We present a formulation of the autoregressive HMM for speech synthesis and compare it to the standard HMM synthesis framework and the trajectory HMM. We give details of how to do efficient parameter estimation and synthesis with the autoregressive HMM and discuss consequences of the autoregressive HMM model. There are substantial similarities between the three models, which we explore. The adv...

Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local image statistics respectively, suggest hybrid models combining the strengths of both models. Our contribution is to train such hybrid models using an auxiliary...

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside...

A complex autoregressive model was established based on the mathematic derivation of the least squares for the complex number domain which is referred to as the complex least squares. The model is different from the conventional way that the real number and the imaginary number are separately calculated. An application of this new model shows a better forecast than forecasts from other conventi...

A smooth transition autoregressive model is estimated for the Southern Oscillation Index, an index commonly used as a measure of El Niño events. Using standard measures there is no indication of nonstationarity in the index. A logistic smooth transition autoregressive model describes the most turbulent periods in the data (these correspond to El Niño events) better than a linear autoregressive ...

We review and synthesize the wide range of non-Gaussian first order linear autoregressive models that have appeared in the literature. Models are organized into broad classes to clarify similarities and differences and facilitate application in particular situations. General properties for process mean, variance and correlation are derived, unifying many separate results appearing in the litera...

Tracking information about fertilizers consumption in the world is very important since they are used to produce agriculture commodities. Brazil consumes a large amount of fertilizers due to its large-scale agriculture fields. Most of these fertilizers are currently imported. The analysis of consumption of major fertilizers, such as Nitrogen-Phosphorus-Potassium (NPK), Sulfur, Phosphate Rock, P...

This paper reviews the analysis of the threshold autoregressive, smooth threshold autoregressive, and Markov switching autoregressive models from the Bayesian perspective. For each model we start by describing a baseline model and discussing possible extensions and applications. Then we review the choice of prior, inference, tests against the linear hypothesis, and conclude with models selectio...

We compare new time-series methods for estimating the death rate of an emerging and re-emerging disease and our approach is based on One-Dimensional Integrated Autoregressive Bilinear Time Series Model and Generalized Integrated Autoregressive Bilinear Time Series Model. The parameters of the proposed models are estimated using Newton-Raphson iterative method and statistical properties of the d...