Preface |
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ix | |
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1 | (40) |
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An elementary result in statistics |
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1 | (10) |
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11 | (3) |
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``Physical'' models with long memory |
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14 | (6) |
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14 | (1) |
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Aggregation of short-memory models |
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14 | (2) |
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16 | (1) |
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17 | (1) |
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Partial differential equations |
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18 | (2) |
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20 | (9) |
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Other data examples, historic overview, discussion |
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29 | (12) |
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29 | (3) |
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The Joseph effect and the Hurst effect |
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32 | (2) |
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34 | (1) |
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35 | (1) |
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Semisystematic errors, unsuspected slowly decaying correlations, the personal equation |
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36 | (3) |
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Why stationary models? Some ``philosophical'' remarks |
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39 | (2) |
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Stationary processes with long memory |
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41 | (26) |
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41 | (4) |
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45 | (5) |
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Stationary increments of self-similar processes |
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50 | (5) |
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Fractional Brownian motion and Gaussian noise |
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55 | (4) |
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59 | (8) |
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67 | (14) |
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67 | (1) |
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Gaussian and non-gaussian time series with long memory |
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67 | (2) |
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Limit theorems for simple sums |
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69 | (4) |
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Limit theorems for quadratic forms |
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73 | (4) |
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Limit theorems for Fourier transforms |
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77 | (4) |
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Estimation of long memory: heuristic approaches |
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81 | (19) |
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81 | (1) |
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81 | (6) |
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The correlogram and partial correlations |
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87 | (5) |
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92 | (2) |
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94 | (1) |
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Least squares regression in the spectral domain |
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95 | (5) |
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Estimation of long memory: time domain MLE |
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100 | (16) |
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100 | (2) |
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Some definitions and useful results |
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102 | (2) |
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104 | (4) |
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Why do we need approximate MLE's? |
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108 | (1) |
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Whittle's approximate MLE |
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109 | (4) |
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An approximate MLE based on the AR representation |
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113 | (3) |
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Definition for stationary processes |
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113 | (2) |
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Generalization to nonstationary processes; a unified approach to Box-Jenkins modelling |
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115 | (1) |
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Estimation of long memory: frequency domain MLE |
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116 | (8) |
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A discrete version of Whittle's estimator |
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116 | (4) |
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Estimation by generalized linear models |
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120 | (4) |
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Robust estimation of long memory |
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124 | (24) |
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124 | (5) |
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Robustness against additive outliers |
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129 | (4) |
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Robustness in the spectral domain |
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133 | (8) |
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141 | (3) |
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Long-range phenomena and other processes |
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144 | (4) |
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Estimation of location and scale, forecasting |
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148 | (24) |
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148 | (1) |
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Efficiency of the sample mean |
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148 | (3) |
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Robust estimation of the location parameter |
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151 | (5) |
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Estimation of the scale parameter |
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156 | (1) |
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Prediction of a future sample mean |
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157 | (2) |
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Confidence intervals for μ and a future mean |
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159 | (5) |
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Tests and confidence intervals for μ with known long-memory and scale parameters |
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159 | (1) |
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Tests and confidence intervals for a future mean, with known long-memory and scale parameters |
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160 | (1) |
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Tests and confidence intervals for μ with unknown long-memory and scale parameters |
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161 | (3) |
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Tests and confidence intervals for a future mean, with unknown long-memory and scale parameters |
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164 | (1) |
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164 | (8) |
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172 | (25) |
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172 | (4) |
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Regression with deterministic design |
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176 | (10) |
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176 | (4) |
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General regression with deterministic design |
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180 | (6) |
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Regression with random design; ANOVA |
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186 | (11) |
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186 | (1) |
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187 | (1) |
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The conditional variance of contrasts |
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188 | (1) |
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Three standard randomizations |
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189 | (2) |
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Results for complete randomization |
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191 | (1) |
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192 | (2) |
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194 | (3) |
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Goodness of fit tests and related topics |
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197 | (14) |
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Goodness of fit tests for the marginal distribution |
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197 | (4) |
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Goodness of fit tests for the spectral density |
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201 | (5) |
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Changes in the spectral domain |
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206 | (5) |
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211 | (7) |
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Processes with infinite variance |
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211 | (2) |
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Fractional GARMA processes |
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213 | (2) |
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Simulation of long-memory processes |
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215 | (3) |
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215 | (1) |
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Simulation of fractional Gaussian noise |
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216 | (1) |
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A method based on the fast Fourier transform |
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216 | (1) |
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Simulation by aggregation |
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217 | (1) |
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Simulation of fractional ARIMA processes |
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217 | (1) |
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218 | (44) |
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218 | (19) |
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Simulation of fractional Gaussian noise |
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218 | (2) |
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Simulation of fractional ARIMA (0,d,0) |
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220 | (3) |
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Whittle estimator for fractional Gaussian noise and fractional ARIMA (p, d, q) |
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223 | (10) |
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Approximate MLE for F E X P models |
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233 | (4) |
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237 | (25) |
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237 | (3) |
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240 | (3) |
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243 | (12) |
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255 | (2) |
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Northern hemisphere temperature data |
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257 | (5) |
Bibliography |
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262 | (40) |
Author index |
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302 | (4) |
Subject index |
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306 | |