Название: Non-Gaussian Autoregressive-Type Time Series
Автор: N. Balakrishna
Издательство: Springer
Год: 2022
Страниц: 238
Язык: английский
Формат: pdf (true), epub
Размер: 19.8 MB

This book brings together a variety of non-Gaussian autoregressive-type models to analyze time-series data. This book collects and collates most of the available models in the field and provide their probabilistic and inferential properties. This book classifies the stationary time-series models into different groups such as linear stationary models with non-Gaussian innovations, linear stationary models with non-Gaussian marginal distributions, product autoregressive models and minification models. Even though several non-Gaussian time-series models are available in the literature, most of them are focusing on the model structure and the probabilistic properties.

The assumption of normality in analysing statistical data is a matter of convenience and it is far from reality. As a result, several non-Gaussian time series models have been introduced in the literature during the last four decades, to describe the salient features of the data, which are not captured by the normal distribution. It is well known that a linear stationary time series model with Gaussian errors provides a Gaussian marginal stationary distribution. However, this is not the case with most of the non-Gaussian distributions, especially when the support is non-negative part of the real line. Of course, one can question the use of non-negative variables to describe the errors in time series. However, while modelling point processes with dependent inter-arrival times, the Markov sequences on non-negative support play an important role. In financial time series, the stationary Markov sequences are used to model stochastic volatility and conditional duration, which are dependent sequences of non-negative random variables.

However, the validity of such models cannot be assessed without a valid inference method. One of the difficulties in dealing with non-Gaussian time series models is that, there is no unified approach to tackle the problem of estimation. If we insist a specific absolutely continuous marginal distribution for the model under consideration, then the error distribution is a member of some non-standard family, and standard methods of estimation may not work. So, each member of the family of non-Gaussian models needs to be handled individually. We mainly focus on the properties of autoregressive-type models, driven by sequences of independent and identically distributed errors. These models generate Markov-dependent time series and one can conveniently use the inference methods available in the literature for such series.

If the time series is linear Gaussian, then all finite-dimentional distributions are multivariate normal. But, in non-Gaussian time series, the joint distributions do not have closed forms, and they are singular in most cases. We focus on the conditions for marginal stationarity, the second-order properties, autocorrelation structure and estimation problems associated with the non-Gaussian time series.

Contents:
1. Basics of Time Series
2. Statistical Inference for Stationary Linear Time Series
3. AR Models with Stationary Non-Gaussian Positive Marginals
4. AR Models with Stationary Non-Gaussian Real-Valued Marginals
5. Some Non-linear AR-type Models for Non-Gaussian Time Series
6. Linear Time Series Models with Non-Gaussian Innovations
7. Autoregressive-Type Time Series of Counts