Chemical sensor based systems that are used for detection, identification, or quantification of various gases are very complex in nature. Sensor response data collected as a multivariate time series signals encounters gradual change of the sensor characteristics(known as sensor drift) due to several reasons. In this thesis, drift component of a silicon carbide Field-Effect Transistor (SiC-FET) sensor data was analyzed using time series. The data was collected from an experiment measuring output response of the sensor with respect to gases emitted by certain experimental object at different temperatures. Augmented Dickey Fuller Test (ADF) was carried out to analyze the sensor drift which revealed that stochastic trend along with deterministic trend characterized the drift components of the sensor. The drift started to rise in daily measurements which contributed to the total drift. / Traditional Autoregressive Integrated Moving Average (ARIMA) and deep learning based Long Short-Term Memory (LSTM) algorithm were carried out to forecast the sensor drift in reduced set of data. However, reduction of the data size degraded the forecasting accuracy and imposed loss of information. Therefore, careful selection of data using only one temperature from the temperature cycle was chosen instead of all time points. This chosen data from sensor array outperformed forecasting of sensor drift than reduced dataset using both traditional and deep learning methods.

Esta tese teve por objetivo central verificar, estatÃstica e analiticamente, o impacto da abertura econÃmica sobre os respectivos graus de abertura, correlacionando, por outro lado, estes resultados com as polÃticas econÃmicas adotadas. Do ponto de vista estatÃstico, a anÃlise centrou-se na identificaÃÃo da ocorrÃncia ou nÃo de quebra estrutural nas sÃries de comÃrcio internacional (ExportaÃÃo/PIB e ImportaÃÃo/PIB) dos principais paÃses da AmÃrica Latina, no perÃodo de 1974 a 2003. Para tanto, foram utilizadas as metodologias de determinaÃÃo endÃgena de quebra de Vogelsang (1997), da estacionaridade das sÃries/erros, os testes ADF e URB (2002) e o filtro de Hodrick-Prescott, mediante a funÃÃo de mudanÃa exponencial. Comprovou-se empiricamente, a relevÃncia da metodologia aqui desenvolvida para testar a estacionaridade de uma sÃrie com quebra utilizando o teste URB e de Vogelsang, seqÃencialmente e em conjunto. O tamanho do trimming nÃo influenciou fortemente os resultados, conforme previsto por Vogelsang (1997). Considerando primeiramente as sÃries de comÃrcio, a maioria delas apresentou quebra estrutural estatisticamente significante nas suas trajetÃrias; raiz unitÃria; tendÃncia quadrÃtica; variaÃÃo positiva das mÃdias de comÃrcio pÃs-quebra em relaÃÃo Ãs prÃ-quebra; crescimento das exportaÃÃes, na dÃcada de 1990, quatro vezes superior Ãs das trÃs dÃcadas do modelo ISI. A maior incidÃncia das datas de quebras ocorreu entre o limiar da dÃcada de 1980 e o inÃcio da de 1990. No caso das exportaÃÃes, em face da consolidaÃÃo do processo de liberalizaÃÃo, e no das importaÃÃes, em virtude da reduÃÃo drÃstica das barreiras tarifÃrias e nÃo tarifÃrias. Dentre os benefÃcios da liberalizaÃÃo para a regiÃo pode-se destacar a estabilizaÃÃo econÃmica, reduÃÃo da inflaÃÃo, melhora do balanÃo de pagamentos, principalmente nos Ãltimos anos; aumento do Ãndice de mudanÃa estrutural do valor agregado de manufaturas comparativamente ao perÃodo de ISI. Em termos das trajetÃrias da medida de abertura [(ExportaÃÃo + ImportaÃÃo) /PIB/ (PIB)], algumas datas de quebra apresentaram resultados que indicam a possÃvel existÃncia de efeitos de potencializarÃo ou de neutralizaÃÃo de uma sÃrie sobre a outra. No caso da medida de abertura do Brasil, o estudo baseou-se nas freqÃÃncias anual, trimestral e mensal. O filtro de Hodrick-Prescott foi determinante na avaliaÃÃo das datas de quebra. Na freqÃÃncia anual, a mesma data de quebra foi encontrada pelas metodologias do Teste de Vogelsang (1997), o de Sachs & Warner (1995) e Wacziarg & Welch (2003) e Hodrick-Prescott, ou seja, 1990, que coincide com a primeira fase do processo de liberalizaÃÃo brasileira. Em termos das freqÃÃncias trimestrais e mensais, a data de quebra encontrada em ambas foi 1998, data em que a taxa anual mÃdia de crescimento das importaÃÃes brasileiras foi quase duas vezes maior do que a do comÃrcio internacional. Atribuiu-se a suavidade da reversÃo da tendÃncia como razÃo para a diferenÃa nas datas de quebra quando se muda a freqÃÃncia. / The main purpose of this thesis is to verify statistical and analytically the economic openness impacts regarding their openness degree in comply with the economic politics results. In light of the substantial movement towards trade liberalization during 80â decade, statistical analysis aimed to identify structural breaks at international trade series (Export/GDP and Import/GDP) of the Latin Americaâs main countries, from 1974 up to 2003. Considering methodologies, it was used Vogelsangâs test (1997) to determine endogenous breaks; ADF and URB (2002) tests were used to classify series/erros in terms of stationarity and the Hodrick-Prescott filter, using the exponential shift function. In this thesis was developed a methodologyâs adaptation to test erros stationarity in a break structural context, using URB and Vogelsang tests together and sequentially which has showed a good performance. Confirming Vogelsangâs prediction (1997), trimmingâs size does not affect strongly the results. Considering first the trade ratios, most of them exhibited a structural break statistically significant in their paths; unit root; quadratic trend; average postbreak trade exceeded average prebreak trade for the majority of countries; 90â export growth exceeded four times ISI three decades performance. In general, statistically significant break dates took place ending 80â or beginning 90â, for exporting it happened due to consolidation of the liberalization process consolidation and regarding imports it was due to the tariffs and non tariffs barriers strongly reduction. Among the liberalizationâs benefits to the region were economic stabilization; lowered inflation; balance-of-payments improvement, mainly during last years; increased manufacturing value-added structural change index comparing to the ISI period. In terms of openness measure paths [(export + import)/(PIB)], it was identified some potentialized and/or neutralized effects of one series over the other at openness degreeâs break dates. At brazilianâs openness measure case, the study was based on annual, quarterly and monthly frequencies and using Hodrick-Prescott filter were significantly important in analysing those break dates. Concerning annual frequency same breaking date founded by Vogelsangâs (1997); Sachs & Warnerâs (1995) and Wacziarg & Welchâs (2003) and Hodrick-Prescott methodologies, that was 1990, coincidentally refers to the first brazilian liberalizationâs phase. In terms of quarterly and monthly frequencies breaking date results were both 1998. Reasons for difference in the time breaks frequencies results were based on tendency reversion smoothness. Besides it was possible to identify only through the filter. Besides it, at this date brazilian import growth were almost twice comparing to the world import growth.

Η παρούσα διατριβή ασχολείται με δύο ιδιαιτέρως σημαντικά και διαχρονικά επίκαιρα ζητήματα στην ανάλυση χρονολογικών σειρών, τα οποία εντάσσονται, υπό ευρεία έννοια, στο πεδίο της Μακροοικονομετρίας. Ειδικότερα, μελετώνται θέματα και μεθοδολογίες ή τεχνικές ιδιαίτερα χρήσιμες για εκείνους τους ερευνητές, οι οποίοι επικεντρώνονται στην ανάλυση της συμπεριφοράς των συναθροιστικών (aggregate) μεγεθών της οικονομίας, βασιζόμενοι στη χρήση δεδομένων χρονοσειρών ή πιο απλά χρονοσειρές (time series). Το πρώτο ζήτημα αφορά στη μελέτη της δυναμικής αλληλεξάρτησης ανάμεσα σε μακροοικονομικές μεταβλητές κάτω από την υιοθέτηση ενός πολλαπλού πλαισίου ανάλυσης χρονοσειρών. Το ενδιαφέρον εστιάζεται κυρίως στην γενικευμένη ή εκτεταμένη έννοια της αιτιότητας κατά Granger, δηλαδή στην επέκταση της τυπικής έννοιας της αιτιότητας κατά Granger σε μεγαλύτερους του ενός ή σε πολλαπλούς ορίζοντες πρόβλεψης. Το δεύτερο ζήτημα αφορά στην παρουσία μη-γραμμικών χαρακτηριστικών σε μακροοικονομικές χρονοσειρές, καθώς και την υποδειγματοποίηση της μη-γραμμικότητας με τη χρήση μη-γραμμικών οικονομετρικών μοντέλων. Επικεντρώνεται δε ιδιαίτερα στον έλεγχο μοναδιαίας ρίζας κάτω από την εναλλακτική υπόθεση της στασιμότητας γύρω από μη-γραμμικές τάσεις της μορφής τάσεων ομαλής μετάβασης (smooth transition trends) στις μακροοικονομικές χρονοσειρές. Ουσιαστικά, η διατριβή διακρίνεται σε δύο κεφάλαια. Στο Κεφάλαιο 1 παρουσιάζεται η τυπική έννοια της αιτιότητας κατά Granger, καθώς και η γενικευμένη ή εκτεταμένη έννοια της αιτιότητας ή η αιτιότητα σε πολλαπλούς ορίζοντες (multi-horizon causality), στο πλαίσιο των διανυσματικών αυτοπαλίνδρομων υποδειγμάτων (VAR). Η τυπική έννοια της αιτιότητας κατά Granger περιορίζεται στη βελτίωση της προβλεψιμότητας σε ορίζοντα πρόβλεψης μίας περιόδου (one-step ahead), ενώ λαμβάνει υπ'όψιν μόνο τις άμεσες ροές πληροφόρησης μεταξύ των μεταβλητών ενδιαφέροντος (direct causality). Ωστόσο, σε υποδείγματα VAR με περισσότερες από δύο μεταβλητές η τυπική έννοια της αιτιότητας μπορεί να επεκταθεί με την μελέτη της βελτίωσης της προβλεψιμότητας σε μεγαλύτερους του ενός ορίζοντες πρόβλεψης. Σε μία περίπτωση όπως η τελευταία, πλην της άμεσης αιτιότητας, δύνανται να μελετηθούν και οι έμμεσες σχέσεις αιτιότητας (indirect causality) που ενδέχεται να προκύψουν μέσω των πρόσθετων μεταβλητών του συστήματος. Το θεωρητικό πλαίσιο της γενικευμένης έννοιας της αιτιότητας που παρουσιάζει η παρούσα διατριβή έχει αναπτυχθεί από τους Dufour and Renault (1998). Παράλληλα, δίνεται ιδιαίτερη βαρύτητα σε δύο πρόσφατες μεθόδους στατιστικής επαγωγής αιτιωδών σχέσεων κατά Granger σε πολλαπλούς ορίζοντες, οι οποίες παρέχουν πρόσθετη πληροφόρηση σχετικά με τη δυναμική αλληλεξάρτηση οικονομικών χρονοσειρών, και πιο συγκεκριμένα σχετικά με τον άμεσο ή έμμεσο χαρακτήρα των αιτιωδών σχέσεων, το διαχωρισμό μεταξύ βραχυχρόνιας και μακροχρόνιας (μη)-αιτιότητας, καθώς και τις πιθανές χρονικές υστερήσεις της αιτιότητας. Τέλος, στα πλαίσια του Κεφαλαίου 1, ερευνάται η δυνατότητα εφαρμογής των μεθόδων αυτών μέσω εμπειρικών εφαρμογών πάνω σε δύο διαχρονικά ζητήματα αιτιωδών σχέσεων ανάμεσα σε οικονομικές μεταβλητές. Στο Κεφάλαιο 2 παρουσιάζονται υποδείγματα ομαλής μετάβασης, καθώς και έλεγχοι μοναδιαίας ρίζας οι οποίοι επιτρέπουν την στασιμότητα γύρω από ομαλές ή βαθμιαίες μεταβάσεις κάτω από την εναλλακτική υπόθεση. Κύριο χαρακτηριστικό των υποδειγμάτων ομαλής μετάβασης είναι η παρουσία μη-γραμμικών τάσεων στη διαχρονική εξέλιξη των χρονοσειρών. Κεντρικό ρόλο στα υποδείγματα αυτά κατέχουν οι διαρθρωτικές μεταβολές (structural changes) στην προσδιοριστική τάση, οι οποίες, δεδομένου ότι αντιπροσωπεύουν μεταβολές της συναθροιστικής συμπεριφοράς, υποδειγματοποιούνται με τη χρήση ενός προσδιοριστικού στοιχείου το οποίο επιτρέπει την βαθμιαία αντί της στιγμιαίας προσαρμογής. Οι έλεγχοι μοναδιαίας ρίζας, οι οποίοι επιτρέπουν περισσότερη ευελιξία στην συνάρτηση της τάσης σε σχέση με την γραμμική εξειδίκευση της προσδιοριστικής τάσης που χρησιμοποιούν οι τυπικοί έλεγχοι μοναδιαίας ρίζας, αποτελούν το επίκεντρο μελέτης του Κεφαλαίου 2 της διατριβής. Η αναγκαιότητα υιοθέτησης πρόσθετων ελέγχων μοναδιαίας ρίζας, όπως οι έλεγχοι μοναδιαίας ρίζας οι οποίοι επιτρέπουν στασιμότητα γύρω από ομαλές μεταβάσεις κάτω από την εναλλακτική υπόθεση, ισχυροποιείται από τα αποτελέσματα της εφαρμογής των ελέγχων αυτών σε ένα σύνολο οικονομικών χρονοσειρών. / This thesis discusses two central research topics in applied time series econometrics that generally belong in the field of Macroeconometrics. In particular, we investigate issues and methods which are of interest to those researchers who want to analyze economic problems or economic aggregates by means of time series data. The first topic deals with the dynamic interrelationships between sets of theory related variables in a multiple time series context. Research interest is primarily focused on the generalized or extended notion of Granger causality, that is the extension of the standard Granger causality concept to higher forecast horizons. The second topic deals with nonlinear behavior of macroeconomic time series, as well as the modelling of nonlinearities in economic time series using nonlinear econometric models. Specific attention is paid to unit root tests that allow stationarity around nonlinear trends in the form of smooth transitions under the alternative. The dissertation consists of two chapters. The first chapter presents the standard concept of Granger causality, along with the generalized or extended notion of causality, also known as multiple-horizon causality, in the vector autoregressive (VAR) framework. The standard notion of Granger causality restricts prediction improvement to a forecast horizon of one period, while it considers only direct flows of information between the variables of interest. However, in VAR models with more than two variables, the concept of standard Granger causality can be extended by studying prediction improvement at forecast horizons greater than one. If this is the case, then, except for direct causality, indirect flows of information might be revealed through the additional variables of the system. The theoretical framework of the extended concept of causality which is presented in the present dissertation has been developed by Dufour and Renault (1998). In addition, special attention is paid to two recent methods for testing hypothesis of non-causality at various horizons which can provide further information on the dynamic interaction of time series, and more specifically on the direct or indirect nature of causal effects, the distinction between short-run and long-run (non)-causality, as wells as the possibility of causal delays. Finally, the potential implementation of these methods is examined through empirical applications on causality relations among different sets of economic variables. Chapter 2 presents smooth transition (STR) trend models, as well as unit root tests that allow stationarity around smooth transitions under the alternative. Smooth transition regression models presume the presence of nonlinear trends in the long-run evolution of time series. A key feature of these models is the presence of structural changes in the deterministic trend which, given that they represent changes in aggregate behavior (economic aggregates), are modelled through a deterministic component that permits gradual rather than instantaneous adjustment between regimes. Unit root tests that permit a more versatile trend function in the unit root procedure, rather than the standard linear trends, are the main concern of Chapter 2. The necessity of employing additional unit root tests, such as unit root tests that allow stationarity around smooth transitions under the alternative, becomes evident through the unit root test results that are observed in an application in a set of economic time series.