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What are the most important statistical ideas of the past 50 years?
Andrew Gelman, Aki Vehtari
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References
16
Box, G. E. P., and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, second edition. San Francisco: Holden-Day.
References on 16
16.1
Abraham, B. (1981). Missing observations in time series, Commun. Stat., A10, 1643--1653.
References on 16.1
16.1.1
- Anderson, T.W. 1971. “The Statistical Analysis of Time Series”. New York: John Wiley and Sons Inc.
16.1.2
- Ashworth B. A Simulation Study of the Interpolation of Missing Data in Time Series Unpublished Report Department of Statistics, University of Waterloo Canada 1978
16.1.3
- Box, G.E.P. and Jenkins, G.M. 1976. “Time Series Analysis Forecasting and Control”. San Francisco: Holden-Day.
16.1.4
- Brubacher, S.R. and Wilson, G.T. 1976. Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand. Applied Statistics, 25: 107–116.
16.2
Abraham, B. and Box, G. E. P. (1978). Deterministic and forecast-adaptive time-dependent models, Appl. Stat., 27, 120--130.
16.3
Adler, J. (2010). R in a Nutshell, O’Reilly Media, Sebastopol, CA.
16.4
Ahn, S. K. (1993). Some tests for unit roots in autoregressive-integrated-moving average models with deterministic trends, Biometrika, 80, 855--868.#### 16.1
16.5
Ahn, S. K. and Reinsel, G. C. (1988). Nested reduced-rank autoregressive models for multiple time series, J. Am. Stat. Assoc., 83, 849--856.
16.6
Ahn, S. K. and Reinsel, G. C. (1990). Estimation for partially nonstationary multivariate autoregres- sive models, J. Am. Stat. Assoc., 85, 813--823.
16.7
Akaike, H. (1971). Autoregressive model fitting for control, Ann. Inst. Stat. Math., 23, 163--180.
16.6
Akaike, H. (1974a). A new look at the statistical model identification, IEEE Trans. Autom. Control, AC-19, 716--723.
16.7
Akaike, H. (1974b). Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes, Ann. Inst. Stat. Math., 26, 363--387.
16.8
Akaike, H. (1976). Canonical correlation analysis of time series and the use of an information criterion, in Systems Identification: Advances and Case Studies (eds. R. K. Mehra and D. G. Lainiotis), Academic Press, New York, pp. 27--96.
16.9
Ali, M. M. (1989). Tests for autocorrelation and randomness in multiple time series, J. Am. Stat. Assoc., 84, 533--540.
16.10
Andersen, T. G., Davis, R. A., Kreiss, J.-P., and Mikosch, T. (2009). Handbook of Financial Time Series, Springer, Berlin.
16.11
Anderson, B. D. O. and Moore, J. B. (1979). Optimal Filtering, Prentice Hall, Englewood Cliffs, NJ. Anderson, R. L. (1942). Distribution of the serial correlation coefficient, Ann. Math. Stat., 13, 1--13.
16.12
Time Series Analysis: Forecasting and Control, Fifth Edition. George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung ○c 2016 John Wiley & Sons. Inc. Published 2016 by John Wiley & Sons. Inc.
16.13
REFERENCES 643 Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distributions, Ann. Math. Stat., 22, 327--351.
16.14
Anderson, T. W. (1971). The Statistical Analysis of Time Series, Wiley, New York.
16.15
Anscombe, F. J. (1961). Examination of residuals, Proceedings of the 4th Berkeley Symposium, Vol. 1, pp. 1--36.
16.16
Anscombe, F. J. and Tukey, J. W. (1963). The examination and analysis of residuals, Technometrics, 5, 141--160.
16.17
Ansley, C. F. (1979). An algorithm for the exact likelihood of a mixed autoregressive moving average process, Biometrika, 66, 59--65.
16.18
Ansley, C. F. and Kohn, R. (1982). A geometrical derivation of the fixed interval smoothing algorithm, Biometrika, 69, 486--487.
16.19
Ansley, C. F. and Kohn, R. (1983). Exact likelihood of vector autoregressive-moving average process with missing or aggregated data, Biometrika, 70, 275--278.
16.20
Ansley, C. F. and Kohn, R. (1985). Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions, Ann. Stat., 13, 1286--1316.
16.21
Ansley, C. F. and Newbold, P. (1980). Finite sample properties of estimators for autoregressiv moving average models, J. Econom., 13, 159--183.
16.22
Astro ̈m, K. J. and Bohlin, T. (1966). Numerical identification of linear dynamic systems from normal operating records, in Theory of Self-Adaptive Control Systems (ed. P. H. Hammond), Plenum Press, New York, pp. 96--111.
16.23
Astro ̈m, K. J. and Wittenmark, B. (1984). Computer Controlled Systems, Prentice Hall, Englewood Cliffs, NJ.
16.24
Athanasopoulos, G., Poskitt, D. S., and Vahid, F. (2012). Two canonical VARMA forms: Scalar component models vis-a`-vis the Echelon form, Econometric Rev.,31, 60--83.
16.25
Bachelier, L. (1900). The ́orie de la spe ́culation, Ann. Sci. E ́ cole Norm. Sup., Paris, Ser. 3, 17, 21--86.
16.26
Bagshaw, M. and Johnson, R. A. (1977). Sequential procedures for detecting parameter changes in a time-series model, J. Am. Stat. Assoc., 72, 593--597.
16.27
Baillie, R. T. (1979). The asymptotic mean squared error of multistep prediction from the regression model with autoregressive errors, J. Am. Stat. Assoc., 74, 175--184.
16.28
Baillie, R. T. and Bollerslev, T. (1992). Prediction in dynamic models with time-dependent conditional variances, J. Econom., 52, 91--113.
16.29
Barnard, G. A. (1949). Statistical inference, J. R. Stat. Soc., B11, 115--139.
16.30
Barnard, G. A. (1959). Control charts and stochastic processes, J. R. Stat. Soc., B21, 239--257.
16.31
Barnard, G. A. (1963). The logic of least squares, J. R. Stat. Soc., B25, 124--127.
Barnard, G. A., Jenkins, G. M., and Winsten, C. B. (1962). Likelihood inference and time series, J. R. Stat. Soc., A125, 321--352.
Bartlett, M. S. (1946). On the theoretical specification and sampling properties of autocorrelated time-series, J. R. Stat. Soc., B8, 27--41.
Bartlett, M. S. (1955). Stochastic Processes, Cambridge University Press, Cambridge.
Basu, S. and Reinsel, G. C. (1996). Relationship between missing data likelihoods and complete data restricted data likelihoods for regression time series models: an application to total ozone data, Appl. Stat., 45, 63--72.
16.32
Bell, W. R. (1984). Signal extraction for nonstationary time series, Ann. Stat., 12, 646--664; correction, 19, 2280, 1991.
16.33
Bell, W. R. (1987). A note on overdifferencing and the equivalence of seasonal time series models with monthly means and models with (0, 1, 1)12 seasonal parts when Θ = 1, J. Bus. Econ. Stat., 5, 383--387.
16.34
Bell, W. R., Chu, Y.-J., and Tiao, G. C. (2012). Comparing mean squared errors of X-12-ARIMA and canonical ARIMA model-based seasonal adjustments, in Economic Time Series: Modeling and Seasonality (eds. W. R. Bell, S. H. Holan, and T. S. McElroy), Chapman & Hall, Boca Raton, FL, pp. 161--184.
16.35
Bell, W. R. and Hillmer, S. C. (1983). Modeling time series with calendar variation, J. Am. Stat. Assoc., 78, 526--534.
16.36
Bell, W. R. and Hillmer, S. C. (1987). Initializing the Kalman filter in the nonstationary case, Proceedings of the American Statistical Association, Business and Economic Statistics Section, pp. 693--697.
16.37
Bell, W. R. and Sotiris, E. (2010). Seasonal adjustment to facilitate forecasting: empirical results, Proceedings of the American Statistical Association, Business and Economic Statistics Section, Alexandria, VA.
16.38
Bera, J. and Higgins, M. (1993). ARCH models: properties, estimation, and testing, J. Econ. Surv., 7, 305--362.
16.39
Beran, J. (1994). Statistics for Long Memory Processes, Chapman & Hall, New York.
16.40
Beran, J. (1995). Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models, J. R. Stat. Soc., B57, 659--672.
16.41
Bergh, L. G. and MacGregor, J. F. (1987). Constrained minimum variance controllers: internal model structure and robustness properties, Ind. Eng. Chem. Res., 26, 1558--1564.
16.42
Berndt, E. K., Hall, B. H., Hall, R. E., and Hausman, J. A. (1974). Estimation inference in nonlinear structural models, Ann. Econ. Soc. Meas., 4, 653--665.
16.43
Bhargava, A. (1986). On the theory of testing for unit roots in observed time series, Rev. Econ. Stud., 53, 369--384.
16.44
Bhattacharyya, M. N. and Layton, A. P. (1979). Effectiveness of seat belt legislation on the Queensland road toll---an Australian case study in intervention analysis, J. Am. Stat. Assoc., 74, 596--603.
16.45
Billingsley, P. (1999). Convergence of Probability Measures, 2nd ed., Wiley, New York.
16.46
Birnbaum, A. (1962). On the foundations of statistical inference, J. Am. Stat. Assoc., 57, 269--306.
16.47
Bloomfield, P. (2000). Fourier Analysis of Time Series: An Introduction, 2nd ed., Wiley, Hoboken, NJ.
16.48
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, J. Econom., 31, 307--327.
16.49
Bollerslev, T. (1987). A conditional heteroskedastic time series model for speculative prices and rates of return, Rev. Econ. Stat., 69, 542--547.
16.50
Bollerslev, T. (1988). On the correlation structure in the generalized autoregressive conditional heteroskedastic process, J. Time Ser. Anal., 9, 121--31.
16.51
Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992). ARCH modelling in finance: a review of the theory and empirical evidence. J. Econom., 52, 5--59.
16.52
Bollerslev, T., Engle, R. F., and Nelson, D. B. (1994). ARCH model, in Handbook of Econometrics IV (eds. R. F. Engle and D. C. McFadden), Elsevier Science, Amsterdam, pp. 2959--3038.
16.53
Bollerslev, T. and Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances, Econom. Rev., 11, 143--172.
16.54
Box, G. E. P. (1966). Use and abuse of regression, Technometrics, 8, 625--629.
16.55
Box, G. E. P. (1980). Sampling and Bayes’ inference in scientific modelling and robustness, J. R Stat. Soc., A143, 383--430.
16.56
Box, G. E. P. (1991a). Feedback control by manual adjustment, Qual. Eng., 4(1), 143--151.
16.57
Box, G. E. P. (1991b). Bounded adjustment charts, Qual. Eng., 4(a), 331--338.
16.58
Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations, J. R. Stat. Soc., B26, 211--243.
16.59
REFERENCES 645 Box, G. E. P. and Hunter, W. G. (1965). The experimental study of physical mechanisms, Techno-
metrics, 7, 23--42.
16.60
Box, G. E. P., Hunter, W. G., and Hunter, J. S. (1978). Statistics for Experimenters, Wiley, NewYork.
16.61
Box, G. E. P. and Jenkins, G. M. (1962). Some statistical aspects of adaptive optimization and control,J. R. Stat. Soc., B24, 297--331.
16.62
Box, G. E. P. and Jenkins, G. M. (1963). Further contributions to adaptive quality control: simulta- neous estimation of dynamics: non-zero costs, Bulletin of the International Statistical Institute, 34th Session, Ottawa, Canada, pp. 943--974.
16.63
Box, G. E. P. and Jenkins, G. M. (1965). Mathematical models for adaptive control and optimization, AIChE J. Chem. E Symp. Ser., 4, 61.
16.64
Box, G. E. P. and Jenkins, G. M. (1968a). Discrete models for feedback and feedforward control, in The Future of Statistics (ed. D. G. Watts), Academic Press, New York, pp. 201--240.
16.65
Box, G. E. P. and Jenkins, G. M. (1968b). Some recent advances in forecasting and control, I, Appl. Stat., 17, 91--109.
16.66
Box, G. E. P. and Jenkins, G. M. (1969). Discrete models for forecasting and control, in Encyclopaedia of Linguistics, Information and Control (eds. A. R. Meaham and R. A. Hudson), Pergamon Press, Elmsford, NY, p. 162.
16.67
Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, revised ed., Holden-Day, San Francisco, CA.
16.68
Box, G. E. P., Jenkins, G. M., and Bacon, D. W. (1967a). Models for forecasting seasonal and nonseasonal time series, in Spectral Analysis of Time Series (ed. B. Harris), Wiley, New York, pp. 271--311.
16.69
Box, G. E. P., Jenkins, G. M., and MacGregor, J. F. (1974). Some recent advances in forecasting and control, Part II, Appl. Stat., 23, 158--179.
16.70
Box, G. E. P., Jenkins, G. M., and Wichern, D. W. (1967b). Least squares analysis with a dynamic model, Technical Report 105, Department of Statistics, University of Wisconsin--Madison.
16.71
Box, G. E. P. and Kramer, T. (1992). Statistical process monitoring and feedback adjustments---a discussion, Technometrics, 34, 251--285.
16.72
Box, G. E. P. and Lucen ̃o, A. (1993). Charts for optimal feedback control with recursive sampling and adjustment, Report 89, Center for Quality and Productivity Improvement, University of Wisconsin--Madison.
16.73
Box, G. E. P. and MacGregor, J. F. (1976). Parameter estimation with closed-loop operating data, Technometrics, 18, 371--380.
16.74
Box, G. E. P. and Pierce, D. A. (1970). Distribution of residual autocorrelations in autoregressive- integrated moving average time series models, J. Am. Stat. Assoc., 65, 1509--1526.
16.75
Box, G. E. P. and Ram ́ırez, J. (1992). Cumulative score charts, Qual. Reliab. Eng., 8, 17--27.
16.76
Box, G. E. P. and Tiao, G. C. (1965). Multiparameter problems from a Bayesian point of view, Ann.Math. Stat., 36, 1468--1482.
16.77
Box, G. E. P. and Tiao, G. C. (1973). Bayesian Inference, Addison-Wesley, Reading, MA.
16.77
Box, G. E. P. and Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems, J. Am. Stat. Assoc., 70, 70--79.
16.78
Box, G. E. P. and Tiao, G. C. (1976). Comparison of forecast and actuality, Appl. Stat., 25, 195--200. Box, G. E. P. and Tiao, G. C. (1977). A canonical analysis of multiple time series, Biometrika, 64,355--365.
16.79
Bray, J. (1971). Dynamic equations for economic forecasting with the G.D.P.--unemployment relation and the growth of G.D.P. in the United Kingdom as an example, J. R. Stat. Soc., A134, 167--209.
16.80
Briggs, P. A. N., Hammond, P. H., Hughes, M. T. G., and Plumb, G. O. (1965). Correlation analysis of process dynamics using pseudo-random binary test perturbations, Proceedings of the Institution of Mechanical Engineers, Advances in Automatic Control, Paper 7, Nottingham, UK, April.
16.81
Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd ed., Springer, New York.
16.82
Brown, R. G. (1962). Smoothing, Forecasting and Prediction of Discrete Time Series, Prentice Hall, Englewood Cliffs, NJ.
16.83
Brown, R. G. and Meyer, R. F. (1961). The fundamental theorem of exponential smoothing, Oper. Res., 9, 673--685.
16.84
Brubacher, S. R. and Tunnicliffe Wilson, G. (1976). Interpolating time series with applications to the estimation of holiday effects on electricity demand, Appl. Stat., 25, 107--116.
16.85
Bruce, A. G. and Martin, R. D. (1989). Leave-𝑘-out diagnostics for time series (with discussion), J. R. Stat. Soc., B51, 363--424.
16.86
Campbell, S. D. and Diebold, F. X. (2005). Weather forecasting for weather derivatives, J. Am. Stat. Assoc., 100, 6--16.
16.87
Chan, N. H. and Wei, C. Z. (1988). Limiting distributions of least squares estimates of unstable autoregressive processes, Ann. Stat., 16, 367--401.
16.88
Chang, I., Tiao, G. C., and Chen, C. (1988). Estimation of time series parameters in the presence of outliers, Technometrics, 30, 193--204.
16.89
Chatfield, C. (1979). Inverse autocorrelations, J. R. Stat. Soc., A142, 363--377.
16.90
Cheang, W. K. and Reinsel, G. C. (2000). Bias reduction of autoregressive estimates in time series regression model through restricted maximum likelihood, J. Am. Stat. Assoc., 95, 1173--1184.
16.91
Cheang, W. K. and Reinsel, G. C. (2003). Finite sample properties of ML and REML estimators in time series regression models with long memory noise, J. Stat. Comput. Simul., 73, 233--259.
16.92
Chen, C. and Liu, L.-M. (1993). Joint estimation of model parameters and outlier effects in time series, J. Am. Stat. Assoc., 88, 284--297.
16.93
Chen, C. and Tiao, G. C. (1990). Random level shift time series models, ARIMA approximation, and level shift detection, J. Bus. Econ. Stat., 8, 170--186.
16.94
Chen, R. and Tsay, R. S. (1993). Nonlinear additive ARX models, J. Am. Stat. Assoc., 88, 955--967.
16.95
Chu, Y-J., Tiao, G. C., and Bell, W. R. (2012). A mean squared error criterion for comparing X-12-ARIMA and model-based seasonal adjustment filters, Taiwan Econ. Forecast Policy, 43, 1--32.
16.96
Cleveland, W. S. (1972). The inverse autocorrelations of a time series and their applications, Tech- nometrics, 14, 277--293.
16.97
Cleveland, W. S. and Tiao, G. C. (1976). Decomposition of seasonal time series: a model for the Census X-11 Program, J. Am. Stat. Assoc., 71, 581--587.
16.98
Cooper, D. M. and Thompson, R. (1977). A note on the estimation of the parameters of the autore- gressive moving average process, Biometrika, 64, 625--628.
16.99
Cooper, D. M. and Wood, E. F. (1982). Identifying multivariate time series models, J. Time Ser. Anal., 3, 153--164.
16.100
Coutie, G. A. (1964) Short Term Forecasting, ICI Monograph 2, Oliver & Boyd, Edinburgh.
16.101
Crawley, M. J. (2007). The R Book, Wiley, Hoboken, NJ.
16.102
Cryer, J. D. and Chan, K.-S. (2010). Time Series Analysis with Applications in R, 2nd ed., Springer, New York.
16.103
Damsleth, E. (1980). Interpolating missing values in a time series, Scand. J. Stat., 7, 33--39.
16.104
Daniel, C. (1959). Use of half-normal plots in interpreting factorial two-level experiments, Techno- metrics, 1, 311--341.
16.105
Davies, N., Triggs, C. M., and Newbold, P. (1977). Significance levels of the Box--Pierce portmanteau statistic in finite samples, Biometrika, 64, 517--522.
16.106
Deistler, M., Dunsmuir, W., and Hannan, E. J. (1978). Vector linear time series models: corrections and extensions, Adv. Appl. Probab., 10, 360--372.
16.107
Deming, W. E. (1986). Out of the Crisis, Center for Advanced Engineering Study, MIT, Cambridge, MA.
16.108
Dent, W. and Min, A. S. (1978). A Monte Carlo study of autoregressive integrated moving average processes, J. Econom., 7, 23--55.
16.109
Dickey, D. A., Bell, W. R., and Miller, R. B. (1986). Unit roots in time series models: tests and implications, Am. Stat., 40, 12--26.
16.110
Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimates for autoregressive time series with a unit root, J. Am. Stat. Assoc., 74, 427--431.
16.111
Dickey, D. A. and Fuller, W. A. (1981). Likelihood ratio tests for autoregressive time series with a unit root, Econometrica, 49, 1057--1072.
16.112
Dickey, D. A. and Pantula, S. G. (1987). Determining the order of differencing in autoregressive processes, J. Bus. Econ. Stat., 5, 455--461.
16.113
Diebold, F. X. and Nerlove, M. (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model, J. Appl. Econom., 4, 1--28.
16.114
Doob, J. L. (1953). Stochastic Processes, Wiley, New York.
16.115
Dudding, B. P. and Jennet, W. J. (1942). Quality control charts, British Standard 600R.
16.116
Dunsmuir, W. and Hannan, E. J. (1976). Vector linear time series models, Adv. Appl. Probab., 8, 339--364.
16.117
Durbin, J. (1960). The fitting of time-series models, Rev. Int. Stat. Inst., 28, 233--244.
16.118
Durbin, J. (1970). Testing for serial correlation in least-squares regression when some of the regressors are lagged dependent variables, Econometrica, 38, 410--421.
16.119
Durbin, J. and Koopman, S. J. (2012). Time Series Analysis by State Space Methods, 2nd ed., Oxford University Press.
16.120
Elliott, G., Rothenberg, T. J., and Stock, J. H. (1996). Efficient tests for an autoregressive unit root, Econometrica, 64, 813--836.
16.121
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987--1008.
16.122
Engle, R. F. (1983). Estimates of the variance of U.S. inflation based on the ARCH model, J. Money Credit Banking, 15, 286--301.
16.123
Engle, R. F. and Bollerslev, T. (1986). Modeling the persistence of conditional variances, Econom. Rev., 5, 1--50.
16.124
Engle, R. F. and Granger, C. W. J. (1987). Co-integration and error correction: representation, estimation, and testing, Econometrica, 55, 251--276.
16.125
Engle, R. F., Lilien, D. M., and Robins, R. P. (1987). Estimating time-varying risk premia in the term structure: the ARCH-M model, Econometrica, 55, 391--407.
16.126
Fan, J. and Yao, Q. (2003). Nonlinear Time Series, Springer, New York.
16.127
Fearn, T. and Maris, P. I. (1991). An application of Box--Jenkins methodology to the control of gluten addition in a flour mill, Appl. Stat., 40, 477--484.
16.128
Fisher, R. A. (1956). Statistical Methods and Scientific Inference, Oliver & Boyd, Edinburgh.
16.129
Fisher, T. J. and Gallagher, C. M. (2012). New weighted portmanteau statistics for time series goodness of fit testing, J. Am. Stat. Assoc. 107, 777--787.
16.130
Fox, A. J. (1972). Outliers in time series, J. R. Stat. Soc., B34, 350--363.
16.131
Francq, C. and Zako ̈ıan, J.-M. (2009). A tour in the asymptotic theory of GARCH estimation, in Handbook of Financial Time Series (eds. T. G. Andersen, R. A. Davis, J.-P. Kreiss, and T. Mikosch), Springer, New York, pp. 85--111.
16.132
Francq, C. and Zako ̈ıan, J.-M. (2010). GARCH Models, Wiley, New York.
16.133
Franses, P. H. and van Dijk, D. (2000). Non-Linear Time Series Models in Empirical Finance, Cambridge University Press, Cambridge.
16.134
Fuller, W. A. (1996). Introduction to Statistical Time Series, 2nd ed., Wiley, New York.
16.135
Gao, J. (2007). Nonlinear Time Series: Semiparametric and Nonparametric Methods, Chapman & Hall/CRC.
16.136
Gardner, G., Harvey, A. C., and Phillips, G. D. A. (1980). Algorithm AS 154. An algorithm for exact maximum likelihood estimation of autoregressive-moving average models by means of Kalman filtering, Appl. Stat., 29, 311--322.
Gersch, W. and Kitagawa, G. (1983). The prediction of time series with trends and seasonalities, J. Bus. Econ. Stat., 1, 253--264.
Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models, J. Time Ser. Anal., 4, 221--238.
Ghysels, E. and Osborn, D. R. (2001). The Econometric Analysis of Seasonal Time Series, Cambridge University Press, Cambridge.
Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993). On the relation between the expected value and the volatility of nominal excess return on stocks, J. Finance, 48, 1779--1801.
Godfrey, L. G. (1979). Testing the adequacy of a time series model, Biometrika, 66, 67--72. Gonza ́lez-Rivera, G. (1998). Smooth transition GARCH models, Stud. Nonlinear Dyn. Econom., 3,
161--178.
Granger, C. W. J. and Anderson, A. P. (1978). An Introduction to Bilinear Time Series Models, Vandenhoek & Ruprecht, Gottingen.
Granger, C. W. J. and Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal., 1, 15--29.
Gray, H. L., Kelley, G. D., and McIntire, D. D. (1978). A new approach to ARMA modelling, Commun. Stat., B7, 1--77.
Grenander, U. and Rosenblatt, M. (1957). Statistical Analysis of Stationary Time Series, Wiley, New York.
Hagerud, G. E. (1997). A new non-linear GARCH model, EFI, Stockholm School of Economics. Haggan, V. and Ozaki, T. (1981). Modeling nonlinear vibrations using an amplitude-dependent
autoregressive time series model, Biometrika, 68, 189--196.
Haldrup, N., Kruse, R., Tera ̈virta, T., and Varneskov, R. T. (2013). Unit roots, non-linearities and
structural breaks, in Handbook of Research Methods and Applications in Empirical Macroeco-
nomics (eds. N. Hashimzade and M. A. Thornton), Edward Elgar Publishing, Ltd., UK
Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Application, Academic Press,
New York.
Hamilton, J. D. (1994). Time Series Analysis, Princeton University Press, Princeton, NJ.
Hannan, E. J. (1960). Time Series Analysis, Methuen, London.
Hannan, E. J. (1970). Multiple Time Series, Wiley, New York.
Hannan, E. J. and Deistler, M. (1988). The Statistical Theory of Linear Systems, Wiley, New York.
Hannan, E. J., Dunsmuir, W. M., and Deistler, M. (1979). Estimation of vector ARMAX models, J. Multivariate Anal., 10, 275--295.
Hannan, E. J. and Kavalieris, L. (1984). Multivariate linear time series models, Adv. Appl. Probab., 16, 492--561.
REFERENCES 649 Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression, J. R.
Stat. Soc., B41, 190--195.
Hannan, E. J. and Rissanen, J. (1982). Recursive estimation of mixed autoregressive moving average
order, Biometrika, 69, 81--94; correction, 70, 303, 1983.
Harris, T. J., MacGregor, J. F., and Wright, J. D. (1982). An overview of discrete stochastic controllers:
generalized PID algorithms with dead-time compensation, Can. J. Chem. Eng., 60, 425--432.
Harrison, P. J. (1965). Short-term sales forecasting, Appl. Stat., 14, 102--139.
Harvey, A. C. (1981). Finite sample prediction and overdifferencing, J. Time Ser. Anal., 2, 221--232.
Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge.
Harvey, A. C. and Phillips, G. D. A. (1979). Maximum likelihood estimation of regression models with autoregressive-moving average disturbances, Biometrika, 66, 49--58.
Harvey, A. C. and Pierse, R. G. (1984). Estimating missing observations in economic time series, J. Am. Stat. Assoc., 79, 125--131.
Harvey, A. C., Ruiz, E., and Shephard, N. (1994). Multivariate stochastic variance models, Rev. Econ. Stud., 61, 247--264.
Harvey, A. C. and Todd, P. H. J. (1983). Forecasting economic time series with structural and Box--Jenkins models: a case study, J. Bus. Econ. Stat., 1, 299--307.
Harvey, D. I., Leybourne, S. J., and Taylor, A. M. R. (2009). Unit root testing in practice: dealing with uncertainty over trend and initial conditions (with commentaries and rejoiner), Econom. Theory, 25, 587--667.
Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts, Biometrika, 61, 383--385.
Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems, J. Am. Stat. Assoc., 72, 320--340.
Haugh, L. D. and Box, G. E. P. (1977). Identification of dynamic regression (distributed lag) models connecting two time series, J. Am. Stat. Assoc., 72, 121--130.
Hauser, M. A. (1999). Maximum likelihood estimators for ARMA and ARFIMA models: a Monte Carlo study, J. Stat. Plan. Infer., 80, 229--255.
He, C., Silvennoinen, A., and Tera ̈svirta, T. (2008). Parameterizing unconditional skewness in non- linear time series with conditional heteroscedasticity, J. Financ. Econ., 6, 208--230.
He, C. and Tera ̈svirta, T. (1999). Fourth moment structure of the GARCH(𝑝,𝑞) process, Econom. Theory, 15, 824--846.
Hillmer, S. C. and Tiao, G. C. (1979). Likelihood function of stationary multiple autoregressive moving average models, J. Am. Stat. Assoc., 74, 652--660.
Hillmer, S. C. and Tiao, G. C. (1982). An ARIMA-model-based approach to seasonal adjustment, J. Am. Stat. Assoc., 77, 63--70.
Hinich, M. J. (1982). Testing for Gaussianity and linearity of a stationary time series, J. Time Ser. Anal., 3, 169--176.
Holt, C. C. (1957). Forecasting trends and seasonals by exponentially weighted moving averages, O.N.R. Memorandum 52, Carnegie Institute of Technology, Pittsburgh, PA.
Holt, C. C., Modigliani, F., Muth, J. F., and Simon, H. A. (1963). Planning Production, Inventories and Work Force, Prentice Hall, Englewood Cliffs, NJ.
Hosking, J. R. M. (1980). The multivariate portmanteau statistic, J. Am. Stat. Assoc., 75, 602--608. Hosking, J. R. M. (1981). Fractional differencing, Biometrika, 68, 165--176.
Hosking, J. R. M. (1996). Asymptotic distributions of the sample mean, autocovariances, and auto-
correlations of long memory time series, J. Econom., 73, 261--284.
650 REFERENCES
Hougen, J. O. (1964). Experience and Experiments with Process Dynamics, Chemical Engineering
Progress Monograph Series, Vol. 60, No. 4, American Institute Chemical Engineers.
Hurst, H. (1951). Long term storage capacity of reservoirs, Trans. Am. Soc. Civil Eng., 116, 778--808. Hutchinson, A. W. and Shelton, R. J. (1967). Measurement of dynamic characteristics of full-scale
plant using random perturbing signals: an application to a refinery distillation column, Trans. Inst. Chem. Eng., 45, 334--342.
Ishikawa, K. (1976). Guide to Quality Control, Asian Productivity Organization, Tokyo.
Jacquier, E., Polson, N. G., and Rossi, P. (1994). Bayesian analysis of stochastic volatility models
(with discussion), J. Bus. Econ. Stat., 12, 371--417.
Jeffreys, H. (1961). Theory of Probability, 3rd ed., Clarendon Press, Oxford.
Jenkins, G. M. (1956). Tests of hypotheses in the linear autoregressive model, I, Biometrika, 41, 405--419, 1954; II, Biometrika, 43, 186--199.
Jenkins, G. M. (1964). Contribution to the discussion of the paper ‘‘Relationships between Bayesian and confidence limits for predictors,’’ by A. R. Thatcher, J. R. Stat. Soc., B26, 176--210.
Jenkins, G. M. (1975). The interaction between the muskrat and mink cycles in North Canada, Pro- ceedings of the 8th International Biometric Conference, Editura Aca- demiei Republicii Socialiste Romania, Bucharest, pp. 55--71.
Jenkins, G. M. (1979). Practical Experiences with Modelling and Forecasting Time Series, Gwilym Jenkins & Partners Ltd., Jersey, Channel Islands.
Jenkins, G. M. and Watts, D. G. (1968). Spectral Analysis and Its Applications, Holden-Day, San Francisco, CA.
Johansen, S. (1988). Statistical analysis of cointegration vectors, J. Econ. Dyn. Control, 12, 231--254. Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector
autoregressive models, Econometrica, 59, 1551--1580.
Johansen, S. and Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration:
with applications to the demand for money, Oxf. Bull. Econ. Stat., 52, 169--210.
Johnson, R. A. and Wichern, D. W. (2007). Applied Multivariate Statistical Analysis, 6th ed., Pearson,
Prentice Hall, Upper Saddle River, NJ.
Jones, R. H. (1980). Maximum likelihood fitting of ARMA models to time series with missing
observations, Technometrics, 22, 389--395.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems, J. Basic Eng., 82,
35--45.
Kalman, R. E. and Bucy, R.S. (1961). New results in linear filtering and prediction theory, J. Basic
Eng., 83, 95--108.
Keenan, D. M. (1985). A Tukey non-additivity-type test for time series nonlinearity, Biometrika, 72,
39--44.
Kendall, M. G. (1945). On the analysis of oscillatory time-series, J. R. Stat. Soc., A108, 93--129. Kitagawa, G. and Gersch, W. (1984). A smoothness priors-state space modeling of time series with
trend and seasonality, J. Am. Stat. Assoc., 79, 378--389.
Kohn, R. and Ansley, C. F. (1986). Estimation, prediction, and interpolation for ARIMA models with
missing data, J. Am. Stat. Assoc., 81, 751--761.
Kolmogoroff, A. (1939). Sur l’interpolation et l’extrapolation des suites stationnaires, C. R. Acad.
Sci. Paris, 208, 2043--2045.
Kolmogoroff, A. (1941a). Stationary sequences in Hilbert space, Bull. Math. Univ. Moscow, 2(6),
1--40.
Kolmogoroff, A. (1941b). Interpolation und Extrapolation von stationa ̈ren zufa ̈lligen folgen, Bull. Acad. Sci. (Nauk) USSR, Ser. Math., 5, 3--14.
REFERENCES 651 Koopmans, L. H. (1974). The Spectral Analysis of Time Series, Academic Press, New York.
Kotnour, K. D., Box, G. E. P., and Altpeter, R. J. (1966). A discrete predictor-controller applied to sinusoidal perturbation adaptive optimization, Inst. Soc. Am. Trans., 5, 255--262.
Lanne, M. and Saikkonen, P. (2005). Nonlinear GARCH models for highly persistent volatility, Econom. J., 8, 251--276.
Le, N. D., Martin, R. D., and Raftery, A. E. (1996). Modeling flat stretches, bursts, and outliers in time series using mixture transition distribution models, J. Am. Stat. Assoc., 91, 1504--1515.
Ledolter, J. (1981). Recursive estimation and adaptive forecasting in ARIMA models with time varying coefficients, in Applied Time Series II (ed. D. F. Findley), Academic Press, New York, pp. 449--472.
Levinson, N. (1947). The Wiener (root mean square) error criterion in filter design and prediction, Math. Phys., 25, 262--278.
Lewis, P. A. W. and Stevens, J. G. (1991). Nonlinear modeling of time series using multivariate adaptive regression splines (MARS), J. Am. Stat. Assoc., 86, 864--877.
Leybourne, S. J. and McCabe, B. P. M. (1994). A consistent test for a unit root, J. Bus. Econ. Stat., 12, 157--166.
Li, W. K. (2004). Diagnostic Checks for Time Series, Chapman & Hall/CRC.
Li, W. K., Ling, S., and McAleer, M. (2003). Recent theoretical results for time series models with
GARCH errors, J. Econ. Surv., 16, 245--269.
Li, W. K. and Mak, T. K. (1994). On the squared residual autocorrelations in non-linear time series
models with conditional heteroscedasticity, J. Time Ser. Anal., 15, 627--636.
Li, W. K. and McLeod, A. I. (1981). Distribution of the residual autocorrelations in multivariate
ARMA time series models, J. R. Stat. Soc., B43, 231--239.
Li, W. K. and McLeod, A. I. (1986). Fractional time series modelling, Biometrika, 73, 217--221.
Ling, S. and McAleer, M. (2002). Stationarity and the existence of moments of a family of GARCH models, J. Econom., 106, 109--117.
Ling, S. and Tong, H. (2011). Score based goodness-of-fit tests for time series, Stat. Sin., 21, 1807--1829.
Liu, J. and Brockwell, P. J. (1988). On the general bilinear time series model, J. Appl. Probab., 25, 553--564.
Liu, L.-M. and Hanssens, D. M. (1982). Identification of multiple-input transfer function models, Commun. Stat., A11, 297--314.
Ljung, G. M. (1986). Diagnostic testing of univariate time series models, Biometrika, 73, 725--730.
Ljung, G. M. (1993). On outlier detection in time series, J. R. Stat. Soc., B55, 559--567.
Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models, Biometrika, 65, 297--303.
Ljung, G. M. and Box, G. E. P. (1979). The likelihood function of stationary autoregressive-moving average models, Biometrika, 66, 265--270.
Loe`ve, M. (1977). Probability Theory I, Springer, New York.
Lundbergh, S. and Tera ̈svirta, T. (2002). Evaluating GARCH models, J. Econom., 110, 417--435.
Lu ̈tkepohl, H. (2006). New Introduction to Multiple Time Series Analysis, Springer, Berlin.
Lu ̈tkepohl, H. and Poskitt, D. S. (1996). Specification of echelon-form VARMA models, J. Bus. Econ. Stat., 14, 69--79.
Luukkonen, R., Saikkonen, P., and Tera ̈svirta, T. (1988a). Testing linearity against smooth transition autoregressive models, Biometrika, 75, 491--499.
Luukkonen, R., Saikkonen, P., and Tera ̈svirta, T. (1988b). Testing linearity in univariate time series, Scand. J. Stat., 15, 161--175.
652 REFERENCES
MacGregor, J. F. (1972). Topics in the control of linear processes with stochastic disturbances, Ph.D.
thesis, University of Wisconsin--Madison.
Mahdi, E. and McLeod, I. A. (2012). Improved multivariate portmanteau test, J. Time Ser. Anal., 33,
211--222.
Mann, H. B. and Wald, A. (1943). On the statistical treatment of linear stochastic difference equations,
Econometrica, 11, 173--220.
Maravall, A. (1993). Stochastic linear trends: models and estimators. J. Econom., 56, 5--37.
Martin, R. D. and Yohai, V. J. (1986). Influence functionals for time series (with discussion), Ann. Stat., 14, 781--855.
McLeod, A. I. and Hipel, K. W. (1978). Preservation of the rescaled adjusted range. I. A reassessment of the Hurst phenomenon, Water Resour. Res., 14, 491--508.
McLeod, A. I. and Li, W. K. (1983). Diagnostic checking ARMA time series models using squared- residual autocorrelations, J. Time Ser. Anal., 4, 269--273.
Melino, A. and Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility, J. Econom., 45, 239--265.
Milhøj, A. (1985). The moment structure of ARCH processes, Scand. J. Stat., 12, 281--292.
Mills, T. C. and Markellos, R. N. (2008). The Econometric Modelling of Financial Time Series, 3rd
ed., Cambridge University Press, Cambridge.
Montgomery, D. C. and Weatherby, G. (1980). Modeling and forecasting time series using transfer
function and intervention methods, AIIE Trans., 289--307.
Monti, A. C. (1994). A proposal for residual autocorrelation test in linear models, Biometrika, 81,
776--780.
Moran, P. A. P. (1954). Some experiments on the prediction of sunspot numbers, J. R. Stat. Soc.,
B16, 112--117.
Muth, J. F. (1960). Optimal properties of exponentially weighted forecasts, J. Am. Stat. Assoc., 55,
299--306.
Nelson, D. B. (1990). Stationarity and persistence in the GARCH(1, 1) model, Econom. Theory, 6, 318--334.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: a new approach, Econometrica, 59, 347--370.
Nelson, D. B. and Cao, C. Q. (1992). Inequality constraints in the univariate GARCH model, J. Bus. Econ. Stat., 10, 229--235.
Newbold, P. (1973). Bayesian estimation of Box--Jenkins transfer function-noise models, J. R. Stat. Soc., B35, 323--336.
Newbold, P. (1974). The exact likelihood function for a mixed autoregressive-moving average process, Biometrika, 61, 423--426.
Newbold, P. (1980). The equivalence of two tests of time series model adequacy, Biometrika, 67, 463--465.
Ng, S. and Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power, Econometrica, 69, 1519--1554.
Nicholls, D. F. and Hall, A. D. (1979). The exact likelihood function of multivariate autoregressive moving average models, Biometrika, 66, 259--264.
Nicholls, D. F. and Quinn, B. G. (1982). Random Coefficient Autoregressive Models: An Introduction, Lecture Notes in Statistics, Vol. 11, Springer, New York.
Osborn, D. R. (1982). On the criteria functions used for the estimation of moving average processes, J. Am. Stat. Assoc., 77, 388--392.
Page, E. S. (1957). On problems in which a change in a parameter occurs at an unknown point, Biometrika, 44, 248--252.
Page, E. S. (1961). Cumulative sum charts, Technometrics, 3, 1--9.
Palm, F. C., Smeekes, S., and Urbain, J. P. (2008). Bootstrap unit-root tests: comparison and exten-
sions, J. Time Ser. Anal., 29, 371--401.
Palma, W. (2007). Long-Memory Time Series: Theory and Methods, Wiley, New York.
Pankratz, A. (1991). Forecasting with Dynamic Regression Models, Wiley, New York.
Pantula, S. G., Gonzalez-Farias, G., and Fuller, W. A. (1994). A comparison of unit root test criteria,
J. Bus. Econ. Stat., 12, 449--459.
Pen ̃a, D. and Rodr ́ıguez, J. (2002). A powerful portmanteau test of lack of fit for time series, J. Am.
Stat. Assoc., 97, 601--610.
Pen ̃a, D. and Rodr ́ıguez, J. (2006). The log of the determinant of the autocorrelation matrix for testing
of lack of fit in time series, J. Stat. Plan. Infer., 136, 2706--2718.
Perron, P. and Qu, Z. (2007). A simple modification to improve the finite sample properties of Ng
and Perron’s unit root tests, Econ. Lett., 94, 12--19.
Petruccelli, J. and Davies, N. (1986). A portmanteau test for self-exciting threshold autoregressive-
type nonlinearity in time series, Biometrika, 73, 687--694.
Phillips, P. C. B. (1987). Time series regression with a unit root, Econometrica, 55, 277--301. Phillips, P. C. B. and Perron, P. (1988). Testing for a unit root in time series regression, Biometrika,
75, 335--346.
Phillips, P. C. B. and Xiao, Z. (1998). A primer on unit root testing, J. Econ. Surv., 12, 423--470.
Pierce, D. A. (1972a). Least squares estimation in dynamic-disturbance time series models, Biometrika, 59, 73--78.
Pierce, D. A. (1972b). Residual correlations and diagnostic checking in dynamic-disturbance time series models, J. Am. Stat. Assoc., 67, 636--640.
Poskitt, D. S. (1992). Identification of echelon canonical forms for vector linear processes using least squares, Ann. Stat., 20, 195--215.
Poskitt, D. S. and Tremayne, A. R. (1980). Testing the specification of a fitted autoregressive-moving average model, Biometrika, 67, 359--363.
Poskitt, D. S. and Tremayne, A. R. (1981). An approach to testing linear time series models, Ann. Stat., 9, 974--986.
Poskitt, D. S. and Tremayne, A. R. (1982). Diagnostic tests for multiple time series models, Ann. Stat., 10, 114--120.
Priestley, M. B. (1980). State-dependent models: a general approach to non-linear time series analysis, J. Time Ser. Anal., 1, 47--71.
Priestley, M. B. (1981). Spectral Analysis and Time Series, Academic Press, New York.
Priestley, M. B. (1988). Non-Linear and Non-Stationary Time Series Analysis, Academic Press,
London.
Quenouille, M. H. (1949). Approximate tests of correlation in time-series, J. R. Stat. Soc., B11, 68--84.
Quenouille, M. H. (1952). Associated Measurements, Butterworth, London.
Quenouille, M. H. (1957). Analysis of Multiple Time Series, Hafner, New York.
Quinn, B. G. (1980). Order determination for a multivariate autoregression, J. R. Stat. Soc., B42, 182--185.
Ramsey, J. B. (1969). Tests for specification errors in classical least-squares regression analysis, J. R. Stat. Soc., B31, 350--371.
Rao, C. R. (1965). Linear Statistical Inference and Its Applications, Wiley, New York.
Rao, J. N. K. and Tintner, G. (1963). On the variate difference method, Aust. J. Stat., 5, 106--116.
REFERENCES 653
654 REFERENCES
Reinsel, G. C. (1979). Maximum likelihood estimation of stochastic linear difference equations with
autoregressive moving average errors, Econometrica, 47, 129--151.
Reinsel, G. C. (1997). Elements of Multivariate Time Series Analysis, 2nd ed., Springer, New York. Reinsel, G. C. and Ahn, V. (1992). Vector autoregressive models with unit roots and reduced rank
structure: estimation, likelihood ratio test, and forecasting, J. Time Ser. Anal., 13, 353--375. Reinsel, G. C. and Tiao, G. C. (1987). Impact of chlorofluoromethanes on stratospheric ozone: a
statistical analysis of ozone data for trends, J. Am. Stat. Assoc., 82, 20--30.
Reinsel, G. C. and Wincek, M. A. (1987). Asymptotic distribution of parameter estimators for
nonconsecutively observed time series, Biometrika, 74, 115--124.
Rivera, D. E., Morari, M., and Skogestad, S. (1986). Internal model control. 4. PID controller design,
Ind. Eng. Chem. Process Des. Dev., 25, 252--265.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages, Technometrics, 1,
239--250.
Robinson, E. A. (1967). Multichannel Time Series Analysis, Holden-Day, San Francisco, CA. Robinson, P. M. (2003). Time Series with Long Memory, Oxford University Press, Oxford.
Said, S. E. and Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models
of unknown order, Biometrika, 71, 599--607.
Said, S. E. and Dickey, D. A. (1985). Hypothesis testing in ARIMA(𝑝,1,𝑞) models, J. Am. Stat.
Assoc., 80, 369--374.
Saikkonen, P. and Luukkonen, R. (1993). Testing for a moving average unit root in autoregressive
integrated moving average models, J. Am. Stat. Assoc., 88, 596--601.
Savage, L. J. (1962). The Foundations of Statistical Inference, Methuen, London.
Schmidt, P. and Phillips, P. C. B. (1992). LM tests for a unit root in the presence of deterministic trends, Oxf. Bull. Econ. Stat., 54, 257--287.
Schuster, A. (1898). On the investigation of hidden periodicities, Terr. Magn. Atmos. Electr., 3, 13--41.
Schuster, A. (1906). On the periodicities of sunspots, Philos. Trans. R. Soc., A206, 69--100. Schwarz, G. (1978). Estimating the dimension of a model, Ann. Stat., 6, 461--464.
Shea, B. L. (1987). Estimation of multivariate time series, J. Time Ser. Anal., 8, 95--109.
Shephard, N. G. (2005). Stochastic Volatility: Selected Readings, Oxford University Press, Oxford. Shewhart, W. A. (1931). The Economic Control of the Quality of Manufactured Product, Macmillan,
New York.
Shin, D. W. and Fuller, W. A. (1998). Unit root tests based on unconditional maximum likelihood
estimation for the autoregressive moving average, J. Time Ser. Anal., 19, 591--599.
Shumway, R. and Stoffer, D. (2011). Time Series Analysis and Its Applications, 3rd ed., Springer,
New York.
Silvey, S. D. (1959). The Lagrangian multiplier test, Ann. Math. Stat., 30, 389--407.
Slutsky, E. (1937). The summation of random causes as the source of cyclic processes (Russian), Probl. Econ. Conditions, 3, 1, 1927; English translation, Econometrica, 5, 105--146.
Solo, V. (1984a). The exact likelihood for a multivariate ARMA model, J. Multivariate Anal., 15, 164--173.
Solo, V. (1984b). The order of differencing in ARIMA models, J. Am. Stat. Assoc., 79, 916--921. Solo, V. (1986). Topics in advanced time series analysis, in Lectures in Probability and Statistics
(eds. G. del Pino and R. Rebolledo), Springer, New York, pp. 165--328.
Sowell, F. (1992). Maximum likelihood estimation of stationary univariate fractionally integrated time series models, J. Econom., 53, 165--188.
Stralkowski, C. M. (1968). Lower order autoregressive-moving average stochastic models and their use for the characterization of abrasive cutting tools, Ph.D. thesis, University of Wisconsin--Madison.
Straumann, D. and Mikosch, T. (2006). Quasi-maximum-likelihood estimation in conditionally het- eroscedastic time series: a stochastic recurrence equations approach, Ann. Stat., 34, 2449--2495.
Subba Rao, T. (1981). On the theory of bilinear models, J. R. Stat. Soc., B43, 244--255.
Subba Rao, T. and Gabr, M. M. (1980). A test for nonlinearity of stationary time series, J. Time Ser.
Anal., 1, 145--158.
Subba Rao, T. and Gabr, M. M. (1984). An Introduction to Bispectral Analysis and Bilinear Time
Series Models, Springer, Berlin.
Tam, W. K. and Reinsel, G. C. (1997). Tests for seasonal moving average unit root in ARIMA
models, J. Am. Stat. Assoc., 92, 725--738.
Tam, W. K. and Reinsel, G. C. (1998). Seasonal moving-average unit root tests in the presence of a
linear trend, J. Time Ser. Anal., 19, 609--625.
Tera ̈svirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive
models, J. Am. Stat. Assoc., 89, 208--218.
Tera ̈svirta, T. (2009). An introduction to univariate GARCH models, in Handbook of Financial Time Series (eds. T. G. Andersen, R. A. Davis, J.-P Kreiss, J.-P., and T. Mikosch), Springer, New York, pp. 85--111.
Tera ̈svirta, T., Tjøstheim, D, and Granger, W. J. (2010). Modelling Nonlinear Economic Time Series, Oxford University Press, Oxford, UK.
Thompson, H. E. and Tiao, G. C. (1971). Analysis of telephone data: a case study of forecasting seasonal time series, Bell J. Econ. Manage. Sci., 2, 515--541.
Tiao, G. C. and Box, G. E. P. (1981). Modeling multiple time series with applications, J. Am. Stat. Assoc., 76, 802--816.
Tiao, G. C., Box, G. E. P., and Hamming, W. J. (1975). Analysis of Los Angeles photochemical smog data: a statistical overview, J. Air Pollut. Control Assoc., 25, 260--268.
Tiao, G. C. and Tsay, R. S. (1983). Multiple time series modeling and the extended sample cross- correlations, J. Bus. Econ. Stat., 1, 43--56.
Tiao, G. C. and Tsay, R. S. (1989). Model specification in multivariate time series (with discussion), J. R. Stat. Soc., B51, 157--213.
Tintner, G. (1940). The Variate Difference Method, Principia Press, Bloomington, IN.
Tjøstheim, D. (1994). Non-linear time series: a selective review, Scand. J. Stat., 21, 97--130.
Tong, H. (1978). On a threshold model, in Pattern Recognition and Signal Processing (ed. C. H. Chen), Sijthoff & Noordhoff, Amsterdam, pp. 101--141.
Tong, H. (1983). Threshold Models in Non-Linear Time Series Analysis, Springer, New York. Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach, Oxford University Press,
Oxford, UK.
Tong, H. (2007). Birth of the threshold autoregressive model, Stat. Sin., 17, 8--14.
Tong, H. and Lim, K. S. (1980). Threshold autoregression, limit cycles, and cyclical data (with
discussion), J. R. Stat. Soc., B42, 245--292.
Tsay, R. S. (1986a). Nonlinearity tests for time series, Biometrika, 73, 461--466.
Tsay, R. S. (1986b). Time series model specification in the presence of outliers, J. Am. Stat. Assoc., 81, 132--141.
Tsay, R. S. (1987). Conditional heteroskedastic time series models, J. Am. Stat. Assoc., 82, 590--604. Tsay, R. S. (1988). Outliers, level shifts, and variance changes in time series, J. Forecasting, 7, 1--20. Tsay, R. S. (1989a). Identifying multivariate time series models, J. Time Ser. Anal., 10, 357--372.
Tsay, R. S. (1989b). Parsimonious parametrization of vector autoregressive moving average models,
J. Bus. Econ. Stat., 7, 327--341.
Tsay, R. S. (1991). Two canonical forms for vector ARMA processes, Stat. Sin., 1, 247--269.
Tsay, R. S. (2010). Analysis of Financial Time Series, 3rd ed., Wiley, Hoboken, NJ.
Tsay, R. S. (2014). Multivariate Time Series Analysis, Wiley, Hoboken, NJ.
Tsay, R. S. and Tiao, G. C. (1984). Consistent estimates of autoregressive parameters and extended
sample autocorrelation function for stationary and nonstationary ARMA models, J. Am. Stat. Assoc., 79, 84--96.
Tsay, R. S. and Tiao, G. C. (1985). Use of canonical analysis in time series model identification, Biometrika, 72, 299--315.
Tuan, P.-D. (1985). Bilinear Markovian representation and bilinear models, Stoch. Process. Appl., 20, 295--306.
Tuan, P.-D. (1986). The mixing property of bilinear and generalized random coefficient autoregressive models, Stoch. Process. Appl., 21, 291--300.
Tukey, J. W. (1961). Discussion, emphasizing the connection between analysis of variance and spectrum analysis, Technometrics, 3, 191--219.
Tunnicliffe Wilson, G. (1970a). Optimal control: a general method of obtaining the feedback scheme which minimizes the output variance, subject to a constraint on the variability of the control variable, Technical Report 20, Department of Systems Engineering, University of Lancaster, Lancaster, UK.
Tunnicliffe Wilson, G. (1970b). Modelling Linear Systems for Multivariate Control, Ph.D. thesis, University of Lancaster, UK.
Tunnicliffe Wilson, G. (1989). On the use of marginal likelihood in time series model estimation, J. R. Stat. Soc., B51, 15--27.
Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S, 4th ed., Springer, New York.
Walker, A. M. (1964). Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series, J. Aust. Math. Soc., 4, 363--384.
Walker, G. (1931). On periodicity in series of related terms, Proc. R. Soc., A131, 518--532.
Wei, W. W. S. (2006). Time Series Analysis, Univariate and Multivariate Methods, 2nd ed., Pearson,
Addison-Wesley.
Weiss, A. A. (1984). ARMA models with ARCH errors, J. Time Ser. Anal., 5, 129--143.
Weiss, A. A. (1986). Asymptotic theory for ARCH models: estimation and testing. Econom. Theory, 2, 107--131.
Whittle, P. (1953). Estimation and information in stationary time series, Ark. Math., 2, 423--434. Whittle, P. (1963). Prediction and Regulation by Linear Least-Squares Methods, English Universities
Press, London.
Wichern, D. W. (1973). The behaviour of the sample autocorrelation function for an integrated
moving average process, Biometrika, 60, 235--239.
Wiener, N. (1949). Extrapolation, Interpolation and Smoothing of Stationary Time Series, Wiley,
New York.
Wincek, M. A. and Reinsel, G. C. (1986). An exact maximum likelihood estimation procedure for regression-ARMA time series models with possibly nonconsecutive data, J. R. Stat. Soc., B48, 303--313.
Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages, Manage. Sci., 6, 324--342.
Wold, H. O. (1938). A Study in the Analysis of Stationary Time Series, Almqvist & Wiksell, Uppsala, Sweden; 2nd ed., 1954.
Wong, H. and Ling, S. (2005). Mixed portmanteau tests for time series, J. Time Ser. Anal., 26,
569--579.
Woodward, W. A. and Gray, H. L. (1981). On the relationship between the S array and the
Box--Jenkins method of ARMA model identification, J. Am. Stat. Assoc., 76, 579--587. Xekalaki, E. and Degiannakis, S. (2010). ARCH Models for Financial Applications, Wiley,
New York.
Yaglom, A. M. (1955). The correlation theory of processes whose 𝑛th difference constitute a stationary
process, Mat. Sb., 37(79), 141.
Yamamoto, T. (1976). Asymptotic mean square prediction error for an autoregressive model with
estimated coefficients, Appl. Stat., 25, 123--127.
Yap, S. F. and Reinsel, G. C. (1995). Results on estimation and testing for a unit root in the
nonstationary autoregressive moving-average model, J. Time Ser. Anal., 16, 339--353.
Young, A. J. (1955). An Introduction to Process Control Systems Design, Longmans Green,
New York.
Yule, G. U. (1927). On a method of investigating periodicities in disturbed series, with special
reference to Wolfer’s sunspot numbers, Philos. Trans. R. Soc., A226, 267--298.
Zadeh, L. A. and Ragazzini, J. R. (1950). An extension of Wiener’s theory of prediction, J. Appl.
Phys., 21, 645.
Zako ̈ıan, J. M. (1994). Threshold heteroscedastic models, J. Econ. Dyn. Control, 18, 931--955.
参考資料(References)
Data Scientist の基礎(2)
https://qiita.com/kaizen_nagoya/items/8b2f27353a9980bf445c
岩波数学辞典 二つの版がCDに入ってお得
https://qiita.com/kaizen_nagoya/items/1210940fe2121423d777
岩波数学辞典
https://qiita.com/kaizen_nagoya/items/b37bfd303658cb5ee11e
アンの部屋（人名から学ぶ数学：岩波数学辞典）英語(24)
https://qiita.com/kaizen_nagoya/items/e02cbe23b96d5fb96aa1
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