How to test a Time Series to be "Constant" over time?
I can think of:
1. No Trend (use linear regression and kernel regression)
2. No Seasonality (? Spectrum analysis with T = 2*pi / max(f(lambda)))
3. Random Noise (Ljung Box, Turning Points, Rank tests)
Please help me add more test to determine how can we get a p-value for the Null Hypothesis" Constant over time"
What exactlly do you mean by 'constant over time'? Do you want to test whether a given time series posses drift or its trend deterministic, against its values fluctuate around some specific value?
You probably mean test for stationarity of a time series (ie. mean and variance remain constant throughout time and autocovariances are also constant and do not depend on time).
You can use ADF, PP, KWSS tests in which you test for a series having a unit root (that is, being I(1) or non-stationary) against the alternative hypothesis that the series is stationary, with mean and variance reamining constant throughout time.
What exactlly do you mean by 'constant over time'? Do you want to test whether a given time series posses drift or its trend deterministic, against its values fluctuate around some specific value?
Maybe I should re-phrase this. How to test for Time Series Seasonality? Like in terms of a p-val?
You can use the Autocorrelation function (ACF):
https://coolstatsblog.com/2013/08/11/how-to-use-autocorreation-function-acf-to-determine-seasonality/
I understand that if I see a periodical structure on ACF plot then there's a seasonal component. but is there some sort of p-val that I can get for H0: Non-Seanonal Component?
Here you'll find description of different seasonality tests: https://ec.europa.eu/eurostat/sa-elearning/seasonality-tests
if you want to get the seasonal component out of the time series, i'd recommend a band-pass filer:
1)Baxter-King:
http://www.benoitmojon.com/pdf/Baxter-King.pdf
2)Christiano-Fitzgerald:
http://www3.econ.muni.cz/~hlousek/teaching/christiano_fitzgerald2003.pdf
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