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Discrete-Time Models for Stock and Currency Markets

Article Quant Q&A · Author: SBF
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Summary

The document asks which discrete-time models can describe stock prices beyond GARCH and whether the same approaches apply to currency markets. The replies point to models with autoregressive structure, including the ARCH family, as candidates for both asset classes. They also mention dynamic linear models and standard time-series models such as ARMA, VAR, and VEC.

The document gives suggestions rather than a worked comparison or empirical evidence. It notes that currency markets may commonly exhibit autoregressive behavior, but offers no data, specifications, or guidance for choosing among models. The suggestions are therefore starting points for further study, not a conclusion that one model best fits both stocks and currencies; market speed alone is not used to establish a distinct model requirement.

Key ideas

  • Autoregressive models, including ARCH-family approaches, are suggested for both stocks and currencies.
  • Dynamic linear models are raised as another possible discrete-time framework.
  • ARMA, VAR, and VEC are named as additional financial time-series models.
  • The replies provide reading suggestions but no empirical model comparison or selection criteria.

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StatisticsVolatilityForex
Full text
# Discrete-time model: stock dynamics


# Discrete-time model: stock dynamics












I am working in the area of probability theory and for a case study I would like to make some calculations in finance. Since I am developing theory for the discrete time, I am interested in models for the stock price in the discrete time. As I remember GARCH is a good one. Could you advise me something else?

It will be nice if you can tell me which model also can be used for the currency markets (since they are quite faster than the stock markets I think there should another relevant models).

## Answer by glyphard (score 3, accepted)

https://quant.stackexchange.com/a/763

This link is to a book that covers this exact question: http://onlinelibrary.wiley.com/doi/10.1002/9783527610006.ch9/summary

Summary: the models that map to both stock markets and currency markets are those that have an autoregressive feature (curreny markets commonly exhibit this feature, limiting the choice of models that apply to both currencies and stocks => *ARCH).

## Answer by Richard Herron (score 2)

https://quant.stackexchange.com/a/752

Have you considered Dynamic Liner Models? I don't know enough about currencies or DLMs to give any more guidance, but it may be worth a few minutes of googling to see if you can apply it.

## Answer by Renoir Vieira (score 0)

https://quant.stackexchange.com/a/644

ARMA, VAR, VEC. Please, check this out. http://www.amazon.com/Analysis-Financial-Time-Ruey-Tsay/dp/0471415448

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.