Testing Stock-Return Stability When the Selected ARMA Model Is White Noise

Summary

The document raises a methodological problem in testing whether stock returns are structurally stable over time. The proposed procedure fits an ARMA model to the full sample, estimates that model separately on two subsamples, and uses an F test to compare coefficients. In the example, model selection chooses an ARMA(0,0), leaving no dynamic coefficients to compare.

This is posed as an open question: the document does not provide a test, an alternative stability measure, or empirical evidence. Its useful point is that a coefficient-comparison procedure depends on having estimated coefficients in the first place, so a white-noise specification makes that particular comparison unavailable. The discussion is limited to the question and does not address stability in other features of returns, such as variance, distribution, or dependence across assets.

Key ideas

• The proposed stability check compares ARMA coefficients estimated on two subsamples.
• An ARMA(0,0) specification has no autoregressive or moving-average coefficients to compare.
• The document identifies a limitation in this particular coefficient-based test.
• It does not offer an alternative test or present empirical results.

Tags

# Inter-temporal structural stability of stock markets


# Inter-temporal structural stability of stock markets












For my bachelor thesis I am trying to determine structural stability of some stock market in the following way:

- Identify an ARMA model for the whole sample

- Split the sample in two parts, and estimate the ARMA model of step one on both sub samples.

- Use the F test to determine whether the coefficients in the first sub sample differ from the second.

If they do then the markets are not stable.

But here is my problem. The best ARMA model is a (0,0) model. So there are no coefficient to compare with the F test. As far as I know, this makes this method unusable. Is this correct, and if so, is there another way to test stability of returns?

Thank you!

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