Notebooks

## Time Series, or Statistics for Stochastic Processes and Dynamical Systems

06 Sep 2013 12:10

Rates of convergence of estimators; analogs to VC-dimension results (see Meir's paper below). Large deviation techniques. Prediction schemes. Are there universal schemes which do not demand exponentially growing volumes of data?

If you have an ergodic process, then the sample-path mean for any nice statistic you care to measure will, almost surely, converge to the distributional mean. This is even true of trajectory probabilities (i.e., if you want to know the probability of a certain finite-length trajectory, simply count how often it happens). So "sit and count" is a reliable and consistent statistical procedure. If the process mixes sufficiently quickly, the rate of convergence might even be respectable. But this doesn't say anything about the efficiency of such procedures, which is surely a consideration. And what do you do for non-ergodic processes? (Take multiple runs and hope they're telling you about different ergodic components?) Non-stationary, even?

I need to learn more about frequency-domain approaches; despite being raised as a physicist, I find the time domain much more natural. After all, the frequency domain is effectively just one choice of a function basis, and there are infinitely many others, which might in some sense be more appropriate to the process at hand. But that's at least in part a rationalization against having to learn more math.

LSE econometrics and its "general-to-specific" modeling procedure is very interesting, and I think possibly even related to stuff I've done, but I need to understand it much better than I do.

(This notebook really needs subdivision.)

Recommended, big picture:
• M. S. Bartlett
• An Introduction to Stochastic Processes, with Special Reference to Methods and Applications [Mini-review]
• "Inference and Stochastic Processes", Journal of the Royal Statistical Society A 130 (1967): 457--478 [JSTOR]
• "Chance or Chaos?", Journal of the Royal Statistical Society A 153 (1990): 321--347 [JSTOR]
• Ishwar V. Basawa and B. L. S. Prakasa Rao, Statistical Inference for Stochastic Processes [Assumes familiarity with normal theoretical statistics, i.e., you have to have already been taught to care about confidence intervals, hypothesis tests, estimation efficiency, etc. But good, given that background.]
• David R. Brillinger, "The 2005 Neyman Lecture: Dynamic Indeterminism in Science", Statistical Science 23 (2008): 48--64, arxiv:0808.0620 [With discussions and response]
• Jianqing Fan and Qiwei Yao, Nonlinear Time Series: Nonparametric and Parametric Methods [Review: Everyone Their Own Oracle]
• Peter Guttorp, Stochastic Modeling of Scientific Data [An introduction to statistical inference for many different kinds of dependent data, not just time series; can be used by scientists and statisticians.]
• Holger Kantz and Thomas Schreiber, Nonlinear Time Series Analysis [An excellent presentation of the nonlinear dynamical systems approach, which comes out of physics]
• Judy Klein, Statistical Visions in Time: A History of Time-Series Analysis, 1662--1938
• Robert Shumway and David Stoffer, Time Series Analysis and Its Applications: With R Applications [A standard applied statistics text, but better than many at creating pathways into theory, and realizing that ARIMA is not the alpha and omega of the subject!]
• Jorma Rissanen, Stochastic Complexity in Statistical Inquiry [Review: Review: Less Is More, or, Ecce data!]
• David Ruelle, Chaotic Evolution and Strange Attractors: The Statistical Analysis of Deterministic Nonlinear Systems [From notes prepared by Stefano Isola]
• Norbert Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series
Recommended, closeups:
• Markus Abel, K. H. Andersen and Guglielmo Lacorata, "Hierarchical Markovian modeling of multi-time systems," nlin.CD/0201027
• Miika Ahdesmäki, Harri Lähdesmäki, Ron Pearson, Heikki Huttunen, and Olli Yli-Harja, "Robust detection of periodic time series measured from biological systems", BMC Bioinformatics 6 (2005): 117 [Open access, yay!]
• Pierre Alquier and Olivier Wintenberger, "Model selection and randomization for weakly dependent time series forecasting", Bernoulli 18 (2012): 883--913, arxiv:0902.2924
• Francesco Audrino and Peter Bühlmann, "Splines for Financial Volatility", Journal of the Royal Statistical Society B 71 (2009): 655--670
• Jushan Bai, "Testing parametric conditional distributions of dynamic models", The Review of Economics and Statistics 85 (2003): 531--549
• Matthew J. Beal, Zoubin Ghahramani and Carl Edward Rasmussen, "The Infinite Hidden Markov Model", in NIPS 14 [Link]
• Patrick Billingsley, Statistical Inference for Markov Processes [Discrete-time and cadlag processes only]
• Denis Bosq, Nonparametric Statistics for Stochastic Processes
• Denis Bosq and Delphine Blanke, Inference and Prediction in Large Dimensions [Mini-review]
• David Brillinger
• "Remarks concerning graphical models for time series and point processes," Revista de Econometria 16 (1996): 1--23
• "Second-order moments and mutual information in the analysis of time series and point processes," Proceedings of the Conference Statistics 2001 Canada [online]
• "Does anyone know when the correlation coefficient is useful?: A study of the times of extreme river flows," Technometrics 43 (2001): 266--273 [JSTOR]
• David R. Brillinger, Brent S. Stewart, Charles L. Littnan, "Three months journeying of a Hawaiian monk seal", pp. 246--264 of Deborah Nolan and Terry Speed (eds.), Probability and Statistics: Essays in Honor of David A. Freedman (2008), arxiv:0805.3019 [A pretty application]
• Prabir Burman, Edmond Chow and Deborah Nolan, "A Cross-Validatory Method for Dependent Data", Biometrika 81 (1994): 351--358 [JSTOR]
• S. Caires and J. A. Ferreira, "On the Non-parametric Prediction of Conditionally Stationary Sequences", Statistical Inference for Stochastic Processes 8 (2005): 151--184
• Luca Capriotti
• "A Closed-Form Approximation of Likelihood Functions for Discretely Sampled Diffusions: the Exponent Expansion", physics/0703180
• "The Exponent Expansion: An Effective Approximation of Transition Probabilities of Diffusion Processes and Pricing Kernels of Financial Derivatives", physics/0602107 = International Journal of Theoretical and Applied Finance 9 (2006): 1179--1199
• Tianjiao Chu and Clark Glymour, "Search for Additive Nonlinear Time Series Causal Models", Journal of Machine Learning Research 9 (2008): 967--991
• George Cybenko and Valentino Crespi, "Learning Hidden Markov Models Using Nonnegative Matrix Factorization", IEEE Transactions on Information Theory 57 (2011): 3963--3970, arxiv:0809.4086 [Though it contains an error, at least in the preprint version, about the capacities of our CSSR algorithm --- we can get model structures right with much less data than they think, though we presented examples using more data than was strictly needed.]
• R. Dahlhaus, "Fitting Time Series Models to Nonstationary Processes", Annals of Statistics 25 (1997): 1--37
• Jérôme Dedecker, Paul Doukhan, Gabriel Lang, José Rafael León R., Sana Louhichi and Clémentine Prieur, Weak Dependence: With Examples and Applications [Mini-review]
• David Degras, "Nonparametric inference of a trend using functional data", arxiv:0812.2749
• Piet de Jong and Jeremy Penzer, "ARMA models in state space form", Statistics and Probability Letters 70 (2004): 119--125 [preprint]
• Piet De Jong, "A Cross-Validation Filter for Time Series Models", Biometrika 75 (1988): 594--600 [JSTOR]
• Victor H. de la Pena, Rustam Ibragimov, and Shaturgun Sharakhmetov, "Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series", math.ST/0611166
• Franklin M. Fisher, "A Correspondence Principle for Simultaneous Equation Models", Econometrica 38 (1970): 73--92 [When are simultaneous systems of equations legitimate limits of models of time-evolution?]
• Emily B. Fox, Mike West, "Autoregressive Models for Variance Matrices: Stationary Inverse Wishart Processes", arxiv:1107.5239
• Andrew M. Fraser, Hidden Markov Models and Dynamical Systems [Review: Statistics of Moving Shadows]
• Neil Gershenfeld, B. Schoner and E. Metois, "Cluster-Weighted Modelling for Time-Series Analysis," Nature 397 (1999): 329--332 [Also described in Gershenfeld's incredible Nature of Mathematical Modeling]
• Gershenfeld and Weigend (eds.), Time Series Prediction: Forecasting the Future and Understanding the Past
• Silvia Goncalves and Halbert White, "Maximum likelihood and the bootstrap for nonlinear dynamic models", Journal of Econometrics 119 (2004): 199--219
• Christian Gouriéroux and Alain Monfort, Simulation-Based Econometric Methods [Review: By Indirection Find Direction Out]
• Kevin D. Hoover and Stephen J. Perez, "Data-Mining Reconsidered: Encompassing and the General-to-Specific Approach to Specification Search," Econometrics Journal 2 (1999): 167--191
• Aapo Hyvärinen, Kun Zhang, Shohei Shimizu, Patrik O. Hoyer, "Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity", Journal of Machine Learning Research 11 (2010): 1709--1731
• Marc Joannides and Francois Le Gland, "Small Noise Asymptotics of the Bayesian Estimator in Nonidentifiable Models", Statistical Inference for Stochastic Processes 5 (2002): 95--130
• M. L. Kleptsyna, A. Le Breton and M.-C. Roubaud, "Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems", Statistical Inference for Stochastic Processes 3 (2000): 173--182
• Rudolf Kulhavy, Recursive Nonlinear Estimation: A Geometric Approach [Includes, explicitly, estimation in time-series systems]
• Guglielmo Lacorata, Ruben A. Pasmanter and Angelo Vulpiani, "Markov-chain approach to a process with long-time memory," nlin.CD/0110010 [A special case of a more general result encompassed in my paper with Cris Moore]
• S. N. Lahiri, Resampling Methods for Dependent Data [Mini-review]
• R. Dean Malmgren, Jake M. Hofman, Luis A. N. Amaral, Duncan J. Watts, "Characterizing Individual Communication Patterns", arxiv:0905.0106
• Ron Meir, "Nonparametric Time Series Prediction Through Adaptive Model Selection," Machine Learning 39 (2000): 5--34 [PDF. Extending the "structural risk minimization" framework due to Vapnik to time series. Unfortunately Meir's approach demands knowledge of the mixing rate of the process, which we don't really know how to estimate, but this is a very encouraging first step. Addendum, 2013: we know how to estimate it now.]
• Gusztáv Morvai, Sidney J. Yakowitz and Paul Algoet, "Weakly Convergent Nonparametric Forecasting of Stationary Time Series," IEEE Trans. Info. Theory 43 (1997): 483--498
• Martin Nilsson, "Generalized Singular Spectrum Time Series Analysis," physics/0205094
• Andrey Novikov, "Optimal sequential multiple hypothesis tests",arxiv:0811.1297
• Maxim Raginsky, Roummel F. Marcia, Jorge Silva and Rebecca M. Willett, "Sequential Probability Assignment via Online Convex Programming Using Exponential Families" [ISIT 2009; PDF]
• Maxim Raginsky, Rebecca M. Willett, C. Horn, Jorge Silva and Roummel F. Marcia, "Sequential anomaly detection in the presence of noise and limited feedback", IEEE Transactions on Information Theory 58 (2012): 5544--5562, arxiv:0911.2904
• James Ramsay, Giles Hooker, David Campbell and Jiguo Cao, "Parameter Estimation for Differential Equations: A Generalized Smoothing Approach", Journal of the Royal Statistical Society forthcoming (2007) [PDF preprint]
• Cavan Reilly and Angelique Zeringue, "Improved predictions of lynx trappings using a biological model", pp. 297--308 in Andrew Gelman and Xiao-Li Meng (eds.), Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives [PDF. "Improved" compared to using standard time-series models with no biological content.]
• P. A. Robinson, "Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology," Physical Review E 67 (2003): 032902 [A polite but devastating demonstration that "detrended fluctuation analysis", per Gene Stanley and co., is an obfuscated way of looking at the power spectrum.]
• George G. Roussas
• Contiguity of Probability Measures: Some Applications in Statistics [Asymptotic theory of approximation, estimation and testing, for discrete-time Markov processes on fairly general state-spaces. Mini-review]
• "Asymptotic distribution of the log-likelihood function for stochastic processes," Zeitschrift für Wahrscheinlickkeitstheorie und verwandte Gebiete 47 (1979): 31--46 [Elegant solution of a basic problem for a pretty broad class of processes; extends work in his book.]
• Daniil Ryabko, "A criterion for hypothesis testing for stationary processes", arxiv:0905.4937
• Daniil Ryabko and Boris Ryabko, "Testing Statistical Hypotheses About Ergodic Processes", arxiv:0804.0510 [Appears to be the same as their "Nonparametric Statistical Inference for Ergodic Processes", IEEE Transactions on Information Theory 56 (2010): 1430--1435
• Nobusumi Sagara, "Nonparametric maximum-likelihood estimation of probability measures: existence and consistency", Journal of Statistical Planning and Inference 133 (2005): 249--271 ["This paper formulates the nonparametric maximum-likelihood estimation of probability measures and generalizes the consistency result on the maximum-likelihood estimator (MLE). We drop the independent assumption on the underlying stochastic process and replace it with the assumption that the stochastic process is stationary and ergodic. The present proof employs Birkhoff's ergodic theorem and the martingale convergence theorem. The main result is applied to the parametric and nonparametric maximum-likelihood estimation of density functions."]
• Christopher C. Strelioff and Alfred W. Hübler, "Medium-Term Prediction of Chaos", Physical Review Letters 96 (2006): 044101
• Masanobu Taniguchi and Yoshihide Kakizawa, Asymptotic Theory of Statistical Inference for Time Series [Finally, a proper statistical treatment which doesn't confine itself to expletive-deleted ARMA processes. Neat information geometry too.]
• Halbert White, Estimation, Inference and Specification Analysis [Review]
• Andrew Gordon Wilson and Zoubin Ghahramani, "Copula Processes", arxiv:1006.1350 [Theoretically interesting, though on the real data example it does at most marginally better than the off-the-shelf GARCH model, at considerably higher computational cost]
• Simon N. Wood, "Statistical inference for noisy nonlinear ecological dynamic systems", Nature 466 (2010): 1102--1104
• Wei Biao Wu, "Nonlinear system theory: Another look at dependence", Proceedings of the National Academy of Sciences 102 (2005): 14150--14154 [New measures of mixing, or decay of dependence, related to coupling arguments, and in principle easily checked from the model's specification.]
• Luis A. Aguirre, Ubiratan S. Freitas, Christophe Letellier and Jean Maquet, "Structure-selection techniques applied to continuous-time nonlinear models," Physica D 158 (2001): 1--18
• Eduardo G. Altmann and Holger Kantz, "Recurrence time analysis, long-term correlations, and extreme events", physics/0503056
• Shun-ichi Amari, "Estimating Functions of Independent Component Analysis for Temporally Correlated Signals," Neural Computation 12 (2000): 2083--2107
• Heather M. Anderson, "Choosing Lag Lengths in Nonlinear Dynamic Models," Monash Econometric Working Paper [online]
• Claudia Angelini, Daniela Cavab, Gabriel Katul, and Brani Vidakovic, "Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence", Physica D 207 (2005): 24--40
• J. A. D. Aston, "Modeling macroeconomic time series via heavy tailed distributions", math.ST/0702844
• Alexander Aue, Siegfried Hörmann, Lajos Horváth and Matthew Reimherr, "Break detection in the covariance structure of multivariate time series models", Annals of Statistics 37 (2009): 4046--4087
• Ishwar V. Basawa and D. J. Scott, Asymptotic Optimal Inference for Non-ergodic Models
• Nathaniel Beck and Jonathan N. Katz
• Tadeusz Bednarski, "Fréchet differentiability in statistical inference for time series", Statistical Methods and Applications 19 (2010): 517--528
• Jose Bento, Morteza Ibrahimi and Andrea Montanari
• "Learning Networks of Stochastic Differential Equations", NIPS 23 (2010), arxiv:1011.0415
• "Information Theoretic Limits on Learning Stochastic Differential Equations", arxiv:1103.1689
• Alain Berlinet and Gérar Biau, "Minimax Bounds in Nonparametric Estimation of Multidimensional Deterministic Dynamical Systems", Statistical Inference for Stochastic Processes 4 (2001): 229--248 ["We consider the problem of estimating a multidimensional discrete deterministic dynamical system from the first n+1 observations. We exhibit the optimal rate function ... the near neighbor estimator achives this optimal rate.... optimal rate function is defined from multidimensonal spacings which are edge lengths of simplicies associated with a triangulation of the Voronoi cells built from the observations." Sounds very cool!]
• Alain Berlinet and Christian Francq, "On the Identifiability of minimal VARMA representations", Statistical Inference for Stochastic Processes 1 (1998): 1--15
• Patrice Bertail, Paul Doukhan and Philippe Soulier (eds.), Dependence in Probability and Statistics ["recent developments in the field of probability and statistics for dependent data... from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. ... section on statistical estimation problems and specific applications". Full blurb, contents]
• D. Blanke, D. Bosq and D. Guegan, "Modelization and Nonparametric Estimation for Dynamical Systems with Noise", Statistical Inference for Stochastic Processes 6 (2003): 267--290
• Adriaan Blommaert, Niel Hens, Philippe Beutels, "Data Mining for Longitudinal Data under Multicollinearity and Time Dependence using Penalized Generalized Estimating Equations", arxiv:1206.1425
• Luke Bornn, Marian Anghel, Ingo Steinwart, "Forecasting with Historical Data or Process Knowledge under Misspecification: A Comparison", arxiv:1205.3845
• David R. Brillinger, "The Nicholson blowfly experiments: some history and EDA", Journal of Time Series Analysis 33 (2012): 718--723
• Noelle Bru, Laurence Despres and Christian Paroissin, "A comparison of statistical models for short categorical or ordinal time series with applications in ecology", math.ST/0702706
• Prabir Burman and Robert H. Shumway, "Estimation of trend in state-space models: Asymptotic mean square error and rate of convergence", arxiv:0911.3469 = Annals of Statistics 37 (2009): 3715--3742
• Alexandre X. Carvalho and Martin A. Tanner, "Mixtures-of-Experts of Autoregressive Time Series: Asymptotic Normality and Model Specification", IEEE Transactions on Neural Networks 16 (2005): 39--56
• Carlos M. Carvalho, Michael S. Johannes, Hedibert F. Lopes, and Nicholas G. Polson, "Particle Learning and Smoothing", Statistical Science 25 (2010): 88--106
• Kung-Sik Chan and Howell H. Tong, Chaos: A Statistical Perspective
• J.-R. Chazottes, P. Collet and B. Schmitt, "Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems", math.DS/0412167
• J.-R. Chazottes, E. Floriani and R. Lima, "Relative Entropy and Identification of Gibbs Measures in Dynamical Systems," Journal of Statistical Physics 90 (1998): 697--725
• Zhuo Chen and Yuhong Yan, "Time Series Models for Forecasting: Testing or Combining?", Studies in Nonlinear Dynamics and Econometrics 11:1 (2007): 3
• Christophe Chesneau, Jalal Fadili, Bertrand Maillot, "Adaptive estimation of an additive regression function from weakly dependent data", arxiv:1111.3994
• Zhiyi Chi, "Large deviations for template matching between point processes", Annals of Applied Probability 15 (2005): 153--174 = math.PR/0503463
• P. Cizek, W. Hardle, V. Spokoiny, "Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models", arxiv:0903.4620 [I'm more interested in the idea of adaptively estimating non-stationary time series here than the finance application...]
• Michael P. Clements and David F. Hendry (eds.), Companion to Economic Forecasting
• Todd P. Coleman and Sridevi S. Sarma, "A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes", Neural Computation 22 (2010): 2002--2030
• P. Collet, S. Martinez and B. Schmitt, "Asymptotic distribution of tests for expanding maps of the interval", Ergodic Theory and Dynamical Systems 24 (2004): 707--722 [Kolmogorov-Smironov-type results for the empirical distribution under the invariant measure of a dynamical system]
• Daniel Commenges and Anne Gegout-Petit, "Likelihood inference for incompletely observed stochastic processes: ignorability conditions", math.ST/0507151 ["We define a general coarsening model for stochastic processes. We decribe incomplete data by means of sigma-fields and we give conditions of ignorability for likelihood inference."]
• Daan Crommelin, "Estimation of Space-Dependent Diffusions and Potential Landscapes from Non-equilibrium Data", Journal of Statistical Physics 149 (2012): 220--233
• Colleen D. Cutler and Daniel T. Kaplan (eds.), Nonlinear Dynamics and Time Series: Building a Bridge between the Natural and Statistical Sciences
• Sophie Dabo-Niang, Ali Laksaci, "Conditional mode regression: Application to functional time series prediction", arxiv:0812.4882
• Sophie Dabo-Niang, Christian Francq and Jean-Michel Zakoïan, "Combining Nonparametric and Optimal Linear Time Series Predictions", Journal of the American Statistical Association 104 (2010): 1554--1565
• Serguei Dachian, Yury A. Kutoyants
• "Hypotheses Testing: Poisson Versus Self-exciting", arxiv:0903.4636 = Scandinavian Journal of Statistics 33 (2006): 391
• "On the Goodness-of-Fit Tests for Some Continuous Time Processes", arxiv:0903.4642 ["We present a review of several results concerning the construction of the Cramer-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for continuous time processes. As the models we take a stochastic differential equation with small noise, ergodic diffusion process, Poisson process and self-exciting point processes"]
• Rainer Dahlhaus and Wolfgang Polonik, "Empirical spectral processes for locally stationary time series", Bernoulli 15 (2009): 1--39, arxiv:902.1448
• Arnak Dalalyan and Markus Reiss, "Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case", math.ST/0505053
• Youri Davydov, "Remarks on Estimation Problem for Stationary Processes in Continuous Time", Statistical Inference for Stochastic Processes 4 (2001): 1--15
• A. De Gregorio and S. M. Iacus, "Adaptive Lasso-type estimation for ergodic diffusion processes", arxiv:1002.1312
• D. Dehay and Yu. A. Kutoyants, "On confidence intervals for distribution function and density of ergodic diffusion process", Journal of Statistical Planning and Inference 124 (2004): 63--73
• Miguel A. Delgado, Javier Hidalgo and Carlos Velasco, "Distribution free goodness-of-fit tests for linear processes", math.ST/0603043 = Annals of Statistics 33 (2005): 2568--2609 [i.e., goodness-of-fit for the autocorrelation function]
• Holger Dette, Philip Preuss, and Mathias Vetter, "A Measure of Stationarity in Locally Stationary Processes With Applications to Testing", Journal of the American Statistical Association 106 (2011): 1113--1124
• Vanessa Didelez, "Graphical models for marked point processes based on local independence", arxiv:0710.5874
• Thomas G. Dietterich, "Machine Learning for Sequential Data" [PDF. Thanks to Gustavo Lacerda for a pointer.]
• Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov, "Sample path properties of the stochastic flows," math.PR/0111011
• Randal Douc, Eric Moulines and Tobias Ryden, "Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime", Annals of Statistics 32 (2004): 2254--2304 = math.ST/0503681
• Holger Drees, "Some aspects of extreme value theory under serial dependence", arxiv:0710.5879
• Pierre Duchesne, "On Testing for Serial Correlation with a Wavelet-Based Spectral Density Estimator in Multivariate Time Series", Econometric Theory 22 (2006): 633--676
• K. Dzhaparidze, Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series
• Michael Eichler
• "Fitting Graphical Interaction Models to Multivariate Time Series", UAI 2006, arxiv:1206.6839
• "Graphical modelling of multivariate time series", math.ST/0610654
• Enrique Figueroa-Lopez and Christian Houdre, "Nonparametric estimation for Levy processes with a view towards mathematical finance", math.ST/0412351
• D. Florens and H. Pham, "Large Deviations in Estimation of an Ornstein-Uhlenbeck Model," Journal of Applied Probability 36 (1999): 60--77
• Christian Francq and Jean-Michel Zakoian, "Bartlett's formula for a general class of nonlinear processes", Journal of Time Series Analysis 30 (2009): 449--465
• Marc K. Francke, Siem Jan Koopman, Aart F. De Vos, "Likelihood functions for state space models with diffuse initial conditions", 10.1111/j.1467-9892.2010.00673.xJournal of Time Series Analysis 31 (2010): 407--414
• Jurgen Franke, Jens-Peter Kreiss and Enno Mammen, "Bootstrap of Kernel Smoothing in Nonlinear Time Series", Bernoulli 8 (2002): 1--37
• T. D. Frank, "Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays", Physical Review E 71 (2005): 031106
• Philip Hans Franses and Dick Van Dijk, Non-Linear Time Series Models in Empirical Finance
• Roland Fried and Vanessa Didelez, "Latent variable analysis and partial correlation graphs for multivariate time series", Statistics and Probability Letters 73 (2005): 287--296
• Cheng-Der Fuh, "Efficient likelihood estimation in state space models", Annals of Statistics 34 (2006): 2026--2068, arxiv:0611376
• Ben D. Fulcher, Max A. Little, Nick S. Jones, "Highly comparative time-series analysis: The empirical structure of time series and their methods", Journal of the Royal Society Interface 10 (2013): 20130048, arxiv:1304.1209
• Irene Gannaz and Olivier Wintenberger, "Adaptative density estimation with dependent observations", math.ST/0510311
• Jiti Gao, Maxwell King, Zudi Lu and Dag Tjostheim, "Specification testing in nonlinear and nonstationary time series autoregression", Annals of Statistics 37 (2009): 3893--3928, arxiv:0911.3736
• Basillis Gidas and Alejandro Murua, "Optimal transformations for prediction in continuous-time stochastic processes: finite past and future", Probability Theory and Related Fields 131 (2005): 479--492
• German Gomez-Herrero, Wei Wu, Kalle Rutanen, Miguel C. Soriano, Gordon Pipa, Raul Vicente, "Assessing coupling dynamics from an ensemble of time series", arxiv:1008.0539
• Georg A. Gottwald and Ian Melbourne, "Testing for chaos in deterministic systems with noise", Physica D 212 (2005): 100--110
• Janez Gradisek, Silke Siegert, Rudolf Friedrich and Igor Grabec, "Analysis of time series from stochastic processes," Physical Review E 62 (2000): 3146--3155
• Grassberger and Nadal (eds.), From Statistical Physics to Statistical Inference and Back
• Robert L. Grossman and Richard G. Larson, "State Space Realization Theorems for Data Mining", arxiv:0901.2735
• Diego Guarin, Alvaro Orozco, Edilson Delgado, "A new surrogate data method for nonstationary time series", arxiv:1008.1804
• David Gubbins, Time Series and Inverse Theory for Geophysicists
• Shota Gugushvili, Peter Spreij, "Parametric inference for stochastic differential equations: a smooth and match approach", arxiv:1111.1120
• Laszlo Gyorfi et al., Nonparametric Curve Estimation from Time Series
• Peter Hall, Soumendra Nath Lahiri and Jorg Polzehl, "On Bandwidth Choice in Nonparametric Regression with Both Short- and Long-Range Dependent Errors", Annals of Statistics 23 (1995): 1921--1936
• Niels Richard Hansen, "Penalized maximum likelihood estimation for generalized linear point processes", arxiv:1003.0848
• Wolfgang Hardle, Helmut Lutkepohl, Rong Chen, "A Review of Nonparametric Time Series Analysis", International Statistical Review 65 (1997): 49--72 [JSTOR]
• Jeffrey D. Hart, "Automated Kernel Smoothing of Dependent Data by using Time Series Cross-Validation", Journal of the Royal Statistical Society B 56 (1994): 529--542 [JSTOR]
• David Harte, "PtProcess: An R Package for Modelling Marked Point Processes Indexed by Time", Journal of Statistical Software 35 (2010): 8
• Florian Hartig, Carsten F. Dormann, "Does "model-free" forecasting really outperform the "true" model? A reply to Perretti et al", arxiv:1305.3544
• Andrew Harvey et al (eds.), State Space and Unobserved Component Models: Theory and Applications
• Stefan Haufe, Guido Nolte, Klaus-Robert Mueller and Nicole Kraemer, "Sparse Causal Discovery in Multivariate Time Series", arxiv:0901.1234 [I am not altogether happy with defining "causes" as "has a non-zero coefficient in a vector autoregression"...]
• David Hendry, Econometrics: Alchemy or Science? [Review by Bruce Hansen]
• David F. Hendry and Bent Nielsen, [Econometric Modeling: A Likelihood Approach Blurb, preface,
• Nadine Hilgert, Vivien Rossi, Jean-Pierre Vila, Verene Wagner, "Identification, Estimation, and Control of Uncertain Dynamic Systems: A Nonparametric Approach", Communications in Statistics: Theory and Methods 36 (2007): 2509--2525
• Junichi Hirukawa and Masanobu Taniguchi, "LAN theorem for non-Gaussian locally stationary processes and its applications", Journal of Statistical Planning and Inference 136 (2006): 640--688
• Scott H. Holan, Robert Lund, and Ginger Davis, "The ARMA alphabet soup: A tour of ARMA model variants", Statistics Surveys 4 (2010): 232--274
• Jinh Hu, Wen-wen Tung, Jianbo Gao and Yinhe Cao, "Reliability of the 0-1 test for chaos", Physical Review E 72 (2005): 056207 [On Gottwald and Melbourne]
• Jianhua Z. Huang and Lijian Yang, "Identification of Non-Linear Additive Autoregressive Models", Journal of the Royal Statistical Society B 66 (2004): 463--477 [JSTOR. Proves consistency under the assumption that the data-generating process is strictly stationary and strongly mixing.]
• Stefano M. Iacus
• "Statistical analysis of stochastic resonance with ergodic diffusion noise," math.PR/0111153
• Simulation and Inference for Stochastic Differential Equations
• "On Lasso-type estimation for dynamical systems with small noise", arxiv:0912.5078
• Ching-Kang Ing, "Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series", Annals of Statistics 35 (2007): 1238--1277, arxiv:0708.2373
• Atsushi Inoue and Lutz Kilian, "In-sample or out-of-sample tests of predictability: which one should we use?", European Central Bank Working Paper [PDF]
• Akihiko Inoue and Yukio Kasahara, "Explicit representation of finite predictor coefficients and its applications", math.ST/0405051 = Annals of Statistics 34 (2006): 973--993
• D. A. Ioannides and D. P. Papanastassiou, "Estimating the distribution function of a stationary process involving measurement errors", Statistical Inference for Stochastic Processes 4 (2001): 181--198
• E. L. Ionides, C. Breto and A. A. King, "Inference for nonlinear dynamical systems", Proceedings of the National Academy of Sciences (USA) 103 (2006): 18438--18443
• S. Ishii and M.-A. Sato, "Reconstruction of chaotic dynamics by on-line EM algorithm," Neural Networks 14 (2001): 1239--1256
• Christine Jacob, "Conditional least squares estimation in nonstationary nonlinear stochastic regression models", Annals of Statistics 38 (2010): 566--597
• Òscar Jordà, "Simultaneous Confidence Regions for Impulse Responses", The Review of Economics and Statistics 91 (2009): 629--647
• C. T. Jose, B. Ismail, S. Jayasekhar, "Trend, Growth Rate, and Change Point Analysis: A Data Driven Approach", Communications in Statistics: Simulation and Computation 37 (2008): 498--506
• Joseph Tadjuidje Kamgaing, Hernando Ombao and Richard A. Davis, "Autoregressive processes with data-driven regime switching", Journal of Time Series Analysis 30 (2009): 505--533
• Daniel M. Keenan, Xin Wang, Steven M. Pincus and Johannes D. Veldhuis, "Modelling the nonlinear time dynamics of multidimensional hormonal systems", Journal of Time Series Analysis 33 (2012): 779--796
• Matthew B. Kennel, "Testing time symmetry in time series using data compression dictionaries", Physical Review E 69 (2004): 056208
• Tae Yoon Kim and Sangyeol Lee, "Kernel density estimator for strong mixing processes", Journal of Statistical Planning and Inference 133 (2005): 273--284
• Jon Kleinberg, "Bursty and Hierarchical Structure in Streams" [PDF]
• D. Kleinhans, R. Friedrich, "Maximum Likelihood Estimation of Drift and Diffusion Functions", physics/0611102
• D. Kleinhans, R. Friedrich, A. Nawroth and J. Peinke, "An iterative procedure for the estimation of drift and diffusion coefficients of Langevin processes", Physics Letters A 346 (2005): 42--46 = physics/0502152 ["The analysis is based on an iterative procedure minimizing the Kullback-Leibler distance between measured and estimated two time joint probability distributions of the process."]
• M. L. Kleptsyna and A. Le Breton, "Statistical Analysis of the Fractional Ornstein-Uhlenbeck Type Process", Statistical Inference for Stochastic Processes 5 (2002): 229--248
• Jens-Peter Kreiss, Efstathios Paparoditis, Dimitris N. Politis, "On the range of validity of the autoregressive sieve bootstrap", Annals of Statistics 39 (2011): 2103--2130, arxiv:12016211
• Clemens Kreutz, Andreas Raue, Jens Timmer, "Likelihood based observability analysis and confidence intervals for predictions of dynamic models", arxiv:1107.0013
• D. Kugiumtzis, "Statically Transformed Autoregressive Process and Surrogate Data Test for Nonlinearity," nlin.CD/0110025
• Uwe Küchler and Michael Sørensen, Exponential Families of Stochastic Processes
• Hans R. Künsch, "State Space and Hidden Markov Models", pp. 109--173 in Ole E. Barndorff-Nielsen, David R. Cox and Claudia Klüppelberg (eds.), Complex Stochastic Systems
• Y. A. Kutoyants
• Statistical Inference for Ergodic Diffusion Processes
• "On the Goodness-of-Fit Testing for Ergodic Diffusion Processes", arxiv:0903.4550
• "Goodness-of-Fit Tests for Perturbed Dynamical Systems", arxiv:0903.4612
• "On Properties of Estimators in non Regular Situations for Poisson Processes", arxiv:0903.4613
• B. Lacaze, "Errorless uniform sampling of complex stationary processes," Signal Processing 83 (2003): 913--917
• Guy Lebanon, Yang Zhao, and Yanjun Zhao, "Modeling temporal text streams using the local multinomial model", Electronic Journal of Statistics 4 (2010): 566--584
• J. Lember and A. Koloydenko, "Adjusted Viterbi training", math.ST/0406237
• Daniel Lemire, "A Better Alternative to Piecewise Linear Time Series Segmentation", cs.DB/0605103
• Matthieu Lerasle, "Adaptive density estimation for stationary processes", Mathematical Methods of Statistics 18 (2009): 59--83, arxiv:0909.0999
• J. K. Lindsey, Statistical Analysis of Stochastic Processes in Time [old draft in Postscript; data and R code]
• Yu. N. Lin'kov, Asymptotic Statistical Methods for Stochastic Processes
• Weidong Liu and Wei Biao Wu, "Simultaneous nonparametric inference of time series", Annals of Statistics 38 (2010): 2388--2421
• E. Locherbach, "Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps", Statistical Inference for Stochastic Processes 5 (2002): 153--177
• Wei-Yin Loh and Wei Zheng, "Regression trees for longitudinal and multiresponse data", Annals of Applied Statistics 7 (2013): 495--522
• Wei Lu, Namrata Vaswani, "The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes" ["under certain assumptions, the power spectral density (PSD) of any random process is equal to the Fourier transform of the time-averaged autocorrelation function"]
• Zudi Lu, Dag Johan Steinskog, Dag Tjostheim and Qiwei Yao, "Adaptively Varying-Coefficient Spatiotemporal Models", Journal of the Royal Statistical Society B 71 (2009): 859--880 [PDF preprint]
• Xiaodong Luo, Tomomichi Nakamura and Michael Small, "Surrogate data method applied to nonlinear time series", nlin.CD/0603004
• Xiaodong Luo, Jie Zhang, Junfeng Sun, Michael Small, Irene Moroz, "Asymptotically pivotal statistic for surrogate testing with extended hypothesis", nlin.CD/0701008
• Xiaodong Luo, Jie Zhang and Michael Small, "Exact nonparametric inference for detection of nonlinear determinism", nlin.CD/0507049 [More exactly, this is an exact test for linear stochasticity --- rejecting the null indicates either nonlinearity or determinism, or both.]
• Cesar Maldonado, "Fluctuation Bounds for Chaos Plus Noise in Dynamical Systems", Journal of Statistical Physics 148 (2012): 548--564
• Enno Mammen and Swagata Nandi, "Change of the nature of a test when surrogate data are applied", Physical Review E 70 (2004): 016121
• Heikki Mannila and Dmitry Rusakov, "Decomposition of Event Sequences into Independent Components" [short and long versions in PS]
• T. K. March, S. C. Chapman and R. O. Dendy, "Recurrence plot statistics and the effect of embedding", physics/0502042
• Inés P. Mariño, Joaquín Míguez, and Riccardo Meucci, "Monte Carlo method for adaptively estimating the unknown parameters and the dynamic state of chaotic systems", Physical Review E 79 (2009): 056218
• Pierre-Francois Marteau, "Time Warp Edit Distances with Stiffness Adjustment for Time Series Matching", cs.IR/0703033
• Norbert Marwan and Jurgen Kurths, "Nonlinear analysis of bivariate data with cross recurrence plots," physics/0201061
• Norbert Marwan, M. Thiel, N. R. Nowaczyk, "Cross Recurrence Plot Based Synchronization of Time Series," physics/0201062
• Norbert Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, "Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data," physics/0201064
• Ikuo Matsuba, Hiroshi Takahashi and shinya Wakasa, "Stochastically Equivalent Dynamical System Approach to Nonlinear Deterministic Prediction", International Journal of Bifurcation and Chaos 16 (2006): 2721--2728 [I can't tell, from the abstract, if they're proposing to use stochastic systems to predict deterministic ones or vice versa; it'd be interesting either way!]
• Muneya Matsui, "A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations", math.ST/0703731
• Brendan P. M. McCabe, Gael M. Martin, David Harris, "Efficient probabilistic forecasts for counts", Journal of the Royal Statistical Society B 73 (2011): 253--272
• Emma J. McCoy, Sofia C. Olhede, David A. Stephens, "Non-Regular Likelihood Inference for Seasonally Persistent Processes", arxiv:0709.0139
• Kevin McGoff, Sayan Mukherjee, Natesh S. Pillai, "Statistical inference for dynamical systems: a review", arxiv:1204.6265
• Patrick E. McSharry and Leonard A. Smith, "Consistent nonlinear dynamics: identifying model inadequacy", nlin.CD/0401024 = Physica D 192 (2004): 1--22
• Jan Mielniczuk, Zhou Zhou and Wei Biao Wu, "On nonparametric prediction of linear processes", Journal of Time Series Analysis 30 (2009): 652--673
• Javier R. Movellan, Paul Mineiro, and R. J. Williams, "A Monte Carlo EM Approach for Partially Observable Diffusion Processes: Theory and Applications to Neural Networks," Neural Computation 14 (20020: 1507--1544
• Eric Moulines, Pierre Priouret and Francois Roueff, "On recursive estimation for time varying autoregressive processes", math.ST/0603047 = Annals of Statistics 33 (2005): 2610--2654
• Jose M. F. Moura and Sanjoy K. Mitter, "Identification and Filtering: Optimal Recursive Maximum Likelihood Approach" [1986 technical report from MIT, found looking for something else, original URL now lost --- presumably long since published]
• Hans-Georg Muller and Ulrich Stadtmuller, "Generalized functional linear models", math.ST/0505638 = Annals of Statistics 33 (2005): 774--805 ["We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function. If, in addition, a variance function is specified, this leads to a functional estimating equation which corresponds to maximizing a functional quasi-likelihood. This general approach includes the special cases of the functional linear model, as well as functional Poisson regression and functional binomial regression. The latter leads to procedures for classification and discrimination of stochastic processes and functional data. ... An essential step in our proposal is dimension reduction by approximating the predictor processes with a truncated Karhunen-Loeve expansion."]
• Ursula U. Müller, Anton Schick and Wolfgang Wefelmeyer, "Estimating the innovation distribution in nonparametric autoregression", Probability Theory and Related Fields 144 (2009): 53--77 ["We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregressive model. The residuals are based on a local linear smoother for the autoregression function."]
• Tomomichi Nakamura, Yoshito Hirata, and Michael Small, "Testing for correlation structures in short-term variabilities with long-term trends of multivariate time series", Physical Review E 74 (2006): 041114
• Tomomichi Nakamura, Xiaodong Luo, and Michael Small, "Testing for nonlinearity in time series without the Fourier transform", Physical Review E 72 (2005): 055201
• Tomomichi Nakamura and Michael Small, "Small-shuffle surrogate data: Testing for dynamics in fluctuating data with trends", Physical Review E 72 (2005): 056216
• Yuval Nardi, Alessandro Rinaldo, "Autoregressive Process Modeling via the Lasso Procedure", arxiv:0805.1179
• Sahand Negahban, Pradeep Ravikumar, Martin J. Wainwright, Bin Yu, "A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers", arxiv:1010.2731
• Ilia Negri, "Efficiency of a class of unbiased estimators for the invariant distribution function of a diffusion process", math.ST/0609590
• Ilia Negri and Yoichi Nishiyama, "Goodness of fit test for ergodic diffusions by tick time sample scheme", Statistical Inference for stochastic Processes 13 (2010): 81--95
• Yoichi Nishiyama, "Goodness-of-fit test for a nonlinear time series", Journal of Time Series Analysis 30 (2009): 674--681
• Jun Ohkubo, "Nonparametric model reconstruction for stochastic differential equations from discretely observed time-series data", Physical Review E 84 (2011): 066702
• Jimmy Olsson, Olivier Cappe, Dandal Douc and Eric Moulines, "Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models", math.ST/0609514
• Sorinel Adrian Oprisan, "An application of the least-squares method to system parameters extraction from experimental data", Chaos 12 (2002): 27--32
• Brahim Ouhbi and Nikolaos Limnios, "Nonparametric estimation for semi-Markov processes based on its hazard rate functions", Statistical Inference for Stochastic Processes 2 (1999): 151--173
• P. Palaniyandi and M. Lakshmanan, "Estimation of System Parameters and Predicting the Flow Function from Time Series of Continuous Dynamical Systems", nlin.CD/0406027
• Milan Palus, "Coarse-grained entropy rate for characterization of complex time series", Physica D 93 (1996): 64--77 [Thanks to Prof. Palus for a reprint]
• Angeliki Papana and Dimitris Kugiumtzis, "Evaluation of Mutual Information Estimators for Time Series", arxiv:0904.4753
• Efstathios Paparoditis, "Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms", Journal of the American Statistical Association 105 (2010): 839--851
• Emanuel Parzen, "Statistical inference on time series by RKHS methods" (1970)
• Charles T. Perretti, Stephan B. Munch, and George Sugihara, "Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data", Proceedings of the National Academy of Sciences 110 (2013): 5253--5257 [See also response by Hartig and Dormann]
• Raffaella Piccarreta, "Graphical and Smoothing Techniques for Sequence Analysis", Sociological Methods and Research 41 (2012): 362--380
• Zacharias Psaradakis, Martin Sola, Fabio Spagnolo and Nicola Spagnolo, "Selecting nonlinear time series models using information criteria", Journal of Time Series Analysis 30 (2009): 369--394
• N. U. Prabhu and Ishawar V. Basawa (eds.), Statistical Inference in Stochastic Processes (1991)
• B. L. S. Prakasa Rao
• Semimartingales and Their Statistical Inference
• Statistical Inference for Diffusion-Type Processes
• E. Racca and A. Porporato, "Langevin equations from time series", Physical Review E 71 (2005): 027101
• Ali Rahimi, Learning to Transform Time Series with a Few Examples [Ph.D. thesis, MIT dept. of electrical engineering and computer science, 2005. PDF]
• Ali Rahimi, Ben Recht and Trevor Darrell, "Learning to Transform Time Series with a Few Examples", tech report [PDF]
• M. B. Rajarshi, Statistical Inference for Discrete Time Stochastic Processes
• M. M. Rao, Stochastic Processes: Inference Theory
• Ramiro Rico-Martinez, K. Krischer, G. Flaetgen, J.S. Anderson and I. G. Kevrekidis, "Adaptive Detection of Instabilities: An Experimental Feasibility Study," nlin.CD/0202057
• Christoph Rieke, Ralph G. Andrzejak, Florian Mormann and Klaus Lehnertz, "Improved statistical test for nonstationarity using recurrence time statistics", Physical Review E 69 (2004): 046111 [link]
• Ricardo Ríos, Luis-Angel Rodríguez, "Penalized estimate of the number of states in Gaussian linear AR with Markov regime", Electronic Journal of Statistics 2 (2008): 1111--1128, arxiv:0807.2726
• John C. Robertson, Ellis W. Tallman and Charles H. Whiteman, "Forecasting using relative entropy," Federal Reserve Bank of Atlanta Working Paper 2002-20 [PDF]
• J. W. C. Robinson, J. Rung, A. R. Bulsara and M. E. Inchiosa, "General measures for signal-noise separation in nonlinear dynamical systems," Physical Review E 63 2000: 011107
• Brois Ryabko, "Applications of Universal Source Coding to Statistical Analysis of Time Series", arxiv:0809.1226
• Boris Ryabko and Jaakko Astola
• "Universal Codes as a Basis for Time Series Testing", cs.IT/0602084
• "Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series", cs.IT/0506094
• Daniil Ryabko
• Manuel S. Santos, "Consistency properties of a simulation-based estimator for dynamic processes", Annals of Applied Probability 20 (2010): 196--213
• Suchi Saria, Daphne Koller, Anna Penn, "Discovering shared and individual latent structure in multiple time series", arxiv:1008.2028
• Joao R. Sato, Sergi Costafreda, Pedro A. Morettin, Michael John Brammer, "Measuring Time Series Predictability Using Support Vector Regression", Communications in Statistics: Simulation and Computation 37 (2008): 1183--1197
• Nicola Scafeta, Patti Hamilton and Paolo Grigolini, "The Thermodynamics of Social Processes: The Teen Birth Phenomenon," cond-mat/0009020 [Not because I believe them about sociology, but because they claim to have new and powerful nonparametric methods for detecting and quantifying memory in time series]
• Thomas Schreiber and Andreas Schmitz, "Surrogate time series," chao-dyn/9909037
• Reiner Schulz and James A. Reggia, "Temporally Asymmetric Learning Supports Sequence Processing in Multi-Winner Self-Organizing Maps", Neural Computation 16 (2004): 535--561 [the "model presented here raises the possibility that SOMs may ultimately prove useful as visualization tools for temporal sequences and as preprocessors for sequence pattern recognition systems."]
• Xiaofeng Shao, "A self-normalized approach to confidence interval construction in time series", Journal of the Royal Statistical Society B 72 (2010): 343--366, arxiv:1005.2137 [Arxiv version includes an important correction to Assumption 2 and related theorems]
• Xiaofeng Shao, Wei Biao Wu, "Asymptotic spectral theory for nonlinear time series", math.ST/0611029
• M. Siefert, J. Peinke and R. Friedrich, "On a quantitative method to analyse dynamical and measurement noise," physics/0108034
• Przemyslaw Sliwa and Wolfgang Schmid, "Monitoring the cross-covariances of a multivariate time series", Metrika 61 (2005): 89--115
• A. Sitz, U. Schwarz, J. Kurths, H. U. Voss, "Estimation of parameters and unobserved components for nonlinear systems from noisy time series," Physical Review E 66 (2002): 016210
• Michael Small and Kevin Judd, "Detecting periodicity in experimental data using linear modeling techniques", physics/9810021
• Vadim N. Smelyanskiy and Dmitry G. Luchinsky, "Inference of stochastic nonlinear oscillators with applications to physiological problems", physics/0403121 [They present this as a Bayesian inference issue, but the core of their work appears, from skimming, to be an efficient method for computing the likelihood, so it'd apply equally well to maximum likelihood inference, for instance.]
• V. N. Smelyanskiy, D. A. Timucin, A. Bandrivskyy and D. G. Luchinsky, "Model reconstruction of nonlinear dynamical systems driven by noise", physics/0310062 [Same as earlier paper --- was this one submitted to PRL?]
• Dmitry A. Smirnov, Vladislav S. Vlaskin and Vladimir I. Ponomarenko, "Estimation of parameters in one-dimensional maps from noisy chaotic time series", Physics Letters A 336 (2005): 448--458
• Song Song and Peter J. Bickel, "Large Vector Auto Regressions", arxiv:1106.3915
• Eduardo D. Sontag, "For differential equations with r parameters, 2r+1 experiments are enough for identification," math.DS/0111135
• D. Sornette and V. F. Pisarenko, "Properties of a simple bilinear stochastic model: estimation and predictability", physics/0703217
• Jean-Pierre Stockis, Jurgen Franke and Joseph Tadjuidje Kamgaing, "On geometric ergodicity of CHARME models", Journal of Time Series Analysiscite> 31 (2010): 141--152
• Tomoya Suzuki, Tohru Ikeguchi, and Masuo Suzuki, "Effects of data windows on the methods of surrogate data", Physical Review E 71 (2005): 056708
• Alexander G. Tartakovsky, "Asymptotic Optimality of Certain Multihypothesis Sequential Tests: Non-i.i.d. Case", Statistical Inference for Stochastic Processes 1 (1998): 265--295
• Marco Thiel, M. Carmen Romano and Jurgen Kurths, "How much information is contained in a recurrence plot?", Physics Letters A 330 (2004): 343--349
• Bo Thiesson, David Maxwell Chickering, David Heckerman, Christopher Meek, "ARMA Time-Series Modeling with Graphical Models", UAI 2004, arxiv:1207.4162
• Madeleine B. Thompson, "A Comparison of Methods for Computing Autocorrelation Time", arxiv:1011.0175
• Tina Toni, David Welch, Natalja Strelkowa, Andreas Ipsen, Michael P.H. Stumpf, "Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems", arxiv:0901.1925
• Wilson Truccolo, John P. Donoghue, "Nonparametric Modeling of Neural Point Processes via Stochastic Gradient Boosting Regression", Neural Computation 19 (2007): 672-705
• Masayuki Uchida and Nakahiro Yoshida, "Information Criteria in Model Selection for Mixing Processes", Statistical Inference for Stochastic Processes 4 (2001): 73--98 ["The emphasis is put on the use of the asymptotic expansion of the distribution of an estimator based on the conditional Kullback-Leibler divergence for stochastic processes. Asymptotic properties of information criteria and their improvement are discusssed."]
• Aad van der Vaart and Harry van Zanten, "Donsker theorems for diffusions: Necessary and sufficient conditions", math.PR/0507412 = Annals of Probability 33 (2005): 1422--1451
• Harry van Zanten, "On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators", Statistical Inference for Stochastic Processes 6 (2003): 199--213 ["In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the 'size' of the class [of functions] in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive."]
• J. H. van Zanten, "On the Uniform Convergence of the Empirical Density of an Ergodic Diffusion", Statistical Inference for Stochastic Processes 3 (2000): 251--262
• Paolo Vidoni, "A simple procedure for computing improved prediction intervals for autoregressive models", Journal of Time Series Analysis 30 (2009): 577--590
• Juan M. Vilar-Fernandez and Ricardo Cao, "Nonparametric Forecasting in Time Series - A Comparative Study", Communications in Statistics: Simulation and Computation 36 (2007): 311--334
• R. Vilela Mendes, R. Lima and T. Araujo, "A Process-Reconstruction Analysis of Market Fluctuations," cond-mat/0102301 [I don't care about the market, but they claim to have a new method for identifying distributions over entire sequences]
• Divakar Viswanath, Xuan Liang, Kirill Serkh, "Metric Entropy and the Optimal Prediction of Chaotic Signals", arxiv:1102.3202
• Li Wang, Lijian Yang, "Spline-backfitted kernel smoothing of nonlinear additive autoregression model", Annals of Statistics 35 (2007): 2474--2503, arxiv:math/0612677
• Qiying Wang and Peter C. B. Phillips, "A specification test for nonlinear nonstationary models", Annals of Statistics 40 (2012): 727--758
• Zijun Wang, "Finite Sample Performances of the Model Selection Approach in Nonparametric Model Specification for Time Series", Communications in Statistics: Theory and Methods 38 (2009): 2302--2330
• Halbert White ,Asymptotic Theory for Econometricians
• Wei Biao Wu
• Herwig Wendt, Patrice Abry and Stephane Jaffard, "Bootstrap for Empirical Multifractal Analysis", IEEE Signal Processing Magazine July 2007, pp. 38--48 [+ technical papers by these authors]
• Han Xiao and Wei Biao Wu, "Covariance matrix estimation for stationary time series", Annals of Statistics 40 (2012): 466--493
• Hongqi Xue, Hongyu Miao, and Hulin Wu, "Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error", Annals of Statistics 38 (2010): 2351--2387
• A. Zeileis and G. Grothendieck, "zoo: S3 Infrastructure for Regular and Irregular Time Series", Journal of Statistical Software 14 (2005): 1--27 = math.ST/0505527 ["zoo is an R package providing an S3 class with methods for indexed totally ordered observations, such as discrete irregular time series. Its key design goals are independence of a particular index/time/date class and consistency with base R and the "ts" class for regular time series."]
• Zhou Zhou, "Nonparametric inference of quantile curves for nonstationary time series", Annals of Statistics 38 (2010): 2187--2217
• M. Zukovic, D. T. Hristopulos, "Spartan Random Processes in Time Series Modeling", 0709.3418
To write/finish:
• CRS, "Learning Rates and Recurrence Times" [a.k.a. "Wait and see"]
• CRS, "Algorithms for Inferring the Statistical Structure of Symbol Sequences: History and Review"

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