Confidence Intervals for Moving Averages with Dependent Observations

Summary

The document asks how to form a confidence interval for a set of long-window moving averages when adjacent values are dependent. The questioner is unsure whether a simple standard deviation based interval is appropriate, given the overlap among observations, and asks for statistical references and software guidance.

One response distinguishes a manually calculated moving average from fitting a moving-average time-series model, and points toward using a model-based prediction interval. Another response refers to a paper but provides only an excerpted pointer in the available text. No confidence-interval procedure, assumptions, or worked example is actually given, so the exchange raises the dependence issue without resolving it. The model-based suggestion concerns prediction intervals and may not directly answer the question about an interval across plotted moving-average values.

Key ideas

• Overlapping moving-average observations are dependent, which complicates interval estimation.
• A response suggests considering a fitted moving-average time-series model and its prediction interval.
• The supplied exchange does not provide a complete confidence-interval method or worked example.
• A prediction interval for a model is not necessarily the same quantity as an interval across plotted moving-average values.

Tags

# How to Calculate Confidence Intervals for Moving Averages Given Nonindependence?


# How to Calculate Confidence Intervals for Moving Averages Given Nonindependence?












I've plotted 30-year moving averages across time for a couple of portfolios, and I was wondering how to calculate a 95% CI for the these moving average data (i.e., across all moving average data points, what is the CI?).

Given the points are clearly not independent of one another, I would think just using ±1.96 SD would be incorrect (as this nonindependence would be a violation of the central limit theorem), but I could be wrong and am not sure how this is done. Any links, book references, and recommended R packages/functions are also appreciated. Thank you!

## Answer by James (score 1)

https://quant.stackexchange.com/a/14719

If you calculated MA by hand without actually fitting a MA(q) time series model, then you are out of luck. I suggest you use R, like in this example that shows how to construct a prediction interval, among other things.

## Answer by Hamid (score 1)

https://quant.stackexchange.com/a/30800

Maybe this paper is helpfull http://www.wiley.com/legacy/wileychi/marketmodels/chapter5.pdf

in page 8 we have

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