**1. Introduction**

The contact of wine distillate with wood is recognised as a pivotal step of the aged wine spirit production, during which its quality increases and sensory fullness can be reached. Scientific evidence exists on the key role of several physicochemical phenomena, particularly the extraction and oxidation reactions involving the wood-derived compounds of low molecular weight, on the chemical changes (quantitative and qualitative aspects of the beverage's volatile and non-volatile composition) and sensory changes (colour, aroma, and taste) occurred [1–3]. Besides, they mainly depend on the ageing technology, the kind of wood used (oak and chestnut), and the length of the ageing process [1,4,5].

Despite the high-quality spirits attained by the traditional ageing technology, using wooden barrels, this expensive and lengthy process led to the search and study of sustainable alternative

technologies. Research has been focused on a technology based on adding wood pieces to the distillate kept in stainless steel tanks, as for other alcoholic beverages [6,7]. Recently, the micro-oxygenation technique, reproducing the oxygen transfer that occurs in the wooden barrel, was applied to optimise this ageing technology. Promising outcomes based on the phenolic composition and colour of the wine spirits in the beginning of ageing were attained [8]. Nevertheless, a comprehensive approach is needed towards the full/robust characterisation of this novel technology, exploring the data acquired over the ageing period through di fferent analytical and statistical methodologies.

Spectroscopic techniques are very useful for food and beverages quality evaluation because they require minimal or no sample preparation (absence of extraction, reactions with some other chemical species, treatment with a chelating agent, masking, sub-sampling, or other manipulation), they are rapid and non-destructive (causing no physicochemical changes during the analysis), and they can be used to simultaneously assess several parameters of a sample. In recent years, significant developments related to the applicability of vibrational spectroscopy combined with multivariate data analysis has been made to give the rapid quantification of several compounds in di fferent matrices or to discriminate di fferent groups of samples. Concerning the alcoholic beverages, the studies were more centred on other drinks than wine spirits. FTIR-ATR (Fourier transform infrared spectroscopy with Attenuated Total Reflection) was used to evaluate di fferent parameter in alcoholic beverages, such as the determination of important quality parameters of beers [9], determination of ethanol content in liquors [10], quantitative analysis of methanol (an adulterant in alcoholic beverages) [11], analysis of ethanol and methanol content in traditional fruit spirits [12], and the authentication of whisky according to its botanical origin [13]. Actually, the studies on wine spirits with FTIR-ATR are scarce. One of them was carried out by Anjos et al. [14], applying the FTIR-ATR methodology to predict the alcoholic strength, methanol, acetaldehyde, and fusel alcohols contents of grape-derived spirits.

In this paper, a new application of functional data analysis (FDA) in the field of quality evaluation using spectroscopic techniques is presented. In recent years, FDA has been used in numerous investigations to analyse processes in continuous time; some examples are energy e fficiency [15], medical research [16], econometrics [17], optimisation problems [18], industrial processes [19], environmental research [20,21], and food science [22]. In all these works, FDA showed its usefulness for the study of functions, defined in a specific interval, without missing the correlation between the observations.

FDA allows the analysis of the entire curves, which represent individual observations of the sample under study, detecting di fferent behaviours throughout the curves [15,23]. Ordoñez et al. [23], in a similar context that this paper, showed significant reasons to analyse the sample with curves instead of individual observations. In addition, the contrast of similarity has been carried out from a vectorial approach, but summarising the curves with a single value; in this case, the mean. This is necessary because the curves, although representing individual data, are formed by a set of observations correlated to each other. Martínez et al. [20] explained how this correlation is not taken into account from a vectorial approach. Furthermore, from this point of view, to contrast the similarity between the samples, a classical analysis of variance (ANOVA) [24,25] and anon-parametric Kruskal's test [26] have been performed. Although this is a simpler approach, it contributes to highlight the strengths of FDA. On the one hand, Martínez et al. [15] presented how di fferent conclusions can be reached for each approach because of the biased sample used in the vector analysis (mean of the curves) or di fferent detection of outliers. On the other hand, among others, Sancho et al. [19] demonstrated that FDA presents more realistic and accurate results, showing how and at which specific part of the curve the groups have di fferent spectrometric behaviours.

The aim of this research is to contrast the similarity between the samples obtained with FTIR-ATR spectrometry for wine spirits aged by di fferent ageing technologies (traditional and alternative), with di fferent kinds of wood (chestnut and oak) and over the ageing period (6, 12, and 18 months), using functional data analysis of variance (FANOVA).

Thus, the second section presents, on the one hand, the data used in this study and, on the other hand, the specific methodology applied to obtain the results. The third section presents the results of the comparison and analysis of the differences between the wine spirit samples. Then, in the fourth section, a discussion is carried out about the results and the information obtained with them. Finally, in Section 5, the conclusions of this work are presented.

### **2. Materials and Methods**
