Abstract not found

Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recognition techniques commonly used as part of a speech recognition system can be described by a graph – this includes Gaussian distributions, mixture models, decision trees, factor analysis, principle component analysis, linear discriminant analysis, and hidden Markov models. Moreover, this paper shows that many advanced models for speech recognition and language processing can also be simply described by a graph, including many at the acoustic-, pronunciation-, and language-modeling levels. A number of speech recognition techniques born directly out of the graphical-models paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov model-based speech recognition by improving structural discriminability. It also includes an example where a graph can be used to represent language model smoothing constraints. As will be seen, the space of models describable by a graph is quite large. A thorough exploration of this space should yield techniques that ultimately will supersede the hidden Markov model.

We compare and review block, sieve and local bootstraps for time series and thereby illuminate theoretical facts as well as performance on nite-sample data. Our (re-) view is selective with the intention to get a new and fair picture about some particular aspects of bootstrapping time series. The generality of the block bootstrap is contrasted by sieve bootstraps. We discuss implementational dis-/advantages and argue that two types of sieves outperform the block method, each of them in its own important niche, namely linear and categorical processes, respectively. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance. Key words and phrases. Autoregression, block bootstrap, categorical time series, context algorithm, double bootstrap, linear process, local bootstrap, Markov chain, sieve bootstrap, stationary process. 1 Introduction Bootstrapping can be viewed as simulating a statistic or statistical pro...

: We compare two theoretically distinct approaches to generating artificial (or "surrogate") data for testing hypotheses about a given data set. The first and more straightforward approach is to fit a single "best" model to the original data, and then to generate surrogate data sets that are "typical realizations" of that model. The second approach concentrates not on the model but directly on the original data; it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics. Examples of these two approaches are provided for two simple cases: a test for deviations from a gaussian distribution, and a test for serial dependence in a time series. Additionally, we consider tests for nonlinearity in time series based on a Fourier transform (FT) method and on more conventional autoregressive moving-average (ARMA) fits to the data. The comparative performance of hypothesis testing schemes based on these two approaches...

Constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models, or to choose between competing classes. This paper discusses a method of building nonlinear models of possibly chaotic systems from data, while maintaining good robustness against noise. The models that are built are close to the simplest possible according to a description length criterion. The method will deliver a linear model if that has shorter description length than a nonlinear model. We show how our models can be used for prediction, smoothing and interpolation in the usual way. We also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series. 1 The Model Selection Problem As our understanding of chaotic and other nonlinear phenomena has grown, it has become apparent that linear models are inadequate to model most dynamical processes. Nevertheless, linear models...

We apply the local linear regression technique for estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functional-coefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better post-sample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and is of appreciable flexibility to analyze complex and multivariate nonlinear structures without suffering from the "curse of dimensionality". The asymptotic properties of the proposed estimators are investigated under the ff-mixing condition. Both simulated and real data examples are used for illustration. Key Words: ff-mixing; Asymptotic normali...

While there has been a great deal of interest in the modelling of non-linearities in economic time series, there is no clear consensus regarding the forecasting abilities of non-linear time series models. We evaluate the performance of two leading non-linear models in forecasting post-war US GNP, the self-exciting threshold autoregressive model and the Markov-switching autoregressive model. Two methods of analysis are employed: an empirical forecast accuracy comparison of the two models, and a Monte Carlo study. The latter allows us to control for factors that may otherwise undermine the performance of the non-linear models. 1 Introduction In recent years there has been a great deal of interest in the modelling of non-linearities in economic time series. While the usefulness of linear time-series models in the tradition of Box and Jenkins (1970) is usually gauged by their predictive ability, there does not appear to be a clear consensus as to whether allowing for non-linearities has l...

Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this paper, we use predictive residuals to construct a test statistic to detect threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The nite-sample performance of the proposed test is studied by simulation. The modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost-of-carrying the contracts. In this particular application, thresholds are determined in part by the transaction costs. We also apply the proposed procedure to U.S. monthly interest rates and two river ow series of Iceland.

In this paper we investigate the multi-period forecast performance of a number of empirical selfexciting threshold autoregressive (SETAR) models that have been proposed in the literature for modelling exchange rates and GNP, amongst other variables. We take each of the empirical SETAR models in turn as the DGP to ensure that the `non-linearity' characterises the future, and compare the forecast performance of SETAR and linear autoregressive models on a number of quantitative and qualitative criteria. Our results indicate that non-linear models have an edge in certain states of nature but not in others, and that this can be highlighted by evaluating forecasts conditional upon the regime.

Abstract. The problem of testing for linearity and the number of regimes in the context of self-exciting threshold autoregressive (SETAR) models is reviewed. We describe least-squares methods of estimation and inference. The primary complication is that the testing problem is non-standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non-standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications Ð annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes. Keywords. SETAR models; Thresholds; Non-standard asymptotic theory; Bootstrap