sPLS-DA to discriminate time series

The main goal of this research is to propose a methodology for classifying time series. Two approaches were used in this methodology: (A1) methods based on the parameters from models, and (A2) methods based on the features of time series. Approach A2 was used in method 1 (M1) and both approaches A1 and A2 were used in methods 2 and 3 (M2 and M3). (M1) Features based on functions such as spectral density, sample Auto Correlation Function (Sample ACF), sample Partial Auto Correlation Function (Sample PACF) and rolling ranges, (M2) Estimates of parameters and features based on a Seasonal Autoregressive Integrated Moving Average (Seasonal ARIMA) model with a Threshold Generalized Autoregressive Conditional Heteroskedastic (TGARCH) model and a Student distribution for residuals (Seasonal ARIMA-TGARCH-Student) and (M3) Estimates of parameters and features based on a Additive Seasonal Holt-Winters prediction function (Additive SH-W). For M2 and M3: Firstly, estimates of the parameters of models were calculated. Secondly, features of residuals from the models, such as the maximum of the spectral density and mean of the values of Sample PACF were computed. The Sparse Partial Least Squares Discriminant Analysis (sPLS-DA) was used to identify groups of time series using the classification variables (features or parameter estimates) from the three methods. The centroid distance and the Balanced classification Error Rate (BER) were used to apply the sPLS-DA. The methodology is described using time series data from a study carried out in the Metropolitan Cathedral of Valencia in 2008 and 2010. The time series data corresponds to the time series of relative humidity from sensors positioned at different points of the apse (positions: cornice or ribs RC, walls W and frescoes F) in the Cathedral in 2008 and 2010. The sensors were monitored with the goal of assisting conservation of the renaissance frescoes in the Cathedral. The classification variables in our study were calculated separately for various seasons of the year (winter, spring and summer) for both 2008 and 2010. For methods 1,2 and 3 in 2008 and M1 and M3 in 2010, the first component from sPLS-DA showed that the time series that are situated in the RC and W positions were classified according to their location. Also, for M1 (2010) the time series in RC, F and W were classified according to their positions. The methodology proposed in this research would be appropriate when there are no major differences between the time series of different groups, and when, according to the characteristics and context of the problem, it is possible to indicate the class of the time series.