Multiscale Hidden Markov Models For Covariance Prediction
This paper presents a novel variant of hierarchical hidden Markov models (HMMs), the multiscale hidden Markov model (MSHMM), and an associated spectral estimation and prediction scheme that is consistent, finds global optima, and is computationally efficient. Our MSHMM is a generative model of multiple HMMs evolving at different rates where the observation is a result of the additive emissions of the HMMs. While estimation is relatively straightforward, prediction for the MSHMM poses a unique challenge, which we address in this paper. Further, we show that spectral estimation of the MSHMM outperforms standard methods of predicting the asset covariance of stock prices, a widely addressed problem that is multiscale, non-stationary, and requires processing huge amounts of data.
 The paper presents an interesting spectral algorithm for multiscale hmm. The derivation and analysis seems correct. However, it is well-known that spectral algorithm is not robust to model mis-specification. It is not clear whether the proposed algorithm will be useful in practice. How will the method compare to EM algorithms and neural network based approaches?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Multiscale Hidden Markov Models For Covariance Prediction
This paper presents a novel variant of hierarchical hidden Markov models (HMMs), the multiscale hidden Markov model (MSHMM), and an associated spectral estimation and prediction scheme that is consistent, finds global optima, and is computationally efficient. Our MSHMM is a generative model of multiple HMMs evolving at different rates where the observation is a result of the additive emissions of the HMMs. While estimation is relatively straightforward, prediction for the MSHMM poses a unique challenge, which we address in this paper. Further, we show that spectral estimation of the MSHMM outperforms standard methods of predicting the asset covariance of stock prices, a widely addressed problem that is multiscale, non-stationary, and requires processing huge amounts of data.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper presents an interesting spectral algorithm for multiscale hmm. The derivation and analysis seems correct. However, it is well-known that spectral algorithm is not robust to model mis-specification. It is not clear whether the proposed algorithm will be useful in practice. How will the method compare to EM algorithms and neural network based approaches?
assistant
 The paper presents an interesting spectral algorithm for multiscale hmm. The derivation and analysis seems correct. However, it is well-known that spectral algorithm is not robust to model mis-specification. It is not clear whether the proposed algorithm will be useful in practice. How will the method compare to EM algorithms and neural network based approaches?