How do you approach the challenge of spectral density estimation in time series?
Instruction: Describe the methodologies for estimating spectral density in a time series and discuss their applications.
Updated
Example Answer
Spectral density describes how a process's variation is distributed across frequencies. I would first check the sampling interval, missing observations, trend, and whether a full-record spectrum is appropriate for the question.
A periodogram is a useful starting point, but it can be noisy. Welch's method averages windowed periodograms from segments to reduce variability, with a tradeoff in frequency resolution. For a regularly sampled machine sensor, I would set the sampling frequency so peaks have meaningful units and compare segment lengths that can resolve the expected cycle. I would also check tapering and edge effects. A spectral peak suggests a periodic component; it does not establish its cause or guarantee a useful forecast.
Make it your own
Name the sampling interval, expected cycle, and the resolution you need.
Why this works
It connects method settings to the phenomenon being measured.
Follow-up to practice
What happens to frequency resolution with shorter segments?