## 1 Introduction  
Parkinson's disease (PD) is a frequent neurodegenerative disorder that is associated with a substantial reduction of dopaminergic neurons especially in substancia nigra pars compacta [1]. The primary motor symptoms of PD comprise tremor at rest, muscular rigidity, bradykinesia, and postural instability [1]. Patients with PD also develop a variety of non-motor symptoms [2] such as sleep disturbances, depression, cognitive impairment, etc. To diagnose, rate and monitor motor and non-motor symptoms of PD, various clinical rating scales such as Unified Parkinson's Disease Rating Scale (UPDRS) [3], Freezing Of Gait Questionnaire (FOG-Q) [4], or Addenbrooke's Cognitive Examination-Revised (ACE - R) [5] have been developed. Nevertheless, reliability of the assessment is often reduced by inter-rater variability [6]. Up to 90% [7] of patients with PD develop a multi-dimensional speech disorder named hypokinetic dysarthria (HD) [8], which is manifested in phonation, articulation, and prosody [9; 10; 11]. In the area of phonation, insufficient breath support, reduction in phonation time, increased acoustic noise, instability of articulatory organs, microperturbations of frequency/amplitude, and harsh breathy voice quality has been observed [9; 12]. HD leads to serious complications in daily communication of patients with PD [13]. Generally, HD was found to be more severe in the advanced stages of PD [14]. As reported by the recent studies, acoustic analysis of HD can provide clinicians with non-invasive and reliable methodology of PD diagnosis, assessment and monitoring [9; 15]. Moreover, this methodology has also been used to monitor the efficiency of PD treatment [10; 16; 17; 18]. In the field of acoustic analysis of PD phonation, the authors mostly focused on the sustained vowel /a/ [9]. Conventional phonatory features such as jitter, shimmer, harmonic-to-noise ratio, degree of unvoiced segments, and formant-based parameters extracted from this vowel have been widely used to diagnose PD [12; 19; 20; 21; 22; 23]. Although [PERSON] et al. [24] employed analysis of sustained phonation for diagnosis of PD even in its early stage, based on the recent review [9], most of the researchers find relevant applications of the phonatory analysis especially in moderate or severe stages of this disorder. For example, the analysis of sustained phonation has been utilized during PD severity assessment. In 2010, [PERSON] et al. [15] enrolled 42 PD patients and parameterized their sustained phonation of vowel /a/ by a set of conventional features that were consequently mapped to UPDRS, part III (motor examination) and the total score of this scale. Using classification and regression trees, they estimated the UPDRS III score with MAE (mean absolute error) equal to 5.95. The total UPDRS score was estimated with MAE = 7.52. A parametric version of this dataset has been made available for research purposes and other research teams further decreased the estimation error [25; 26; 27]. Another work that deals with the automatic clinical scores estimation was published by [PERSON] et al. [21]. In this study, they acquired sustained phonation of vowels /a/,/e/, /i/,/o/, /u/ in 84 PD patients. Modeling conventional and advanced features by random forests provided the estimation of UPDRS III with MAE = 5.70. In addition, the authors estimated several other clinical scores such as UPDRS, part IV (complications of therapy) with MAE = 1.30 or Beck depression inventory (BDI) with MAE = 3.12. Even though HD is one of the most problematic aspects of PD, the number of longitudinal studies investigating the evolution of HD in PD over time (based on the acoustic analysis) is very limited [28; 29; 30; 31]. If we focus specifically on longitudinal monitoring of sustained phonation, then, in fact, we can identify only one study, which is published by [PERSON] et al. [31].