Correlation Analysis in Curve Registration of Time Series

Time series data is an important object of data mining. In analysis of time series, misjudgment of correlation will occur if time lags are not considered. Therefore, there exists mutual restraint between correlation and time lags in time series. Based on the exploration of correlation and simultaneousness of time series, the correlation identification and curve registration methods for double sequences are given in this paper. Concretely, the study investigates the reasons and characteristics of two types of errors in correlation analysis in the view of time warping, and then deduces the correlation coefficient's bounds in a certain significance level by its asymptotic distribution. Further, a correlation identification method based on time-lag series is proposed. Finally, the curve registration model of maximizing the correlation coefficient is presented with a broader application than AISE. Smoothing-generalized expectation maximization(S-GEM) algorithm is used to solve the time warping function of the new model. The experimental results on simulated and real data demonstrate that the proposed correlation identification approach is more effective than 3 correlation coefficients and Granger causality test in recognition of spurious regression. The registration method provided is obviously performed better than the classicalcontinuous monotone registration method(CMRM), Self-modeling registration(SMR) and maximum likelihood registration(MLR) in most situations. Linear correlation of double series and functional curve registration are considered here, and the results can provide the theoretical basis for correlation identification and time alignment in regression and reference direction for correlation analysis and curves registration of multiple series.

[1]  T. Gasser,et al.  Alignment of curves by dynamic time warping , 1997 .

[2]  Peter C. B. Phillips,et al.  New Tools for Understanding Spurious Regressions , 1998 .

[3]  Giada Adelfio,et al.  Simultaneous seismic wave clustering and registration , 2012, Comput. Geosci..

[4]  Bernard W. Silverman,et al.  Incorporating parametric effects into functional principal components analysis , 1995 .

[5]  T. Gasser,et al.  Statistical Tools to Analyze Data Representing a Sample of Curves , 1992 .

[6]  Birgitte B. Rønn,et al.  Nonparametric maximum likelihood estimation for shifted curves , 2001 .

[7]  Wang Jian-dong,et al.  Distance Metric Learning Based on Side Information Autogeneration for Time Series , 2013 .

[8]  Eamonn J. Keogh,et al.  Time series shapelets: a new primitive for data mining , 2009, KDD.

[9]  J. Ramsay,et al.  Curve registration by local regression , 2000 .

[10]  Theo Gasser,et al.  Asymptotic and bootstrap confidence bounds for the structural average of curves , 1998 .

[11]  T. Gasser,et al.  Synchronizing sample curves nonparametrically , 1999 .

[12]  H. Müller,et al.  Functional Convex Averaging and Synchronization for Time-Warped Random Curves , 2004 .

[13]  Lin Ziyu,et al.  A New Algorithm on Lagged Correlation Analysis Between Time Series: TPFP , 2012 .

[14]  Daniel Gervini,et al.  Nonparametric maximum likelihood estimation of the structural mean of a sample of curves , 2005 .

[15]  Hao Jin,et al.  Computational Statistics and Data Analysis the Spurious Regression of Ar(p) Infinite-variance Sequence in the Presence of Structural Breaks , 2022 .

[16]  C. Granger,et al.  Spurious regressions in econometrics , 1974 .

[17]  Philip S. Yu,et al.  Applying data mining in investigating money laundering crimes , 2003, KDD '03.

[18]  Xueli Liu,et al.  Simultaneous curve registration and clustering for functional data , 2009, Comput. Stat. Data Anal..

[19]  Gareth M. James.  Curve alignment by moments , 2007, 0712.1425.

[20]  T. Gasser,et al.  Self‐modelling warping functions , 2004 .