There are many approaches to do time series analyses, for example MTM. But the results are different. So I hope to know if there is a most effective or how to identify which method is effective.
Someone has told me that Zhaohua Wu achieved a very effective method in this problem. He is from Center for Ocean-Atmospheric Prediction Studies (COAPS), Florida State University. Unfortunately, I didn't find the paper.
What method is "most effective" depends on your ultimate objective and your priorities, and on the quality and quantity of your data. I would first consider smoothing with a running window that will remove seasonal variability and periods under 1 year. A box-car filter (equal weights to 12 consecutive months) would be the simplest, but it has end effects that are easily improved by tapering, such as would be provided by a cosine window or a Hanning window.
If a smoothing window is not adequate for your purposes, you'll have to specify why not in order to determine what would constitute an improvement.
If you intend to look at coherence or transfer functions, the smoothing is not even necessary. You can just ignore the information a frequencies about 1 cycle / year.
Good luck!
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