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- Mixture Models (2)
- changepoint test (2)
- hidden variables (2)
- mixture (2)
- nonparametric regression (2)
- AR-ARCH (1)
- Autoregression (1)
- CUSUM statistic (1)
- EM algorith (1)
- EM algorithm (1)
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Nonlinear and Nonparametric Methods for Analyzing Financial Time Series
(1999)
- We consider nonparametric generalization of various well-known financial time series models and study estimates of the trend and volatility functions and forecasts based on kernel smoothers as well as on neural networks.
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Maximum Likelihood Estimators for Markov Switching Autoregressive Processes with ARCH Component
(2009)
- We consider a mixture of AR-ARCH models where the switching between the basic states of the observed time series is controlled by a hidden Markov chain. Under simple conditions, we prove consistency and asymptotic normality of the maximum likelihood parameter estimates combining general results on asymptotics of Douc et al (2004) and of geometric ergodicity of Franke et al (2007).
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Portfolio management and market risk quantification using neural networks
(1999)
- We discuss how neural networks may be used to estimate conditional means, variances and quantiles of nancial time series nonparametrically. These estimates may be used to forecast, to derive trading rules and to measure market risk.
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Nonparametric Estimates for Conditional Quantiles of Time Series
(2003)
- We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t-1. We discuss an estimate which we get by inverting a kernel estimate of the conditional distribution function, and prove its asymptotic normality and uniform strong consistency. We illustrate the good performance of the estimate for light and heavy-tailed distributions of the innovations with a small simulation study.
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Changepoint tests for INARCH time series
(2011)
- In this paper, we discuss the problem of testing for a changepoint in the structure of an integer-valued time series. In particular, we consider a test statistic of cumulative sum (CUSUM) type for general Poisson autoregressions of order 1. We investigate the asymptotic behaviour of conditional least-squares estimates of the parameters in the presence of a changepoint. Then, we derive the asymptotic distribution of the test statistic under the hypothesis of no change, allowing for the calculation of critical values. We prove consistency of the test, i.e. asymptotic power 1, and consistency of the corresponding changepoint estimate. As an application, we have a look at changepoint detection in daily epileptic seizure counts from a clinical study.
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Weak Dependence of Functional INGARCH Processes
(2010)
- We introduce a class of models for time series of counts which include INGARCH-type models as well as log linear models for conditionally Poisson distributed data. For those processes, we formulate simple conditions for stationarity and weak dependence with a geometric rate. The coupling argument used in the proof serves as a role model for a similar treatment of integer-valued time series models based on other types of thinning operations.
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Mixtures of Nonparametric Autoregression, revised
(2009)
- We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.
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Mixtures of Nonparametric Autoregressions
(2009)
- We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.
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Some asymptotics for local least-squares regression with regularization
(2007)
- We derive some asymptotics for a new approach to curve estimation proposed by Mr'{a}zek et al. cite{MWB06} which combines localization and regularization. This methodology has been considered as the basis of a unified framework covering various different smoothing methods in the analogous two-dimensional problem of image denoising. As a first step for understanding this approach theoretically, we restrict our discussion here to the least-squares distance where we have explicit formulas for the function estimates and where we can derive a rather complete asymptotic theory from known results for the Priestley-Chao curve estimate. In this paper, we consider only the case where the bias dominates the mean-square error. Other situations are dealt with in subsequent papers.
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Quantile Sieve Estimates for Time Series
(2007)
- We consider the problem of estimating the conditional quantile of a time series at time \(t\) given observations of the same and perhaps other time series available at time \(t-1\). We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.
