This paper presents a method to autonomously find periodicities in a signal. It is based on the same idea of using Fourier Transform and autocorrelation function presented in Vlachos et al. 2005. While showing interesting results this method does not perform well on noisy signals or signals with multiple periodicities. Thus, our method adds several new extra steps (hints clustering, filtering and detrending) to fix these issues. Experimental results show that the proposed method outperforms the state of the art algorithms. A time series is defined by its 3 main components : the trend component, the periodic component and the random component. Trend analysis and prediction are topics that have been greatly studied BID10 and will not be treated in the article, therefore every time series will be assumed stationary regarding its mean and variance, so this study focus the periodic component. The ability to detect and find the main characteristic of this component is not as easy as the trend component. Yet, the ability to detect periodicities in a time series is essential to make precise forecasts.A periodicity is a pattern in a time series that occurs at regular time intervals. More precisely, the time series is said cyclical, if the time intervals at which the pattern repeats itself can't be precisely defined and is not constant. On the opposite, there are seasonal time series in which the pattern repeats itself at constant and well defined time intervals. Thus, cyclical patterns are more difficult to detect due to their inconsistency and the fact that they usually repeat themselves over large periods of time and therefore require more data to be identified. Nevertheless, seasonal patterns are very common in time series such as those related to human behaviour which usually have periodicities like hours and calendar (time of day, day of week, month of year). This kind of feature is well known and can be easily tested to see if they are beneficial or not. Unfortunately, when it comes to time series related to other phenomenons, the periodicities are not trivially found. For instance, tides level are multi-periodic time series correlated to both moon cycles and sun cycles; and females menstrual cycles are related to hormonal changes. The ability to detect periodicity in time series is fundamental when it comes to forecasting BID5 . Once a periodic pattern has been detected, numerous techniques can be used to model this later and improve forecasts BID1 . However, periodicities detection is not easy and has been greatly studied in the existing literature, but most of current techniques are unable to detect periodicities without the need of preprocessing data BID12 or have trouble detecting multiple periodicities BID11 . This paper is organised as follow: we first present the Fourier transform and the Autoperiod algorithm BID11 used to detect periodicities in a signal. Then we propose a new fully automated method, named Clustered Filtered Detrended Autoperiod (CFD-Autoperiod), which also combines the advantages of frequency domain and time domain while being robust to noise and able to handle multi periodicities. Noise robustness is achieved using a density clustering on hints provided by the frequency analysis. Multi-periodicities are more precisely detected by both using detrending and filtering. Finally, we demonstrate that CFD-Autoperiod outperforms previous methods.
This paper presents a method to autonomously find multiple periodicities in a signal, using FFT and ACF and add three news steps (clustering/filtering/detrending)
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