown date with long-memory disturbances Journal of Time Series Analysis 19 1998 369 376
175. Wright, J.H., 2000. Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns. FRB International Finance Discussion Paper No. 2000-685.
176. C.H. Young Asymptotic behaviour of trigonometric series 1974 Chinese University Hong Kong
177. P. Zaffaroni Gaussian inference on certain long-range dependent volatility models Journal of Econometrics 115 2003 199 258
178. E. Zivot, and D.W.K. Andrews Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis Journal of Business and Economic Statistics 10 1992 251 270