A Rearch On Periodicty Of Time Series Data

Periodic phenomenon, which is a repeating pattern over time, is common in dailylife and scientific research. Time series data which captures the evolution of data valueover time actually is a reality of a certain stochastic process. Along with thedevelopment of computer technology, a lot of time series data has been accumulated,especially the large data sets where periodicity widely exists. Considering thecomplexity of the real phenomenon and uncontrollable factors interference, periodicphenomenon in data is also complex. More and more researchers begin to pay attentionon it. In some researches, the periodicity itself is the research object. In the traditionaltime series analysis, only stationery time series can be modeled in classic way. Thus,discovering and eliminating the periodicity is an important problem of time seriespretreatment. Therefore, how to analyze the time series of the periodic components andhow to define the time sequence of periodic components are interesting problems in thetime series data analysis.First of all, a classification of periodicity was given to clarify the problem. Definethe periodicity in time series, and proposed the main problems to work on. The first aimis to discover the rate of the periodicity. To face the challenge, a lot of work has beendone:1. Based on spectrum analysis of time series, a classic method called periodogramcan discover the hidden periodicity. We present the advantages and disadvantages of themethod by numerical examples.2. Considering that time series is said to be periodic if it can be divided intoequal-length segment which is almost similar, the way to detect the periodicity isthrough measuring the similarity of two time series. We research the popular way tocalculate similarity, and proposed a way to improve it.3. Static distance, especially Euclidean distance, is the most basic and commonway to define similarity which is very sensitive to noise. We propose a new way basedon symbolic representation of the original time series. To transform a real valued data toa symbolic sequence: firstly, a piecewise linear cumulative approximation (PAA) method is used to reduce the dimension of data, secondly, based on the SAX technique,we improve it by adding dynamic characteristics to the new symbolic sequence. By thatway, the object becomes simpler than before and main characters are reserved. The newalgorithm of periodicity detection follows the idea of shifting and comparing the timeseries for all possible values. Real data experiment illustrates the operability, andsimulated data experiment proves the accuracy.The research provides an effective way of discovering the rate of periodicity intime series which can analysis the data in deferent distinguishability and confidencecoefficient.