Finding periodicity of trajectory time series in python

Question

I am doing a time series analysis and I am trying to find the periodicity of my time-series. I have done the following code and found the graphs (see attached):

    # Periodicity of the two trajectories
from statsmodels import api as sm
# convert dataframe to array
np_df= np.asarray(df['Combined'], dtype=float)
# remove mean to create signal oscillating around 0
np_df= np_df- np.mean(np_df)
#get the autocorrelation coefficient
acf= sm.tsa.acf(np_df, nlags=len(np_df))

plt.figure(figsize = (10, 8))
lag = np.arange(len(np_df)) / 2. / 24.
plt.plot(lag, acf)
plt.xlim((0, 120))
plt.xlabel('Lags (days)')
plt.ylabel('Autocorrelation')

plt.figure(figsize = (10, 8))
plt.plot(lag, acf)
plt.xlim((0, 22))
plt.xlabel('Lags (days)')
plt.ylabel('Autocorrelation')

Using fft pack to find periodicity

from scipy import fftpack
ft_df= fftpack.fft(np_df, axis=0)
freq= fftpack.fftfreq(np_df.shape[0], time[1]-time[0])
periods= 1/freq
plt.figure()
plt.plot(periods, abs(ft_df)*1e-3, 'o')
plt.xlim(0,22)
plt.xlabel('Period')
plt.ylabel('Power ($cdot10^3$)')
plt.show()

My question is i think the periodicity, from what i can interpret is 1 and maybe 2.5? Am I correct in my method and interpretation?

Thanks in advance!

Answer 1

I'm no pro at signal analysis, so take this with a grain of salt...

Your autocorrelation shows that 15 lags (ish) is your highly correlated. So that would be your best estimate. That said, either a signal is or is not periodic. If it is periodic, I'd expect to see a 1.0 autocorrelation at some lag, not 0.85 or such. Perhaps there is some noise or something.

I'm not quite sure what your are doing with the fftfreq, perhaps somebody else could lend a hand there.