Literature review: related methods for assembling synthetic series

Methods related to assembling a long series from pieces that were not included in the method list (BASELINES.md): they have no implementation, come from another field or use the real train directly instead of a generator pool.

Analogues from other fields

Method	Idea	Literature	Implementation
Unit selection (concatenative speech synthesis)	Selection and ordering of speech fragments by the sum of target cost + concatenation cost, Viterbi search. A conceptual analogue of assembly from a window pool	Hunt A., Black A. Unit selection in a concatenative speech synthesis system using a large speech database. ICASSP 1996. doi:10.1109/ICASSP.1996.541110	Festival (C++, speech only) — cstr.ed.ac.uk/projects/festival
Video Textures	A transition matrix between frames by similarity; a random walk on the Markov chain gives an endless video	Schödl A., Szeliski R., Salesin D., Essa I. Video Textures. SIGGRAPH 2000. doi:10.1145/344779.345012	no official one; on a pool it coincides with matched-block from BASELINES.md; its frame distance is the seam cost of the solvers there (greedy, ATSP, PCTSP)
Motion Graphs	A graph of motion clips with transitions at similar poses, path search under constraints	Kovar L., Gleicher M., Pighin F. Motion Graphs. SIGGRAPH 2002. doi:10.1145/566654.566605	no official one
Graphcut textures	Optimal seam between overlapping patches via min-cut; in 1D it coincides with image quilting	Kwatra V., Schödl A., Essa I., Turk G., Bobick A. Graphcut textures: image and video synthesis using graph cuts. SIGGRAPH 2003. doi:10.1145/882262.882264	no official one

Diffusion generation of long content

Method	Idea	Literature	Implementation
RePaint	Inpainting with an unconditional diffusion model: the known part is resampled at every step	Lugmayr A. et al. RePaint: Inpainting using denoising diffusion probabilistic models. CVPR 2022. arXiv:2201.09865	github.com/andreas128/RePaint — images only, a separate diffusion model for series is needed
MultiDiffusion	Overlapping windows are reconciled at every denoising step (averaging of overlaps)	Bar-Tal O., Yariv L., Lipman Y., Dekel T. MultiDiffusion: Fusing diffusion paths for controlled image generation. ICML 2023. arXiv:2302.08113	github.com/omerbt/MultiDiffusion — for Stable Diffusion; for series this is a custom implementation on top of Diffusion-TS
DiffCollage	A factor graph of overlapping pieces, parallel generation of content of arbitrary length	Zhang Q., Song J., Huang X., Chen Y., Liu M.-Y. DiffCollage: Parallel generation of large content with diffusion models. CVPR 2023. arXiv:2303.17076	no official code; project page

Resampling the real series (bootstrap and surrogates)

Method	Idea	Literature	Implementation
Moving block bootstrap	Concatenation of random overlapping blocks of fixed length	Künsch H. The jackknife and the bootstrap for general stationary observations. Ann. Statist. 17(3), 1989. doi:10.1214/aos/1176347265	arch (MovingBlockBootstrap), tsbootstrap
Circular block bootstrap	The same, with the series wrapped into a circle — all points are equally likely	Politis D., Romano J. A circular block-resampling procedure for stationary data. In: LePage R., Billard L. (eds.) Exploring the Limits of Bootstrap, Wiley, 1992 (book chapter, no open link)	arch (CircularBlockBootstrap), tsbootstrap
Stationary bootstrap	The block length is random (geometric) — the result is stationary	Politis D., Romano J. The stationary bootstrap. JASA 89(428), 1994. doi:10.1080/01621459.1994.10476870	arch (StationaryBootstrap), tsbootstrap, recombinator
Optimal block length	Automatic selection of the block length for the stationary / circular bootstrap	Politis D., White H. Automatic block-length selection for the dependent bootstrap. Econometric Reviews 23(1), 2004. doi:10.1081/ETC-120028836	arch (optimal_block_length)
Seasonal block bootstrap	Blocks start at the same seasonal phase, so seasonality is not broken	Dudek A., Leśkow J., Paparoditis E., Politis D. A generalized block bootstrap for seasonal time series. J. Time Series Analysis 35(2), 2014. ideas.repec.org	no ready-made Python one
Sieve bootstrap	Fitting AR(p) with growing p, resampling the residuals, generation by recursion	Bühlmann P. Sieve bootstrap for time series. Bernoulli 3(2), 1997. projecteuclid.org	tsbootstrap (SieveBootstrap)
Markov bootstrap	Resampling via a kernel estimate of the transition density of a Markov chain	Rajarshi M. Bootstrap in Markov-sequences based on estimates of transition density. Ann. Inst. Statist. Math. 42, 1990. doi:10.1007/BF00050835	tsbootstrap (its own variation: HMM over blocks)
AAFT surrogates	Random Fourier phases with matching of the value distribution	Theiler J. et al. Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 1992. doi:10.1016/0167-2789(92)90102-S	nolitsa
IAAFT surrogates	Iterative matching of both the spectrum and the value distribution	Schreiber T., Schmitz A. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77, 1996. doi:10.1103/PhysRevLett.77.635	nolitsa

Augmentations of real series

Method	Idea	Literature	Implementation
Window warping / window slicing	Speeding up or slowing down a segment of the series and returning to the original length; cutting out sub-windows	Le Guennec A., Malinowski S., Tavenard R. Data augmentation for time series classification using convolutional neural networks. AALTD @ ECML/PKDD 2016. HAL	tsgm (tsgm.models.augmentations), tsaug
DBA augmentation	Synthetic series as weighted DTW barycentres of real ones	Forestier G., Petitjean F., Dau H. A., Webb G. I., Keogh E. Generating synthetic time series to augment sparse datasets. ICDM 2017. IEEE Xplore; DBA: Petitjean F. et al. Pattern Recognition 44(3), 2011. doi:10.1016/j.patcog.2010.09.013	tsgm (DTWBarycentricAveraging), MSD-IRIMAS/Augmenting-TSC-Elastic-Averaging