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Scaling Returns Correctly When Comparing Stochastic Volatility Models

Article Quant Q&A · Author: user22108
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Summary

The document describes a comparison of log-volatility series from a standard stochastic volatility model and a moving average stochastic volatility model. The questioner initially interprets a graph as suggesting that the standard model understates volatility when volatility is low, but is unsure whether the visual difference reflects model behavior.

The reported resolution is that the input return series had been transformed using a factor of 400 applied to log price changes. Removing that scale factor materially changed the comparison, and the plotted series then appeared to overlap. This illustrates that data units and preprocessing can affect estimated or displayed volatility and should be checked before drawing conclusions from a model comparison. The source offers only the author's account of the correction and a visual observation; it provides no model diagnostics, statistical tests, or general evidence that either specification is superior.

Key ideas

  • The example compares standard and moving average stochastic volatility specifications.
  • The input returns were defined as scaled log price changes, with a factor of 400.
  • Ignoring a scaling factor can change the apparent comparison of volatility estimates.
  • A graph alone does not establish that one volatility model systematically understates volatility.

Tags

VolatilityStatisticsEquities
Full text
# Standard Stochastic Volatility Models VS Moving Average Stochastic Volatility Model


# Standard Stochastic Volatility Models VS Moving Average Stochastic Volatility Model












Hi... I am comparing the log-volatility of two SV models with an application to MATLAB. Since I am a rookie in this field, I do not know if I am wrong in interpreting the graph. In my opinion the only thing I can say is that the standard SV model underestimate the volatility in the volatility is small but I am not sure of my graph. Have you ever seen something like that? Am I completely wrong?

Here the references for the models: for the SV-MA model see: Chan, J.C.C. (2013). Moving Average Stochastic Volatility Models with Application to Inflation Forecast, Journal of Econometric, 176 (2), 162-172.

and for the standard model see: Chan, J.C.C. and Hsiao, C.Y.L (2014). Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence. In: I. Jeliazkov and X.S. Yang (Eds.),Bayesian Inference in the Social Sciences, 159-180, John Wiley & Sons, New York.

## Answer by user22108 (score 3, accepted)

https://quant.stackexchange.com/a/27631

Finally I have found the answer on my own. The problem was related to the trasformation of the dataset. The original code used: ${{y}_{t}}=400*(\log ({{P}_{t}})-\log ({{P}_{t-1}}))$ as dataset. Initially I did not care about multipling by 400 because I thought it was usless. Instead it makes a big difference. Now the two series are completely overlapped, I think it depends on how MATLAB manages the figures in the spreadsheet.

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.