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EN
In this paper author presents an overview of what are HMMs, fundamental problems associated with HMMs, algorithms used for training HMMs, and their application for automatic speech recognition. As a practical realization of presented technologies, author developed a software implementing Hidden Markov Models, together with basic audio processing and speech parametrization capabilities. On basis of that libraries a simple isolated word recognizer was implemented.
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As European Union countries are facing particularly difficult economic management decisions with challenging political and social ramifications, we try to find groups of countries which face a similar challenge of improving their competitiveness indicators. We focus on the dependent mixture model which additionally allows us to investigate the dynamic pattern of the competitiveness index and pillars organized into three sub-indices time series. This methodology will provide an opportunity to investigate which countries feature a similar level of competitiveness stability (are able to sustain their level of competitiveness) and which have similar regime-switching propensities. These results may contribute to the current policy discussion on measures for achieving the sustainable competitiveness of the European Union economies, EU strategy and reform programmes in separate member states.(original abstract)
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Content available remote Perfect tree-like Markovian distributions
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We show that if a strictly positive joint probability distribution for a set of binary variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is show to hold also for multivariate nondegenerate normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probabilisty distributions.
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Content available remote On Maximal Social Preference
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EN
Mathematics and physics are based on two numbers: Archimedes' constant π = 3,14... and e = 2,71... - Napier's constant. The former reflects the ratio of the perimeter of a figure to its diameter and maximizes the area, given the diameter. The solutions are the disk and the circle. The latter represents the accumulated capital paid by a bank after one year from investing one unit of money at an annual interest rate of 100% under continuous compounding. The ratio of the disk's perimeter to its diameter, i.e. π, governs omnipresent cyclical motion, whereas Napier's constant determines natural growth - exponential growth. Nature mixes both kinds of behaviour: there is equilibrium - vortices, and the cobweb model, dynamic growth. Our general remarks are corroborated by the theory of linear differential equations with constant coefficients. Social life - democracy and quality - despite the deceptive chaos of accidental behaviour, is also governed by a beautiful numeral law. This social number is λ = ⅔ whose notation is derived from the Greek λαοζ meaning crowd, people, assembly. The social number, Łyko's number, is defined by the fundamental theorem. If each alternative of a maximal relation of a given profile has its frequency in this profile greater than ⅔, then such relation is a group preference. This sufficient condition separates a decisional chaos from a stable economic and voting order - the preference. Also our everyday language makes use of λ . We distinguish with it upper states - elitist ones, from ordinary standards. The ⅔ rule implies that in each group one third of the population prevails, while the rest are just background actors. The number λ also appears, a bit of a surprise, in classical theorems of geometry.(original abstract)
EN
During modeling of short-run exchange rate fluctuations, there is usually a need for taking into consideration some random-type conditions, i.e. it is necessary to abandon the fundamental exchange rate theories in favor of probabilistic modeling. Among stochastic models, of special interest are Markov models. The main advantages of Markov models include a relative simplicity of construction, easy inferences, well-known estimation methods and especially consistence of properties of these models with the observed properties of many real phenomena. Application of switching models is based on a general assumption that the examined time series can be presented as sequences of random variables of a known type of conditional distribution in all regimes. Known from literature propositions concerning the modeling of exchange rate with the use of switching models did not provide sufficiently good forecasts of the future exchange rate levels because of, among others, low frequency of data used for the construction of the model (quarterly or monthly data). The authors are going to continue the examination of the PLN exchange rate fluctuation with the use of Markov models that was started in this paper. The next stage of their work will be connected with conducting empirical research concerning the occurrence of calendar anomalies in the Polish currency market. For this purpose, a new method based on the Markov chains theory will be applied, which offers a new perspective to this problem. Testing o f the calendar time hypothesis has been considered so far mostly in the aspect of comparison of daily expected values and variances of exchange rate return rates. Then, on the basis of the da ta concerning exchange rates for high measurement frequency, a Ma rkov switching model will be constructed and used for description of the PLN depreciation and appreciation period.
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Prawidłowe oszacowanie kierunku zmian kursu wymiany może zmniejszyć ryzyko inwestycji w walutę lub może pozwolić na osiągnięcie większych dochodów z tej inwestycji. W opracowaniu tym autorzy przedstawiają propozycję zastosowania modeli Markowa do wykrycia i opisania prawidłowości rządzących procesem zmienności kursu walutowego. W pierwszej części została wykorzystana teoria łańcuchów Markowa do badania anomalii kalendarzowych występujących n a rynku walutowym związanych z efektem weekendowym lub efektem stycznia. W artykule przedstawiona została również metoda o parta na teorii łańcuchów Markowa, k tó ra może posłużyć d o zbadania wzajemnych powiązań pomiędzy zmiennością wolumenu obrotu oraz zmiennością cen dla terminowych kontraktów walutowych. W drugiej części zostaną przedstawione zagadnienia związane z budową i estymacją parametrów przełącznikowych modeli Markowa. W oparciu o modele przełącznikowe można prognozować zmiany kursu walutowego. Praca ma charakter teoretyczny. Badania empiryczne zostaną przeprowadzone w późniejszym terminie.
EN
We prove existence of time consistent equilibria in a wide class of dynamic models with re-cursive payoffs and generalized discounting involving both behavioral and normative applica-tions. Our generalized Bellman equation method identifies and separates both: recursive andstrategic aspects of the equilibrium problem and allows to precisely determine the sufficientassumptions on preferences and stochastic transition to establish existence. In particularwe show existence of minimal state space stationary Markov equilibrium (a time-consistentsolution) in a deterministic model of consumption-saving with beta-delta discounting andits generalized versions involving magnitude effects, non-additive payoffs, semi-hyperbolic orhyperbolic discounting (over possibly unbounded state and unbounded above reward space).We also provide an equilibrium approximation method for a hyperbolic discounting model. (original abstract)
EN
The aim of the study is to measure the influence of cycle length and progression rates on differences between final results obtained using different approaches concerning time of transition to another state in Markov models (at the beginning, at the end of the cycle or half-cycle correction - HCC) and to estimate an optimal cycle length for which HCC should always be applied. A hypothetical, two-state Markov model was built. Assuming different progression rates, four methods concerning time of transition were compared. For each rate, the threshold values were determined, i.e. the maximal cycle length for which the difference between HCC/ 'life-table' (LT) method and 'beginning'/'end' methods were not greater than 5%. Cycles longer than the estimated threshold are assumed to imply the application of HCC/LT. Under few assumptions, the threshold cycle length for annual progression of 0.05 was 1 year or 2 years, for 5% and 0% discount rate, respectively. The threshold cycle lengths became shorter for lower progression rates (2 weeks for 0.90 rate). The results obtained for single intervention cannot be easily repeated for incremental outcomes; however, some general relationships can be determined(original abstract)
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In distribution companies, it is particularly important to organize transport processes properly and minimize unnecessary mileage. A high level of readiness of transport means is also required, which guarantees the execution of every order. It enables to achieve rational fleet management, compliance with service intervals and an even workload. The use of transport means is also influenced by the way a company is managed and decisions made at the strategic level. This article shows how the choices made by the management board regarding trade partners (manufacturers) influenced the degree and legitimacy of owned rolling stock use. For this purpose, two different business steps were compared. Markov’s processes were used in the study.
EN
We compare thc number of lost cells in switches managed by the PushOut mechanism and scheduled under an arbitrary service policy, by applying the comparison of stochastic processes in the strong stochastic ordering sense. New telecommunication networks will provide Quality of Service differentiation. This implies buffer management mechanisms such as the PushOut mechanism to warrant quality for loss-sensitive sessions. Using sample-path arguments, we present the relationships between the speed of scheduling policies and the number of lost cells under PushOut mechanism.
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The paper presents the application of Hidden Markov Models to poem generation in Polish language. It also includes the program description and results discussin.
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We apply multitype, continuous time, Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly, the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models, in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E. coli. We use well established methods, incorporating maximum likelihood techniques, to estimate speciation rates as well as the rates of transition between different states of the models. From the analysis, we not only derive new results, but we also verify some preexisting notions about virulent behavior in bacterial strains.
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The paper presents a formalised procedure of the identification of financial stability EWI (Early Warning Indicators) for the Polish banking sector, in which a two-step procedure was applied. First, the author used a logit model to estimate of the biggest Polish banks' probabilities of default (PDs). Next, the calculated individual banks' PDs were used to prepare aggregated domestic banking system stability. In the last step, employing a set of multivariate Markov-switching models with distributed lags (MMSM-DL), the author applied this measure to identify EWI from the candidate macro, private and public debt, banking sector, financial markets and property prices indicators. The best performing EWI were selected with application of area under the receiver operating characteristic (AUROC) metrics and compared with an output of a popular logistic regression (LR) model. To the best author's knowledge, this article presents for the first time a fully formalised analytical framework based on the MMSM-DL approach that combines microprudential and macroprudential data for the Polish banks financial stability EWI identification. Moreover, the survey supports the hypothesis that the Polish banking sector is stable with use of a formalised econometric procedure.(original abstract)
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W opracowaniu przedstawiono warunki identyfikacji ukrytych modeli Markowa (Hidden Markov Models - HMM) niektórych typów. Punktem wyjścia rozważań są dwuwymiarowe, częściowo obserwowalne procesy spełniające następujące warunki: składowa nieobserwowalna jest łańcuchem Markowa, zaś składowa obserwowalna tworzy ciąg warunkowo niezależnych zmiennych losowych, przy czym rozkład n-tej zmiennej zależy jedynie od stanu łańcucha w chwili n. Modele te, w ekonometrii znane także pod nazwą przełącznikowych modeli Markowa (Markov Switching Models), doczekały się licznych uogólnień i są szeroko stosowane w analizie finansowych szeregów czasowych. W pracy przedstawiono znane z literatury fakty dotyczące identyfikacji modeli HMM, w których warunkowe rozkłady zmiennych obserwowalnych pochodzą z identyfikowalnych rodzin mieszanek rozkładów. Obok modeli HMM z ukrytymi łańcuchami Markowa rozważano modele, w których ukryte procesy są łańcuchami Markowa wyższego rzędu. (fragment tekstu)
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Większość badań ekonometrycznych w przypadku stóp zwrotu z notowań obserwowanych na rynkach papierów wartościowych wskazuje na brak zgodności ich rozkładów z rozkładem normalnym. Za główne przyczyny odrzucania hipotezy o rozkładzie normalnym uważane są silna asymetria oraz podwyższona kurtoza, w porównaniu z rozkładem normalnym analizowanych szeregów czasowych. Modelami wyjaśniającymi, zarówno skośność, jak i podwyższoną kurtozę rozkładu, mogą być nieliniowe modele progowe. Dla celów modelowania finansowych szeregów czasowych najczęściej wykorzystywane są modele TAR, SET AR, gdzie przełączanie między reżimami zależne jest od konkretnych wartości zmiennej obserwowalnej oraz przełącznikowe modele Markowa, w których przełączanie między reżimami jest oparte na nieobserwowalnym procesie Markowa. Przedstawiony przykład empiryczny wskazuje, że istnieje możliwość wykorzystania zaproponowanego w opracowaniu modelu SWARCH do opisu finansowych szeregów czasowych. Model SWARCH okazał się równie dobrze dopasowanym modelem do danych empirycznych, jak model ARCH, na co wskazują podobne wartości kryterium informacyjnego Schwarza. Należy zauważyć, że w dalszych analizach należałoby przebadać kolejne spółki, przy założeniu dowolnej postaci modelu SWARCH(k,q). (fragment tekstu)
EN
Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the general (mixture) model and its special (single-component) case, it may be desirable to ensure that the prior assumptions introduced into both structures are compatible in the sense that the prior distribution in the nested model amounts to the conditional prior in the mixture model under relevant parametric restriction. The study provides the rudiments of setting compatible priors in Bayesian univariate finite mixture and Markov-switching models. Once some primary results are delivered, we derive specific conditions for compatibility in the case of three types of continuous priors commonly engaged in Bayesian modeling: the normal, inverse gamma, and gamma distributions. Further, we study the consequences of introducing additional constraints into the mixture model's prior on the conditions. Finally, the methodology is illustrated through a discussion of setting compatible priors for Markov-switching AR(2) models. (original abstract)
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Content available remote Cyclical Fluctuations in Transport. Turning Points Detection
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This paper presents the preliminary analysis of the characteristics of cyclical fluctuations in the freight transport market in Poland. The aim of the analysis is to identify, based on the estimated turning points (using the Bry Boschan method, as well as Hidden Markov Models), expansion and contraction phases in freight transport. These results are compared with the business climate indicators calculated on the basis of survey research in the freight transport.(original abstract)
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W artykule analizuje się ukryte modele Markowa (Hidden markov Models - HMM) niektórych typów. Jednym z istotnych problemów pojawiających się przy estymacji tego typu modeli jest zagadnienie identyfikacji związane z odpowiedzią na pytanie czy modele o różnych zbiorach parametrów nie generują obserwowalnych procesów o tych samych rozkładach skończenie wymiarowych. W pracy przedstawiono znane z literatury fakty dotyczące identyfikacji modeli HMM, w których warunkowe rozkłady zmiennych obserwowalnych pochodzą z identyfikowalnych rodzin mieszanek rozkładów. W artykule rozważano modele, w których ukryte procesy są łańcuchami Markowa wyższego rzędu. Okazuje się, że badanie identyfikacji powyższych modeli, podobnie jak w przypadku niektórych klasycznych HMM, sprowadzić można do badania identyfikacji tzw. grupowych łańcuchów Markowa. W pracy podano warunek dostateczny identyfikacji modeli HMM wyższego rzędu. (abstrakt oryginalny)
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In the paper we present conditions of identifiability of certain Hidden Markov Models (HMMs). The problem of identifiability of HMMs is related to possibility of estimation of model's parameters problem (it is worth to know if two distinct sets of parameters could produced the same finite-dimensional distributions of the observable process). This problem is connected with the problem of identifiability of lump able Markov chains. This is so especially when the same conditional distributions are connected with distinct states of underlying Markkov chain. We show that identifiability of certain extension of HMMs (underlying process being Markov chain of higher order and more complex relation of unobservable and observable parts of process) could be considered in the same way. We present some sufficient condition for identifiability such models. (original abstract)
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This paper investigates the international financial market integration as a trigger for regime switching behavior of Indian implied volatility index and its regime-dependent conditional correlations with the selected developed markets. The 2-state dynamic regression model reveals two different regimes using state-dependent variables during the time period 2009 to 2016. The results found that Hong Kong and US markets have a significant effect on the Indian market during highly volatile state, and there is a clear decoupling effect among these markets when the Indian market is stable. The predicted turning point probabilities indicate that the bull market state is persistent. (original abstract)
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Ze względu na brak obserwowalności realizacji VaR oraz innych, stosowanych popularnie na rynku kapitałowym, miar ryzyka, nie istnieje bezpośrednia możliwość oceny średniego błędu estymatora. Stosowanie analitycznych wzorów pozwalających na wyznaczenie wariancji estymatora jest sprzeczne z założeniem o braku stałości rozkładów zmiennych obserwowanych na rynku finansowym. W pracy przedstawiono analizę porównawczą metod oceny jakości prognoz ryzyka. Omówione zostały własności testów służących ocenie jakości prognoz VaR. Analizie poddano test ilości przekroczeń oraz testy niezależności przekroczeń w czasie. Pokazano, że powszechnie stosowane testy zaproponowane w latach 90. ubiegłego stulecia charakteryzują się gorszymi własnościami statystycznymi w porównaniu z testem Engla i Manganellego z 2004 r. W części empirycznej do oceny ryzyka wykorzystano cztery modele VaR, które oceniono z wykorzystaniem rozważanych procedur testowych.(abstrakt oryginalny)
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Models for risk measurement in capital market rise problems with their evaluation due to the lack of possibility to observe real VaR series. Analytical formulas cannot be used in case of time-changing distributions of financial variables. In consequence, in the last two decades a lot of testing procedures have been proposed to verify quality of risk models. In the paper, we presented comparative analysis of methods for evaluating VaR forecasts. We analysed test for the number of VaR exceptions as well as tests for autocorrelation of VaR violations. We showed that widely used tests from the 1990s have lower power that the proposition of Engle and Mangianelli from 2004. In the empirical part we used four VaR models for WIG20 index which were applied with testing procedures.(original abstract)
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