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I have quote observations for 9 FX rates, which I would like to analyze via multivariate dynamic linear model (e.g., Chapter 16 in West and Harrison Bayesian Forecasting and Dynamic Models (1997).

In general, missing observations in a multivariate series can be handled like any other parameter in a Bayesian analysis: estimate both parameters and missing data given observed data and an inclusion indicator (e.g., Chapter 18 in Gelman et al. Bayesian Data Analysis (2013).

But the above multivariate time series is extremely sparse (i.e., largely asynchronous): 97.7% of timestamps have only 1 variable (of a possible 9) observed, and another 2.1% of timestamps have only 2 variables observed. In no cases do I have more than 7 variables observed at the same time.

Question: Given the almost complete lack of synchronization in my data set, what options do I have to perform a multivariate analysis on this data set?

What have I tried

  1. Synchronize the quotes by time aggregates (e.g., statistical summaries per second/minute);
  2. Rely on the missing data model to work despite having almost no multivariate observations in the series.
  3. The paper Peluso et al A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns (2015) solves the same problem on a similarly asynchronous data set (~67-96% missing observations per timestamp), but seems to use a non-sequential Monte Carlo algorithm to do so. I'm keenly interested in a sequential approach given a) a lack of computing power at my disposal and the desire to run on a longer period than the above paper (e.g., 20 years vs. 11 months) and b) the desire to run the algorithm online vs. offline.
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  • $\begingroup$ Could you give (more) complete references to the sources you cite? $\endgroup$ Commented Jul 25, 2022 at 16:55
  • $\begingroup$ Added links to both. Gelman is downloadable for non-commercial use. $\endgroup$
    – MikeRand
    Commented Jul 26, 2022 at 2:44

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