How do you interpret and utilize the output of a wavelet transform in analyzing time series data?
Instruction: Explain the process and application of wavelet transforms in time series analysis, including how to interpret its output for practical analysis.
Updated
Example Answer
I would begin by checking which transform was used. A continuous wavelet transform gives coefficients indexed by time and scale from comparison with a selected wavelet, not scaled copies of the observed signal itself. The mapping from scale to physical frequency depends on the wavelet and sampling interval.
I would plot coefficient magnitude or power with clearly labeled axes, then examine localized features against the original series. For sensor monitoring, a brief region of high power might be worth investigating alongside operating records. Edge effects, missing data, and wavelet settings can create misleading patterns, so I would check their influence before interpreting a feature. A scalogram can help localize activity; it does not prove its cause or make a forecasting method validated.
Make it your own
Name the transform, wavelet, sampling interval, and feature you would investigate.
Why this works
It connects coefficients to an interpretable time and scale.
Follow-up to practice
How would you check whether a feature is an edge artifact?