I am new here, so my apologies if I am breaking any rules with this post (please let me know).

I would like to perform spectral and wavelet analysis (in R) on a climate-proxy time series to identify dominant periodicities. Being relatively new to this field, I’m aiming to construct a clear workflow for my methodology, which includes preprocessing, data analysis, and interpretation.

I found many workflows for time series forecasting but not for spectral and wavelet analysis.

Here is my current workflow based on my understanding:

1- Data acquisition

2- Preprocessing

2.1 Data cleaning (deal with missing values and outliers)
2.2 Creating a time series (I am working in R so that means using functions like ts or zoo)
2.3 Visual inspection
2.4 Exploratory data analysis (histograms, boxplot and the like)
2.5 Testing Stationarity (ADF or KPSS tests)
2.6 Spacing (use interpolation if spacing us uneven)
2.7 Detrending or differencing (depending on whether the trend is deterministic or stochastic)
2.8 Smoothing (not sure if it is advisable to analyze a smoothed time series)

3- Spectral analysis

3.1 Choosing a proper method (based on the time series and method assumptions)
3.2 Perform spectral analysis
3.3 Perform Red Fit (AR1) to identify significant spectral peaks
3.4 Interpretation of results

4- Wavelet analysis

4.1 Choosing a proper method
4.2 Perform wavelet analysis
4.3 Interpretation of results

I would very much appreciate any comments and/or suggestions on my workflow.

Thanks!