I am currently investigating environmental time series and algorithms to determine when an 'unexpected' event/reading has occured in the series. I am currently constructing the gaussian probability density function (pdf) based on historical readings and checking if 'new' readings are acceptable according to a threshold in the pdf. As time goes by the pdf threshold becomes too large. Also, my time series contains daily and seasonal components.

I have received advice to use spectral analysis (using an FFT) on new month's data to compute the new month's periodicities. I have done so and now am faced with the question of how and what to do with the periodic frequencies in order to help determine what/when an unexpected reading is (according to the distribution).

I was thinking that perhaps it is possible to update a time series' pdf according to it's fourier transform?

Could some one guide on this.

Thanks,

Wess