# On a mixture autoregressive model

@article{Wong2000OnAM, title={On a mixture autoregressive model}, author={C. S. Wong and W. K. Li}, journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, year={2000}, volume={62} }

We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co‐workers to the mixture autoregressive (MAR) model for the modelling of non‐linear time series. The models consist of a mixture of K stationary or non‐stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series. The stationarity…

## 280 Citations

On a logistic mixture autoregressive model

- Business
- 2001

SUMMARY We generalise the mixture autoregressive, MAR, model to the logistic mixture autoregressive with exogenous variables, LMARX, model for the modelling of nonlinear time series. The models…

On a Mixture Autoregressive Conditional Heteroscedastic Model

- Computer Science
- 2001

The MAR-ARCH models appear to capture features of the data better than the competing models and are applied to two real datasets and compared to other competing models.

Prediction with Mixture Autoregressive Models

- Mathematics
- 2006

Mixture autoregressive (MAR) models have the attractive property that the shape of the conditional distribution of a forecast depends on the recent history of the process. In particular, it may have…

On Mixture Double Autoregressive Time Series Models

- Mathematics
- 2017

This article proposes a mixture double autoregressive model by introducing the flexibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently…

A Gaussian Mixture Autoregressive Model for Univariate Time Series

- Mathematics
- 2015

The Gaussian mixture autoregressive model studied in this article belongs to the family of mixture autoregressive models, but it differs from its previous alternatives in several advantageous ways. A…

Mixture transition distribution (MTD) modeling of heteroscedastic time series

- Computer ScienceComput. Stat. Data Anal.
- 2003

Constrained Estimation of Mixture Vector Autoregressive Model

- Computer Science

An accurate method for computing standard errors is presented for the model with and without parameter constraints, and a hypothesis-testing approach based on likelihood ratio tests is proposed, which aids in the selection of unnecessary parameters and leads to the greater efficiency at the estimation.

A Mixture Autoregressive Model Based on Student's t-Distribution

- Mathematics
- 2018

A new mixture autoregressive model based on Student’s t–distribution is proposed. A key feature of our model is that the conditional t–distributions of the component models are based on…

AN APPLICATION OF THE MIXTURE AUTOREGRESSIVE MODEL: A CASE STUDY OF MODELLING YEARLY SUNSPOT DATA

- Mathematics
- 2003

Many nonlinear time series models have been proposed in the literature in the past two decades. Numerous successful applications of these models are reported. These models usually specify a nonlinear…

## References

SHOWING 1-10 OF 36 REFERENCES

Modeling flat stretches, bursts, and outliers in time series using mixture transition distribution models

- Computer Science
- 1996

The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series and the stationarity and autocorrelation properties of the models are derived.

THRESHOLD TIME SERIES MODELS AS MULTIMODAL DISTRIBUTION JUMP PROCESSES

- Mathematics
- 1992

. Recent contributions by Tong and others in modelling time series exhibiting threshold points have generally been based on approximating non-linear processes by piecewise linear time series models.…

Mixture models for time series

- Mathematics
- 1995

In this paper we extend the class of zero-order threshold autoregressive models to a much richer class of mixture models. The new class has the important property of duality which, as we show,…

Modelling and Residual Analysis of Nonlinear Autoregressive Time Series in Exponential Variables

- Mathematics
- 1985

Abstract : An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by analysis of a long series of…

Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation

- Mathematics
- 1982

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional…

First-order autoregressive gamma sequences and point processes

- MathematicsAdvances in Applied Probability
- 1980

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are…

Time series analysis, forecasting and control

- Computer Science
- 1970

This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.

Using Bootstrap Likelihood Ratio in Finite Mixture Models

- Mathematics
- 1994

The maximum likelihood estimator is shown to converge to the subset characterized by the same density function, and connection is made to the bootstrap method proposed by Aitkin and co-workers and McLachlan for testing the number of components in a finite mixture and deriving confidence regions in a infinite mixture.

The estimation of the order of a mixture model

- Mathematics
- 1997

We propose a new method to estimate the number of different populations when a large sample of a mixture of these populations is observed. It is possible to define the number of different populations…