The final step in the FSSA algorithm is reconstruction of the functional singular spectrum analysis (fssa) objects into additive functional time series (fts) objects that capture different pieces of information of the original fts object. We then look at fts plots to analyze the data further.
We reconstruct for the univariate call center example using the following.
gr <- list(1,2:3,4:5,6:7,8:20)
Q <- freconstruct(U, gr)We can use suitable fts plots to view each reconstruction separately and obtain information about the orignal fts object.
Here we see the general trend of call center data which shows that early in the day, few calls come in but as the day goes on more comes in then as evening approaches, the number of calls to the center drops.
plot(Q[[1]],type="3Dsurface",ylab = " ", xlab = "Intraday intervals")Visualization of the fts objects that capture periodicity is best done using line plots for this specific example.
plot(Q[[2]], main="Line Plot of the Second Reconstruction",xlab = "Intraday Intervals",ylab = "Sqrt of Callcenter", type='line')plot(Q[[3]], main="Line Plot of the Third Reconstruction",xlab = "Intraday Intervals",ylab = "Sqrt of Callcenter", type='line')plot(Q[[4]], main="Line Plot of the Fourth Reconstruction",xlab = "Intraday Intervals",ylab = "Sqrt of Callcenter", type='line')plot(Q[[5]], main="Line Plot of Fifth Reconstruction (Noise)",xlab = "Intraday Intervals",ylab = "Sqrt of Callcenter", type='line')We see that the first reconstruction clearly captures trend information of how the number of calls to the center is small in the early hours of a day, then increases in the afternoon, and drops in the evening. We also clearly see the periodic behavior in the fts object where we see the different types of call center behavior reflected in the seven different curves of the periodic reconstructions representative of the seven days of a week.