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...

We propose a tree-structured heterogeneous autoregressive (tree-HAR) process as a simple and parsimonious model for the estimation and prediction of tick-by-tick realized correlations. The model can account for different time and other relevant predictors’ dependent regime shifts in the conditional mean dynamics of the realized correlation series. Testing the model on S&P 500 and 30-year treasu...

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...

In recent years, sustainable development has become a focal issue in the globalization process due to environmental uncertainty global context, which attracted extensive attention of scholars. This study explores dynamic transmission mechanism and time-varying impacts among green finance, renewable energy China on basis stochastic volatile vector autoregressive (TVP-VAR-SV) model using time-ser...

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...