In this topic we give an overview of the package.
The classes of models currently fitted by the package are listed below. Each are defined within an object that contains the data, current parameter values, and other model characteristics.
is described under the topic dthmm. This model can be simulated or fitted to data by defining the required model structure within an object of class "dthmm".
is described under the topic mmglm1.
is described under the topic mmglmlong1.
is described under the topic mmpp. This model can be simulated or fitted to data by defining the required model structure within an object of class "mmpp".
The main tasks performed by the package are listed below. These can be achieved by calling the appropriate generic function.
can be performed by the function simulate.
can be performed by the functions BaumWelch (EM algorithm), or neglogLik together with nlm or optim (Newton type methods or grid searches).
can be extracted with the function residuals.
can be extracted with the function summary.
can be calculated with the function logLik.
can be performed by the function Viterbi.
All other functions in the package are called from within the above generic functions, and only need to be used if their output is specifically required. We have referred to some of these other functions as “2nd level” functions, for example see the topic mmpp-2nd-level-functions.
anywhere in the manual are only listed within this topic.
topics summarising general structure are indexed under the keyword “documentation” in the Index.
Many of the functions contained in the package are based on those of Walter Zucchini (2005).
Baum, L.E.; Petrie, T.; Soules, G. & Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics 41(1), 164--171. 10.1214/aoms/1177697196
Charnes, A.; Frome, E.L. & Yu, P.L. (1976). The equivalence of generalized least squares and maximum likelihood estimates in the exponential family. J. American Statist. Assoc. 71(353), 169--171. 10.2307/2285762
Dempster, A.P.; Laird, N.M. & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Royal Statist. Society B 39(1), 1--38. URL: https://www.jstor.org/stable/2984875
Elliott, R.J.; Aggoun, L. & Moore, J.B. (1994). Hidden Markov Models: Estimation and Control. Springer-Verlag, New York. 10.1007/978-0-387-84854-9
Harte, D. (2019). Mathematical Background Notes for Package “HiddenMarkov”. Statistics Research Associates, Wellington. URL: https://www.statsresearch.co.nz/dsh/sslib/manuals/notes.pdf
Hartley, H.O. (1958). Maximum likelihood estimation from incomplete data. Biometrics 14(2), 174--194. 10.2307/2527783
Klemm, A.; Lindemann, C. & Lohmann, M. (2003). Modeling IP traffic using the batch Markovian arrival process. Performance Evaluation 54(2), 149--173. 10.1016/S0166-5316(03)00067-1
MacDonald, I.L. & Zucchini, W. (1997). Hidden Markov and Other Models for Discrete-valued Time Series. Chapman and Hall/CRC, Boca Raton.
McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models (2nd Edition). Chapman and Hall, London.
Rabiner, L.R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77(2), 257--286. 10.1109/5.18626
Roberts, W.J.J.; Ephraim, Y. & Dieguez, E. (2006). On Ryden's EM algorithm for estimating MMPPs. IEEE Signal Processing Letters 13(6), 373--376. 10.1109/LSP.2006.871709
Ryden, T. (1994). Parameter estimation for Markov modulated Poisson processes. Stochastic Models 10(4), 795--829. 10.1080/15326349408807323
Ryden, T. (1996). An EM algorithm for estimation in Markov-modulated Poisson processes. Computational Statistics & Data Analysis 21(4), 431--447. 10.1016/0167-9473(95)00025-9
Zucchini, W. (2005). Hidden Markov Models Short Course, 3--4 April 2005. Macquarie University, Sydney.