Venue: ICLR 2017 conference

Reviews:

final_score: rating: null
review_content: One well known limitation of GARCH is that its predictive distribution for the next time step is Gaussian. Empirically, it has been shown that when fitting this model to financial data, the residuals are still heavy-tailed. To solve this problem, there are many variants of GARCH that that include heavy-tailed distributions for the noise, instead of Gaussians. Stochastic volatility models have also heavy-tailed predictive distributions. The authors should compare with stronger baselines to really quantify the gains produced by their method with respect to previous work.

It seems that using recurrent neural networks in this setting is not very well justified. The amount of training data used is not very large (1500 data points) and also financial data has very little structure. Therefore, it is unlikely that the proposed neural networks are able to learn any feature representations that would justify them as an alternative to other modeling approaches such as Gaussian processes for example or other simpler models such as linear models (e.g. GARCH).

The evaluation process is also a bit strange. The authors evaluate their methods in a window with the last 500 data points. However, the most common approach for evaluating the predictive performance of models for financial time series is to use a sliding window approach in which the model is used to predict only the next point output of the training window. After this, the training window is moved one step forward, the model is retrained and the process repeats. By doing this, the model is always updated with the most up to date data. Why is that the authors do not use this evaluation approach?


review_title: Lack of heavy tails in the 1 step-ahead predictive distribution of GARCH and evaluation approach

final_score: rating: 6: Marginally above acceptance threshold
review_content: The authors propose a recurrent variational neural network approach to modelling volatility in financial time series. This model consists of an application of Chung et al.’s (2015) VRNN model to volatility forecasting, wherein a Variational Autoencoder (VAE) structure is repeated at each time step of the series. 

The paper is well written and easy to follow (although this reviewer suggests applying a spelling checking, since the paper contains a number of harmless typos). 

The paper’s main technical contribution is to stack two levels of recurrence, one for the latent process and one for the observables. This appears to be a novel, if minor contribution. The larger contribution is methodological, in areas of time series modelling that are both of great practical importance and have hitherto been dominated by rigid functional forms. The demonstration of the applicability and usefulness of general-purpose non-linear models for volatility forecasting would be extremely impactful.

I have a few comments and reservations with the paper:
1) Although not  mentioned explicitly, the authors’ framework are couched in terms of carrying out one-timestep-ahead forecasts of volatility. However, many applications of volatility models, for instance for derivative pricing, require longer-horizon forecasts. It would be interesting to discuss how this model could be extended to forecast at longer horizons.
 
2) In Section 4.4, there’s a mention that a GARCH(1,1) is conditionally deterministic. This is true only when forecasting 1 time-step in the future. At longer horizons, the GARCH(1,1) volatility forecast is not deterministic. 

3) I was initially unhappy with the limitations of the experimental validation, limited to comparison with a baseline GARCH model. However, the authors provided more comparisons in the revision, which adds to the quality of the results, although the models compared against cannot be considered state of the art. It would be well advised to look into R packages such as `stochvol’ and ‘fGarch’ to get implementations of a variety of models that can serve as useful baselines, and provide convincing evidence that the modelled volatility is indeed substantially better than approaches currently entertained by the finance literature.

4) In Section 5.2, more details should be given on the network, e.g. number of hidden units, as well as the embedding dimension D_E (section 5.4)

5) In Section 5.3, more details should be given on the data generating process for the synthetic data experiments. 

6) Some results in the appendix are very puzzling: around jumps in the price series, which are places where the volatility should spike, the model reacts instead by huge drops in the volatility (Figure 4(b) and (c), respectively around time steps 1300 and 1600). This should be explained and discussed.

All in all, I think that the paper provides a nice contribution to the art of volatility modelling. In spite of some flaws, it provides a starting point for the broader impact of neural time series processing in the financial community.

review_title: A relevant contribution to time series modelling with flexible nonlinear models

final_score: rating: null
review_content: Thank you for an interesting read.

Though I'm not very familiar with machine learning applications in Finance, I do notice that the GARCH method you were comparing with has been published around 30 years. Have you ever considered comparing with some recent machine learning methods for volatility, e.g. see the following paper which tested a Gaussian process?

https://papers.nips.cc/paper/5376-gaussian-process-volatility-model.pdf
review_title: comparison to recent methods

final_score: rating: 5: Marginally below acceptance threshold
review_content: 
The authors propose a recurrent neural network approach for constructing a
stochastic volatility model for financial time series. They introduce an
inference network based on a recurrent neural network that computes the
approximation to the posterior distribution for the latent variables given the
past data. This variational approximation is used to maximize the marginal
likelihood in order to learn the parameters of the model. The proposed method
is validated in experiments with synthetic and real-world time series, showing
to outperform parametric GARCH models and a Gaussian process volatility model.

Quality:

The method proposed seems technically correct, with the exception that in
equation (19) the inference model is doing filtering and not smoothing, in the
sense that the posterior for z_t' only depends on those other z_t and x_t
values with t<t', but in the true posterior p(Z|X) each z_t depends on all the
X. This means the proposed learning method is inefficient. The reference below
shows how to perform smoothing too and the results in that paper show indeed that
smoothing produces better results for learning the model.

Sequential Neural Models with Stochastic Layers Fraccaro, Marco and S\o nderby,
S\o ren Kaae and Paquet, Ulrich and Winther, Ole In NIPS 2016.

It is not clear if the method proposed in the above reference would perform better 
just because of using smoothing when learning the model parameters.

Clarity:

The paper is clearly written and easy to read.

For the results on real-world data, in Table 1, how is the NLL computed? Is the
average NLL across the 162 time series?

Originality:

The method proposed is not very original. Previous work has already used the
variational approach with the reparametrization trick to learn recurrent neural
networks with stochastic units (see the reference above). It seems that the main
contribution of the authors is to apply this type of techniques to the problem
of modeling financial time series.

Significance:

The results shown are significant, the method proposed by the authors
outperforms previous approaches. However, there is a huge amount of techniques
available for modeling financial time-series. The number of GARCH variants is
probably close to hundreds, each one claiming to be better than the others.
This makes difficult to quantify how important the results are.

review_title: Lack of smoothing for learning and lack of novelty

final_score: rating: 5: Marginally below acceptance threshold
review_content: Thank you for an interesting read.

I found the application of VRNN type generative model to financial data very promising. But since I don't have enough background knowledge to judge whether the performance gap is significant or not, I wouldn't recommend acceptance at this stage. 

To me, the biggest issue for this paper is that I'm not sure if the paper contains significant novelty. The RNN-VAE combination has been around for more than a year and this paper does not propose significant changes to it. Maybe this paper fits better to an application targeting conference, rather than ICLR. But I'm not exactly sure about ICLR's acceptance criteria, and maybe the committee actually prefer great performances and interesting applications?
review_title: An interesting application of RNN generative model to financial data

Meta-review: This paper presents an interesting application of variational methods for time series, in particular VRNN-like approaches, for stochastic volatility. Applications such as these are clearly in the scope of the conference, which was a point that one of the reviewer brought up. That said, questions of context, especially with regards to relation to different approaches, especially smoothing are relevant. Also, the number of methods GRACH and stochastic volatility is immense and this makes assessing the impact of this very hard to do and is more is needed to address this point. This paper is certainly interesting, but given these concerns, the paper is not yet rady for acceptance at the conference.
Decision: Reject