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References
This list is a work in progress.
Optimization Library Used - Optimc https://code.google.com/p/optimc/
Akaike, H. (1978), Time series analysis and control through parametric models, Applied Time Series Analysis, D.F. Findley (ed.), Academic Press, New York.
Ansley, C.F. (1979), An algorithm for the exact likelihood of a mixed autoregressive moving-average process, Biometrika, 66, 59–65.
Box, G.E.P. and Jenkins, G.M. (1976), Time Series Analysis: Forecasting and Control, Revised Edition, Holden-Day, San Francisco.
Brockwell, P.J. and Davis, R.A. Introduction to Time Series and Forecasting (Springer Texts in Statistics)
Hannan, E.J. and Rissanen, J. (1982), Recursive estimation of mixed autoregressive moving-average order, Biometrika, 69, 81–94.
Gardner, G, Harvey, A. C. and Phillips, G. D. A. (1980) Algorithm AS154. An algorithm for exact maximum likelihood estimation of autoregressive-moving average models by means of Kalman filtering. Applied Statistics 29, 311–322.
Harvey, A. C. and McKenzie, C. R. (1982) Algorithm AS182. An algorithm for finite sample prediction from ARIMA processes. Applied Statistics 31, 180–187.
Harvey, A.C. (1990), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge.
Harvey, A. C. (1993) Time Series Models, 2nd Edition, Harvester Wheatsheaf, sections 3.3 and 4.4.
Hyndman, R. J., & Khandakar, Y. (2008). Automatic time series forecasting: The forecast package for R. Journal of Statistical Software, 27(1), 1–22. https://doi.org/10.18637/jss.v027.i03
Hyndman, R. J., & Athanasopoulos. G. Forecasting: Principles and Practice https://otexts.com/fpp2/
Jones, R.H. (1980), Maximum likelihood fitting of ARMA models to time series with missing observations, Technometrics, 22, 389–395.
Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis, 2nd Edition, Springer-Verlag, Berlin.
Melard G., Algorithm AS 197: A Fast Algorithm for the Exact Likelihood of Autoregressive-Moving Average Models, Journal of the Royal Statistical Society. Series C (Applied Statistics) Vol. 33, No. 1 (1984), pp. 104-114
Tunnicliffe–Wilson G (1979) Some efficient computational procedures for high order ARMA models J. Statist. Comput. Simulation 8 301–309
Forecasting Functions for Time Series and Linear Models ( R Forecast Package by Rob J Hyndman ) https://www.rdocumentation.org/packages/forecast/versions/8.12
uroot: Unit Root Tests for Seasonal Time Series in R ( Authors : Javier López-de-Lacalle [aut], Georgi N. Boshnakov [cre]) https://cran.r-project.org/web/packages/uroot/index.html
urca: Unit Root and Cointegration Tests for Time Series Data in R ( Authors: Bernhard Pfaff [aut, cre], Eric Zivot [ctb], Matthieu Stigler [ctb]) https://cran.r-project.org/web/packages/urca/index.html
pmdarima: ARIMA estimators for Python https://github.com/alkaline-ml/pmdarima
statsmodels.tsa.statespace.sarimax.SARIMAX https://thequackdaddy.github.io/statsmodels.github.io/0.9.0/generated/statsmodels.tsa.statespace.sarimax.SARIMAX.html#statsmodels-tsa-statespace-sarimax-sarimax
http://www.johndcook.com/blog/2012/07/25/trick-for-computing-log1x/
"An Overview of Software Development for Special Functions", Cody, W. J., Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, 1975, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.
Computer Approximations, Hart, Et. Al., Wiley and sons, New York, 1968.
K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May 1969.
"Chebyshev Approximations for the Natural Logarithm of the Gamma Function", W. J. Cody and K. E. Hillstrom, Math. Comp. 21, 1967, pp. 198-203.
Milton Abramowitz, I.A. Stegun, Handbook of Mathematical Functions. (Dover Books on Mathematics)
GW Cran, KJ Martin, GE Thomas, Remark AS R19 (on Google Code) and Algorithm AS 109: A Remark on Algorithms AS 63: The Incomplete Beta Integral and AS 64: Inverse of the Incomplete Beta Integeral, Applied Statistics, Volume 26, Number 1, 1977, pages 111-114.
John Burkardt's C Translation of the Incomplete Beta Integral http://people.sc.fsu.edu/~jburkardt/
Armido Didonato, Alfred Morris, Jr, Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios, ACM Transactions on Mathematical Software, Volume 18, Number 3, pages 360-373, 1992.
J. M. Blair, C. A. Edwards, and J. H. Johnson, "Rational Chebyshev Approximations for the Inverse of the Error Function", Mathematics of Computation, 30 (1976) 827-830
Burg, J.P. (1975). Maximum Entropy Spectral Analysi s. Available online at http://sepwww.stanford.edu/theses/sep06/
Cedrick Collomb's C++ Implemnetation of Burg's Algorithm http://www.emptyloop.com/technotes/
Yule, G. Udny (1927) "On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers", Philosophical Transactions of the Royal Society of London, Ser. A, Vol. 226, 267–298.]
Walker, Gilbert (1931) "On Periodicity in Series of Related Terms", Proceedings of the Royal Society of London, Ser. A, Vol. 131, 518–532.
Michael Jenkins, Joseph Traub, Algorithm 419: Zeros of a Complex Polynomial, Communications of the Association for Computing Machinery, Volume 15, Number 2, February 1972, pages 97-99.
Ripley, B. D. (2002) Time series in R 1.5.0. R News, 2/2, 2–7. http://www.r-project.org/doc/Rnews/Rnews_2002-2.pdf
Gnu Regression, Econometrics and Time-series Library http://gretl.sourceforge.net/
Algorithms For Minimization Without Derivatives, Richard P. Brent
Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , Jorge Nocedal (Author), Stephen Wright
Argonne National Laboratory. MINPACK Project. June 1983 ,Jorge J. More', David J. Thuente
J. A. Nelder and R. Mead, A simplex method for function minimization. Compuer Journal,7,308-313
Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 20, No. 3 (1971), pp. 338-345, R O'Neill
Numerical Methods for Unconstrained Optimization and Non-Linear Equations, Dennis, Schnabel
"A Limited Memory Algorithm for Bound Constrained Optimization", SIAM Journal on Scientific Computing 16 (5): 1190–1208, Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge; Zhu, Ciyou
Practical methods of optimization (2nd ed.),Fletcher, Roger (1987),
MINPACK http://www.netlib.org/minpack/
EISPACK http://www.netlib.org/eispack/