A periodogram-based metric for time series classification

Clustering heteroskedastic time series by model-based procedures

“…The topic of classification of time series has recently received a lot of contributions, in particular in time series data mining (see, for example, Agrawal et al, 1994), computer science (Gray and Markel, 1976), economic time series (Caiado et al, 2006). Liao (2005) provides an extensive review of studies in clustering and discrimination of time series.…”

Classification of Time-Series Data Based on Several Lag Windows

“…Using simulation, they compared the raw-periodogram based metrics with the ones proposed by Piccolo (1990) and the ones based on coefficients of autocorrelation, partial autocorrelation, and inverse autocorrelation. Caiado et al (2006) shows that a metric based on the logarithm of the normalized periodogram and a metric based on autocorrelation coefficients distinguish autoregressive movingaverage(ARMA) models from ARIMA models with high success rate while neither the Euclidean metric nor the metric by Piccolo (1990) perform very well.…”

“…Bohte et al (1980) and Kovačić (1996) considered distance metrics based on autocorrelation and cross-correlation structures of the compared time series. Caiado et al (2006) proposed new metrics based on the raw periodogram Fourier-transformed from autocovariance functions. Using simulation, they compared the raw-periodogram based metrics with the ones proposed by Piccolo (1990) and the ones based on coefficients of autocorrelation, partial autocorrelation, and inverse autocorrelation.…”

“…We evaluate the performance under various simulation scenarios. Simulation results reveal that the metrics used in this study split the time series into the preassigned clusters better than do the raw-periodogram based ones proposed by Caiado et al (2006). Our metrics are applied to an economic time-series dataset.…”

Measuring the Distance between Sets of ARMA Models

“…We limit ourselves to mentioning some applications: clustering time series data (see [1,2]), data mining problems (see [3]), time series classification (see [4]), selecting between direct and indirect model-based seasonal adjustment (see [5]), the analysis of Granger causality (see [6]), comparing autocorrelation structures of multiple time series (see [7]). …”