How to test whether a signal is periodic or not?

[stevenphy2]

Hi all, let's say I have generated some discrete data as a function of time.
And when I plot it, it looks like that it is periodic.
Is there any scientific way to check whether or not the discrete data is really periodic?
And determine the period, if possible?
Many thanks.

 

[EnumaElish]

You could define the statistical regression model y = b0 + b1 x + u and then introduce quarterly, monthly, weekly, etc. "dummy variables" into the model. For example, quarterly periodicity will be indicated if the quarterly dummies are significant as a group.

 

[JSuarez]

The best (and standard) way to test for periodic components is by using spectral analysis. If you are using a statistics/numerics package (like Statistica, Matlab, etc.), then check their tools (FFT, smoothing windows, etc.) for that.

 

[EnumaElish]

stevenphy2, see http://www.statoek.vwl.uni-mainz.de/Bilder_allgemein/AP_Nr._45_.pdf, maybe also http://forums.eviews.com/viewtopic.php?f=5&t=843 (S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 are the monthly dummies).

 

[pmacias]

There are several methods that can be used to test whether a signal is periodic or not. One approach is to use Fourier analysis, which involves transforming the signal into its frequency domain and looking for specific patterns in the frequency spectrum that indicate periodicity. Another method is to use autocorrelation, which involves comparing the signal with a delayed version of itself to see if there is a repeating pattern. Additionally, you can also visually inspect the signal and look for any regular patterns or repetitions. If the signal is found to be periodic, the period can be determined by measuring the time between each repeated pattern. It is important to note that these methods may not always provide a definitive answer, and it is always best to consult with a statistician or expert in signal analysis for a more accurate assessment.

 

[CellCoree]

Yes, there are scientific methods to test whether a signal is periodic or not. One way is to use Fourier analysis, which decomposes a signal into its component frequencies. A periodic signal will have a dominant frequency and its harmonics, while a non-periodic signal will have a more random frequency distribution. The period of a periodic signal can also be determined using Fourier analysis by identifying the frequency at which the signal repeats.

Another method is to use autocorrelation, which measures the similarity of a signal with itself at different time lags. A periodic signal will have a high autocorrelation at the period of the signal, while a non-periodic signal will have a low autocorrelation at any lag.

Additionally, you can use statistical tests such as the chi-square test or the Kolmogorov-Smirnov test to determine the significance of the periodicity in your data.

It is important to note that these methods may not work for all types of signals and may require some preprocessing or data cleaning. It is always best to consult with a statistician or expert in signal analysis to determine the most appropriate method for your specific data.