Estimating the Probability That a Time-Series Peak or Trough Will Persist

Summary

The document frames a challenge in identifying local highs and lows at the end of a time series. A smoother can help estimate turning points within observed data, but an apparent endpoint peak or trough may disappear when new observations arrive. The author asks how to choose a smoothing method and bandwidth for the series and how to estimate the probability that a candidate turning point will remain valid as future observations arrive.

No estimator, smoothing rule, or probability model is proposed, and the document supplies no empirical examples or evidence. It is a research question rather than a worked method. Its central limitation is that the answer depends on assumptions about the data-generating process and future observations, which are left unspecified; the request also notes that several new samples might alter the candidate turning point.

Key ideas

• Turning points inside a series are easier to identify than those at its current endpoint.
• A new observation can invalidate an apparent peak or trough near the edge of the data.
• Smoother choice and bandwidth depend on the characteristics of the time series.
• The document asks for a probability model of turning-point persistence but does not provide one.

Tags

# Time series edge minmax probability


# Time series edge minmax probability












Not sure if someone had encountered this problem before: say given a time series, we need to determine the minmax. Usually we need to use some kernel smoother to extract second-derivative. It is easy to get minmax inside the series. But at the edge or end of the series, minmax is not deterministic because if newer abrupt sample come in to disrupt the trend then previous peak/trough would be changed. So I think this is a two-sided question:

- what smoother should be used, in particular smoother bandwidth, given the time series characteristics?

- How to determine the probability of the minmax from current available samples and one (or multiple) unknown incoming samples? Something like Prob(P_{minmax}|x_{t+1},x_{t},...x_{1}) and x_{t+1} is unknown incoming samples. Note that x_{t+1} could mean multiple new samples that disrupt previous minmax.

I don't think spline type of interpolation would help in the case. Not sure if I had described the issue clearly.

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