How to determine multiple Periodicities present in Timeseries data?

user_14485257 0
Viewed 200

My objective is to detect all kinds of seasonalities and their time periods that are present in a timeseries waveform.

I'm currently using the following dataset: https://www.kaggle.com/rakannimer/air-passengers

At the moment, I've tried the following approaches:

1) Use of FFT:

import pandas as pd
import numpy as np
from statsmodels.tsa.seasonal import seasonal_decompose
 
#https://www.kaggle.com/rakannimer/air-passengers
df=pd.read_csv('AirPassengers.csv')
 
df.head()

frequency_eval_max = 100
A_signal_rfft = scipy.fft.rfft(df['#Passengers'], n=frequency_eval_max)
n = np.shape(A_signal_rfft)[0] # np.size(t)
frequencies_rel = len(A_signal_fft)/frequency_eval_max * np.linspace(0,1,int(n))

fig=plt.figure(3, figsize=(15,6))
plt.clf()
plt.plot(frequencies_rel, np.abs(A_signal_rfft), lw=1.0, c='paleturquoise')
plt.stem(frequencies_rel, np.abs(A_signal_rfft))
plt.xlabel("frequency")
plt.ylabel("amplitude")

This results in the following plot: enter image description here

But it doesn't result in anything conclusive or comprehensible.

Ideally I wish to see the peaks representing daily, weekly, monthly and yearly seasonality.

Could anyone point out what am I doing wrong?

2) Autocorrelation:

from pandas.plotting import autocorrelation_plot
plt.rcParams.update({'figure.figsize':(10,6), 'figure.dpi':120})
autocorrelation_plot(df['#Passengers'].tolist())

After doing which I get a plot like the following: enter image description here

But how do I read this plot and how can I derive the presence of the various seasonalities and their periods from this?

3) SLT Decomposition Algorithm

df.set_index('Month',inplace=True)
df.index=pd.to_datetime(df.index)
#drop null values
df.dropna(inplace=True)
df.plot()

result=seasonal_decompose(df['#Passengers'], model='multiplicable', period=12)

result.seasonal.plot()

This gives the following plot: enter image description here

But here I can only see one kind of seasonality.

So how do we detect all the types of seasonalities and their time periods that are present using this method?

Hence, I've tried 3 different approaches but they seem either erroneous or incomplete.

Could anyone please help me out with the most effective approach (even apart from the ones I've tried) to detect all kinds of seasonalities and their time periods for any given timeseries data?

autocorrelation time-series scipy fft python
2 Answers

I still think a Fourier analysis is the way to go, its just that the 0-frequency result is shadowing any insight.

This is essentially the square of the average of your data set, and all records are positive, far from the typical sinusoidal function you would analyze with Fourier Transforms. So simply subtract the average of your dataset to your dataset before doing the FFT and see how it looks. This would also help with the autocorrelation technique.

Also, you MUST give units to your frequency values. Do not settle for the raw values from the FFT. Those are related to the sampling frequency and span of your dataset. Reason about it and adequately label the daily, weekly, monthly and anual frequencies in your chart.

user_117152590

using FFT, you can get the fundamental frequency. you can then use a low-pass filter or just manually select the first n frequencies. these frequencies will correspond to the 'seasonalities'. transform your filtered FFT into time domain and you can visualize the most basic underlying repetitions, you can easily calculate the time period of those repetitions and visualize it by individually plotting the F0,F1,... in time domain.

user_115530660
Related