## 4 Discussion

Table 1: Summary of computational time for training each model and Pearson correlation coefficient for validating EEG prediction using the detrended cross-correlation function and ridge regression. The notations of **, *, and n.s (not significant) denote \(p<0.01\), \(p<0.05\), and \(p>0.05\), respectively. of similarity in the TRFs generated by the detrended cross-correlation function and ridge regression, the influence of trial duration should also be considered. Therefore, this study was extended to analyze a publicly available dataset featuring longer EEG trials in response to natural narrative speech in this section [37]. The open dataset is briefly summarized as follows. The 128-channel EEG data in response to narrative speech were recorded from 17 subjects, and the EEG data were segmented to have a duration of 10 and 60 s. The performance of the detrended cross-correlation function to generate long-speech TRFs was evaluated. The detrended cross-correlation function generated TRFs comparable to those generated by ridge regression, with an averaged correlation coefficient across 128 channels of 0.91 as seen in Figure 5. Moreover, although there was no difference in reconstructing EEG data, the computation of the detrended cross-correlation function was more efficient. These results indicated that the detrended cross-correlation can also effectively and comparably capture neural responses to long continuous speech. Recently, SI methods have been applied to investigate the neural source dynamics in response to continuous stimuli [38; 39] and the neural response to the temporal fine structure of continuous stimuli [40]. However, the computational demands of these methods increase due to the significant large quantity of cortices at the source level or the necessity of a high sampling rate for temporal fine structure analysis. Thus, the detrended cross-correlation function, which inherently provides better computational efficiency, may be properly employed. The validation of source level analysis and temporal fine structure will be performed in the near future. Although the detrended cross-correlation function exhibited performance comparable to ridge regression in exploring neural responses to continuous features (such as speech envelope and speech spectrogram), further investigation to examine neural responses to discrete features such as phonemic onset and semantic dissimilarity should be considered [31; 37]. As the detrended cross-correlation function may generate a more zero-centered  
Figure 5: Feasibility of TRF generation from neural signals in response to long-duration speech. EEG data were segmented to 10 s and 60 s to test the feasibility of the detrended cross-correlation function to generate the speech TRF. The upper and lower panels show the speech TRF at the typical channel of Cz, the correlation coefficient between the TRFs by the detrended cross-correlation and ridge regression, Pearson correlation coefficients for validating EEG prediction using the detrended cross-correlation function and ridge regression, and computational time per each sweep. The notations of ** and n.s denote \(p<0.01\) and not significant, respectively. TRF (i.e., dampening trends) compared to those generated by the ridge regression function, careful consideration is needed to employ the discrete features. This will be systematically investigated in future studies.