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I am given a time series data. I read that there are several types of such a data, namely, Random Walk, Moving Averages and the White Noise. This I discovered here.
Before doing any analysis, should I first to determine the type of time series or is it sufficient to check for (weak) stationarity?
At the end, I have to do spectral analysis.
I dont know much about spectral analysis, but judging from this source (https://www.stat.ncsu.edu/people/bloomfield/courses/st730/slides/sns-04-2.pdf) you can derive the spectral density function by figuring out what type of data generating process could underlie your time series. To explore this, just testing for stationarity is insufficient. For example, both an AR(1) with coefficient lower than 1 in absolute terms and a white noise process are (weakly) stationary processes. However, their autocorrelation structure differs.
I would advise you to inspect the autocorrelation functions and partial autocorrelation functions to determine what kind of arima(p,i,q) fits your time series best. Here is a link to a nice post that explores this topic more indepth Estimate ARMA coefficients through ACF and PACF inspection. Without additional information of your time series it is impossible for us to determine what kind of process might have generated it.
