# Stochastic Modeling and Optimal Time-Frequency Estimation of Task-Related HRV
## 4 Conclusions  
In this paper, we propose a time-varying stochastic model, based on the definition of LSCPs, for task-related HRV measured during a novel chirp-breathing task. The proposed inference method allows the evaluation of the MSE TF spectrum, derived from the proposed stochastic model, using either individual model parameters or the parameters estimated from a common process. For comparison, other TF spectral estimates are computed, namely the spectrogram with different window lengths and the WVS without any smoothing kernel. The MSE optimal spectral estimator evaluated with the estimated parameters minimizes bias and variance of the spectral estimates for LSCPs, and therefore its use is preferable for extracting further features from the spectral estimates.  
The LSCP model parameters are used as response variables in a regression analysis using several physiological covariates as predictors. The regression analysis shows correlation of the LSCP parameters with gender, age, levels of stress and fitness. The presented results are consistent with those of more extensive studies examining the relationship between HRV and physiological variables. Since each model parameter relates to a different aspect of the underlying LSCP, this approach may be useful to search for physiological factors that determine individual differences in the HRV.  
The proposed complete framework for the study of task-related HRV in relation to factors describing both mental and physical health has general validity for the analysis of non-stationary data, and especially in the case of task-related HRV.  
Further research can be addressed to identify new spectral measures to be extracted from the improved TF estimates since the traditional estimation of the spectral power divided in the low- and the high- frequency band is of limited interest for time-varying signals.  
Data curation, P.J.; Funding acquisition, M.S.; Investigation, R.A.; Methodology, R.A. and M.S.; Validation, R.A.; Writing--original draft, R.A.; Writing--review and editing, R.A. and M.S.  
This research was funded by the eSSENCE strategic research programme.  
A preliminary version of this work was presented as part of the Ph.D. thesis \"Statistical inference and time-frequency estimation for non-stationary signal classification\" by [PERSON], defended at Centre for Mathematical Sciences, Lund University, Sweden, on the 4 th of October 2019. The content here published has been used according to Lund University policy.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations (in alphabetic order) are used in this manuscript:  
\begin{tabular}{l l l} AIC & Akaike information criterion \\ BMI & body-mass index \\ ECG & electrocardiography \\ HATS & Hankel-Toeplitz separation \\ HRV & heart rate variability \\ LSCP & locally stationary chirp process \\ LSCP\({}_{c}\) & LSCP with parameters estimated from a common process \\ LSCP\({}_{i}\) & LSCP with individually estimated parameters \\ \end{tabular}  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Coeff. Est.** & **S.E.** & \(p\)**-Value** \\ \hline Gender (M) & \(-0.85140\) & \(0.36593\) & \(0.02233\) \\ Age & \(-0.06354\) & \(0.01897\) & \(0.00121\) \\ Fit (Underweight) & \(1.59192\) & \(0.97033\) & \(0.10453\) \\ Fit (Overweight) & \(-0.12594\) & \(0.43446\) & \(0.77262\) \\ Fit (Obese) & \(-2.43821\) & \(0.98378\) & \(0.01515\) \\ \hline \end{tabular}
\end{table}
Table 8: Regression model for parameter \(c\).