Time series forecasting plays a crucial role in marketing, finance and many other quantitative fields. A large amount of methodologies has been developed on this topic, including ARIMA, Holt-Winters, etc. However, their performance is easily undermined by the existence of change points and anomaly points, two structures commonly observed in real data, but rarely considered in the aforementioned methods. In this paper, we propose a novel state space time series model, with the capability to capture the structure of change points and anomaly points, as well as trend and seasonality. To infer all the hidden variables, we develop a Bayesian framework, which is able to obtain distributions and forecasting intervals for time series forecasting, with provable theoretical properties. For implementation, an iterative algorithm with Markov chain Monte Carlo (MCMC), Kalman filter and Kalman smoothing is proposed. In both synthetic data and real data applications, our methodology yields a better performance in time series forecasting compared with existing methods, along with more accurate change point detection and anomaly detection.
Minor comments:
- page 3. “The observation equation and transition equations together (i.e., Equation (1,2,3)) together define “ - one “together” should be removed
- page 4. “From Figure 2, the joint distribution (i.e., the likelihood function ” - there should be additional bracket
- page 7. “We can further integral out αn “ -> integrate out
Major comments:
The paper is well-written. The paper considers structural time-series model with seasonal component and stochastic trend, which allow for change-points and structural breaks.
Such type of parametric models are widely considered in econometric literature, see e.g.
[1] Jalles, João Tovar, Structural Time Series Models and the Kalman Filter: A Concise Review (June 19, 2009). FEUNL Working Paper No. 541. Available at SSRN: https://ssrn.com/abstract=1496864 or http://dx.doi.org/10.2139/ssrn.1496864 
[2] Jacques J. F. Commandeur, Siem Jan Koopman, Marius Ooms. Statistical Software for State Space Methods // May 2011, Volume 41, Issue 1.
[3] Scott, Steven L. and Varian, Hal R., Predicting the Present with Bayesian Structural Time Series (June 28, 2013). Available at SSRN: https://ssrn.com/abstract=2304426 or http://dx.doi.org/10.2139/ssrn.2304426 
[4] Phillip G. Gould, Anne B. Koehler, J. Keith Ord, Ralph D. Snyder, Rob J. Hyndman, Farshid Vahid-Araghi, Forecasting time series with multiple seasonal patterns, In European Journal of Operational Research, Volume 191, Issue 1, 2008, Pages 207-222, ISSN 0377-2217, https://doi.org/10.1016/j.ejor.2007.08.024.
[5] A.C. Harvey, S. Peters. Estimation Procedures for structural time series models // Journal of Forecasting, Vol. 9, 89-108, 1990
[6] A. Harvey, S.J. Koopman, J. Penzer. Messy Time Series: A Unified approach // Advances in Econometrics, Vol. 13, pp. 103-143.
They also use Kalman filter and MCMC-based approaches to sample posterior to estimate hidden components.
There are also non-parametric approaches to extraction of components from quasi-periodic time-series, see e.g.
[7] Artemov A., Burnaev E. Detecting Performance Degradation of Software-Intensive Systems in the Presence of Trends and Long-Range Dependence // 16th International Conference on Data Mining Workshops (ICDMW), IEEE Conference Publications, pp. 29 - 36, 2016. DOI: 10.1109/ICDMW.2016.0013
[8] Alexey Artemov, Evgeny Burnaev and Andrey Lokot. Nonparametric Decomposition of Quasi-periodic Time Series for Change-point Detection // Proc. SPIE 9875, Eighth International Conference on Machine Vision, 987520 (December 8, 2015); 5 P. doi:10.1117/12.2228370;http://dx.doi.org/10.1117/12.2228370
In some of these papers models of structural brakes and change-points are also considered, see e.g. 
- page 118 in [6]
- papers [7, 8]
There were also Bayesian approaches for change-point detection, which are similar to the model of change-point, proposed in the considered paper, e.g.
[9] Ryan Prescott Adams, David J.C. MacKay. Bayesian Online Changepoint Detection // https://arxiv.org/abs/0710.3742
[10] Ryan Turner, Yunus Saatçi, and Carl Edward Rasmussen. Adaptive sequential Bayesian change point detection. In Zaïd Harchaoui, editor, NIPS Workshop on Temporal Segmentation, Whistler, BC, Canada, December 2009.
Thus,
- the paper does not provide comparison with relevant econometric literature on parametric structural time-series models,
- the paper does not provide comparison with relevant advanced change-point detection methods e.g. [7,8,9,10]. The comparison is provided only with very simple methods,
- the proposed model itself looks very similar to what can be found across econometric literature,
- the datasets, used for comparison, are very scarce. There are datasets for anomaly detection in time-series data, which should be used for extensive comparison, e.g. Numenta Anomaly Detection Benchmark.
Therefore, also the paper is well-written, 
- it lacks novelty,
- its topic does not perfectly fit topics of interest for ICLR,
So, I do not recommend this paper to be published.