Time Series, or Statistics for Stochastic Processes and Dynamical Systems

07 Oct 2024 11:17

Rates of convergence of estimators; distribution-free learning theory. 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.)

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]
Randal Douc and Eric Moulines and David S. Stoffer, Nonlinear Time Series: Theory, Methods, and Applications with R Examples
Jianqing Fan and Qiwei Yao, Nonlinear Time Series: Nonparametric and Parametric Methods
Peter Guttorp, Stochastic Modeling of Scientific Data [An introduction to statistical inference for many different kinds of dependent data, not just time series; designed to be read by quantitatively-trained scientists, as well as statisticians and probabilists]
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
Kevin McGoff, Sayan Mukherjee, and Natesh Pillai, "Statistical inference for dynamical systems: A review", Statistics Surveys 9 (2015): 209--252, arxiv:1204.6265
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]

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
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.]
Allan Dafoe, "First Do No Harm: The Risks of Modeling Temporal Dependence" [PDF preprint]
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?]
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]
Giles Hooker, Stephen P. Ellner, "Goodness of fit in nonlinear dynamics: Misspecified rates or misspecified states?", Annals of Applied Statistics 9 (2015): 754--776, arxiv:1312.0294
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
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]
Yun Shin Lee and Stefan Scholtes, "Empirical prediction intervals revisited", International Journal of Forecasting 30 (2014): 217--234
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 Transactions on Information 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 (New York: Wiley, 2004) [PDF. "Improved" compared to using standard time-series models with no biological content. Comment, 26 October 2021: Having just re-read this paper and tried to implement it in connection with another project, I am unable to get the behavior they display with the parameters they report for the posterior mode. Whether this is due to an implementation failure on my part, a misprint, or something else, I couldn't begin to say, but I leave this note here as a marker in case it helps anyone else.]
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."]
Yi Shen and Tony S. Wirjanto, "Stationarity Tests for Time Series -- What Are We Really Testing?", arxiv:1505.01163
Christopher C. Strelioff and Alfred W. Hübler, "Medium-Term Prediction of Chaos", Physical Review Letters 96 (2006): 044101
X. Z. Tang, E. R. Tracy, A. D. Boozer, A. deBrauw, and R. Brown, "Symbol sequence statistics in noisy chaotic signal reconstruction", Physical Review E 51 (1995): 3871
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.]
Bo Thiesson, David Maxwell Chickering, David Heckerman, Christopher Meek, "ARMA Time-Series Modeling with Graphical Models", pp. 552--560 in UAI 2004, arxiv:1207.4162
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.]
- "Recursive estimation of time-average variance constants", Annals of Applied Probability 19 (2009): 1529--1552, arxiv:0908.4540 [This is an ingenious way of getting at the asymptotic variance of the mean, but it doesn't, from my reading, seem to have any statistical advantages over the bootstrap methods given by (e.g.) Lahiri (sec. 3.2.1). The computational advantage in memory would however be massive.]

Isidore Fleischer and Anthony Kooharian, "On the Statistical Treatment of Stochastic Processes", Annals of Mathematical Statistics 29 (1958): 544--549
Norbert Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series

Robert Lunde and CRS, "Bootstrapping Generalization Error Bounds for Time Series", arxiv:1711.02834
Daniel J. McDonald and CRS
- "Empirical Macroeconomics and DSGE Modeling in Statistical Perspective", arxiv:2210.16224
- "Rademacher complexity of stationary sequences", arxiv:1106.0730
Daniel J. McDonald, CRS and Mark Schervish
- "Estimating $\beta$-mixing coefficients", AISTATS 2011, arxiv:1103.0941
- "Generalization error bounds for stationary autoregressive models", arxiv:1103.0942
- "Estimating Beta-Mixing Coefficients via Histograms", Electronic Journal of Statistics 9 (2015): 2855--2883, arxiv:1109.5998
- "Nonparametric Risk Bounds for Time-Series Forecasting", arxiv:1212.0463
CRS, Causal Architecture, Complexity and Self-Organization in Time Series and Cellular Automata [Ph.D. thesis, UW-Madison, 2001]
CRS, Abigail Z. Jacobs, Kristina Lisa Klinkner and Aaron Clauset, "Adapting to Non-stationarity with Growing Expert Ensembles", arxiv:1103.0949
CRS and Kristina Lisa Klinkner, "Blind Construction of Optimal Nonlinear Predictors for Discrete Sequences", pp. 504--511 of Uncertainty in Artificial Intelligence: Proceedings of the Twentieth Conference (UAI 2004), cs.LG/0406011

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
Oren Anava, Elad Hazan, Shie Mannor, Ohad Shamir, "Online Learning for Time Series Prediction", arxiv:1302.6927
Brian D. O. Anderson Manfred Deistler Jean‐Marie Dufour, On the Sensitivity of Granger Causality to Errors‐In‐Variables, Linear Transformations and Subsampling", Journal of Time Series Analysis 40 (2019): 102--123
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
Ouerdia Arkoun, Serguei Pergamenchtchikov, "Sequential robust efficient estimation for nonparametric autoregressive models", arxiv:1304.4848
J. A. D. Aston, "Modeling macroeconomic time series via heavy tailed distributions", math.ST/0702844
Francesco Audrino, Lorenzo Camponovo, "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models", arxiv:1312.1473
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
- "What to Do (and Not to Do) with Time-Series Cross-Section Data", American Political Science Review 89 (1995): 634--647 [JSTOR]
- Commentary by the authors, American Political Science Review 100 (2006): 676--677
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
  - 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. ... statistical estimation problems and specific applications"]
  - 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", Annals of Statistics 37 (2009): 3715--3742, arxiv:0911.3469
  - 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
  - Ngai Hang Chan and Ching-Kang Ing, "Uniform moment bounds of Fisher’s information with applications to time series", Annals of Statistics 39 (2011): 1526--1550
  - 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
  - Yining Chen, "Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency", arxiv:1111.6291
  - 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
  - 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."]
  - 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, "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
  - Youri Davydov, "Remarks on Estimation Problem for Stationary Processes in Continuous Time", Statistical Inference for Stochastic Processes 4 (2001): 1--15
  - Miguel A. Delgado, Javier Hidalgo and Carlos Velasco, "Distribution free goodness-of-fit tests for linear processes", Annals of Statistics 33 (2005): 2568--2609, math.ST/0603043 [i.e., goodness-of-fit for the autocorrelation function]
  - Alysha M. De Livera, Rob J. Hyndman and Ralph D. Snyder, "Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing", Journal of the American Statistical Association 106 (2011): 1513--1527
  - 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
  - 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
  - Lisandro Javier Fermin, Ricardo Rios, Luis Angel Rodriguez, "A Robbins–Monro Algorithm for Non-Parametric Estimation of NAR Process with Markov Switching: Consistency", Journal of Time Series Analysis 38 (2017): 809--837 [a stochastic approximation method]
  - Enrique Figueroa-Lopez and Christian Houdre, "Nonparametric estimation for Levy processes with a view towards mathematical finance", math.ST/0412351
  - 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
  - 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
  - Pierre Gaillard, Paul Baudin , "A consistent deterministic regression tree for non-parametric prediction of time series", arxiv:1405.1533
  - 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
  - Mihai C. Giurcanu, "Oracle M-Estimation for Time Series Models", Journal of Time Series Analysis 38 (2017): 479--504
  - 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
  - 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
  - Bruce E. Hansen and Kenneth D. West, "Generalized Method of Moments and Macroeconomics", Journal of Business and Economic Statistics (2002) [Reprint]
  - Wolfgang Hardle, Helmut Lutkepohl, Rong Chen, "A Review of Nonparametric Time Series Analysis", International Statistical Review 65 (1997): 49--72 [JSTOR]
  - Moritz Hardt, Tengyu Ma, Benjamin Recht, "Gradient Descent Learns Linear Dynamical Systems", Journal of Machine Learning Research 19 (2018): 29
  - 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]
  - 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
  - David Hendry, Econometrics: Alchemy or Science? [Review by Bruce Hansen]
  - David F. Hendry and Bent Nielsen, Econometric Modeling: A Likelihood Approach
  - 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
  - Siegfried Hörmann, "Augmented GARCH sequences: Dependence structure and asymptotics", arxiv:0805.2214
  - 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.]
  - 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", Annals of Statistics 34 (2006): 973--993, math.ST/0405051
  - 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
  - Jean Jacod and Michael Sorensen, "A review of asymptotic theory of estimating functions", Statistical Inference for Stochastic Processes 21 (2018): 415--434
  - 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
  - Matthew B. Kennel, "Testing time symmetry in time series using data compression dictionaries", Physical Review E 69 (2004): 056208
  - Igor L. Kheifets, "Specification tests for nonlinear dynamic models", arxiv:1410.3533
  - Tae Yoon Kim and Sangyeol Lee, "Kernel density estimator for strong mixing processes", Journal of Statistical Planning and Inference 133 (2005): 273--284
  - Young Min Kim, Soumendra N. Lahiri and Daniel J. Nordman, "A Progressive Block Empirical Likelihood Method for Time Series", Journal of the American Statistical Association 108 (2013): 1506--1516
  - Jon Kleinberg, "Bursty and Hierarchical Structure in Streams" [PDF]
  - D. Kleinhans, R. Friedrich, "Maximum Likelihood Estimation of Drift and Diffusion Functions", physics/0611102
  - Juanjuan Kong, Lijie Gu, Lijian Yang, "Prediction Interval for Autoregressive Time Series via Oracally Efficient Estimation of Multi‐Step‐Ahead Innovation Distribution Function", Journal of Time Series Analysis 39 (2018): 690--708
  - Hira L. Koul and Winfried Stute, "Nonparametric model checks for time series", Annals of Statistics 27 (1999): 204--236
  - 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
    - "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"]
  - 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.]
  - Elizabeth Ann Maharaj, Pierpaolo D'Urso, and Jorge Caiado, Time Series Clustering and Classification [Review in JASA]
  - 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
  - Nikolai Matni, Stephen Tu, "A Tutorial on Concentration Bounds for System Identification", arxiv:1906.11395
  - 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
  - Patrick E. McSharry and Leonard A. Smith, "Consistent nonlinear dynamics: identifying model inadequacy", Physica D 192 (2004): 1--22, nlin.CD/0401024
  - Jan Mielniczuk, Zhou Zhou and Wei Biao Wu, "On nonparametric prediction of linear processes", Journal of Time Series Analysis 30 (2009): 652--673
  - Eric Moulines, Pierre Priouret and Francois Roueff, "On recursive estimation for time varying autoregressive processes", Annals of Statistics 33 (2005): 2610--2654, math.ST/0603047
  - Jose M. F. Moura and Sanjoy K. Mitter, "Identification and Filtering: Optimal Recursive Maximum Likelihood Approach" [1986 technical report from MIT; PDF preprint --- presumably long since published]
  - Hans-Georg Muller and Ulrich Stadtmuller, "Generalized functional linear models", Annals of Statistics 33 (2005): 774--805, math.ST/0505638
  - 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, 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
  - Yoichi Nishiyama, "Goodness-of-fit test for a nonlinear time series", Journal of Time Series Analysis 30 (2009): 674--681
  - Daniel J. Nordman and Soumendra N. Lahiri, "Convergence rates of empirical block length selectors for block bootstrap", Bernoulli 20 (2014): 958-978
  - 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, Randal 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
    - "A sieve bootstrap test for stationarity," Statistics and Probability Letters 62 (2003): 263--274
    - "Blockwise bootstrap testing for stationarity", Statistics and Probability Letters 76 (2006): 562--570
  - 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
  - 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
  - Suhasini Subba Rao, "Orthogonal Samples for Estimators in Time Series", Journal of Time Series Analysis forthcoming (2018)
  - 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
    - "An impossibility result for process discrimination", arxiv:0809.1053
    - "Characterizing predictable classes of processes", arxiv:0905.4341
    - "Discrimination between B-Processes is Impossible", Journal of Theoretical Probability 23 (2010): 565--575
    - "Clustering processes", arxiv:1005.0826
  - Manuel S. Santos, "Consistency properties of a simulation-based estimator for dynamic processes", Annals of Applied Probability 20 (2010): 196--213
  - 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]
  - Francois G. Schmitt and Yongxiang Huang, Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications
  - 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
  - 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
  - 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
  - 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
  - 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
  - Ingo Steinwart, Marian Anghel, "Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise", Annals of Statistics 37 (2009): 841--875, arxiv:0707.0322
  - 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
  - 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
  - Masayuki Uchida and Nakahiro Yoshida, "Information Criteria in Model Selection for Mixing Processes", Statistical Inference for Stochastic Processes 4 (2001): 73--98
  - Yoshimasa Uematsu, "Penalized Likelihood Estimation in High-Dimensional Time Series Models and its Application", arxiv:1504.06706
  - 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
  - Michael Wolf and Dan Wunderli, "Bootstrap Joint Prediction Regions", Journal of Time Series Analysis forthcoming (2014)
  - Wei Biao Wu
    
    and Jan Mielniczuk, "Kernel Density Estimation for Linear Processes", Annals of Statistics 30 (2002): 1441--1459
  - 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]
  - Yingcun Xia, Howell Tong, "Feature Matching in Time Series Modeling", arxiv:1104.3073
  - Han Xiao and Wei Biao Wu, "Covariance matrix estimation for stationary time series", Annals of Statistics 40 (2012): 466--493
  - Chen Xu, Yao Xie, "Conformal prediction for dynamic time-series", arxiv:2010.09107
  - 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
  - Ting Zhang, Hwai-Chung Ho, Martin Wendler, Wei Biao Wu, "Block Sampling under Strong Dependence", arxiv:1312.5807
  - Yuexu Zhao, Zhengyan Lin, "Limit theorems for kernel density estimators under dependent samples", arxiv:1305.5882
  - Zhibiao Zhao and Wei Biao Wu, "Confidence bands in nonparametric time series regression", Annals of Statistics 36 (2008): 1854--1878, arxiv:0808.1010
  - Zhou Zhou, "Nonparametric inference of quantile curves for nonstationary time series", Annals of Statistics 38 (2010): 2187--2217
  - Nicolas L. Ziebarth, Karen C. Abbott and Anthony R. Ives, "Weak population regulation in ecological time series", Ecology Letters 13 (2010): 21--31
  - 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"
  Co-conspirators to be named later + CRS, "SPASM" [If I don't end up just encouraging from the sidelines...]