List

International Journal of Forecasting (1992), 18(3), 439-454.

P. J. Brockwell1 and R. J. Hyndman2

  1. Statistics Department, Colorado State University, Fort Collins, CO 80523, USA.
  2. Statistics Department, University of Melbourne, Parkville, Vic. 3052, Australia.

Abstract: The use of non-linear models in time series analysis has expanded rapidly in the last ten years, with the development of several useful classes of discrete-time non-linear models. One family of processes which has been found valuable is the class of self-exciting threshold autoregressive (SETAR) models discussed extensively in the books of Tong (1983, 1990). In this paper we consider problems of modelling and forecasting with continuous-time threshold autoregressive (CTAR) processes. Techniques for analyzing such models have been proposed by Tong and Yeung (1991) and Brockwell, Hyndman and Grunwald (1991). In this paper we define a CTAR(p) process X(t) with boundary width 2δ>0 as the first component of a p-dimensional Markov process X(t), defined by a stochastic differential equation. We are primarily concerned with the problems of model-fitting and forecasting when observations are available at times 1, 2, …, N; however, the techniques considered apply equally well to irregularly spaced observations. For practical computations with CTAR processes we approximate the process X(t) by a linearly interpolated discrete-time Markov process whose transitions occur at times jn/n, j = 1, 2, …, with n large. This model is used to fit ‘narrow boundaryÙ CTAR models to both simulated and real data.

Keywords: Non-linear forecasting; Threshold autoregression; State-space representation; Maximum likelihood estimation; Continuous-time autoregression.

Online article

  Posts

1 2 3 5
December 7th, 2016

Exploring the influence of short-term temperature patterns on temperature-related mortality: a case-study of Melbourne, Australia

October 13th, 2016

Reconciling forecasts: the hts and thief packages

September 20th, 2016

smoothAPC package for R

September 20th, 2016

stR package for R

September 14th, 2016

Grouped functional time series forecasting: an application to age-specific mortality rates

August 30th, 2016

Forecasting large collections of related time series

August 22nd, 2016

thief package for R

June 21st, 2016

Exploring time series collections used for forecast evaluation

June 9th, 2016

Associations between outdoor fungal spores and childhood and adolescent asthma hospitalisations

May 25th, 2016

ISCRR time series workshop

May 19th, 2016

Visualising Forecasting Algorithm Performance using Time Series Instance Spaces

May 6th, 2016

Automatic foRecasting using R

February 29th, 2016

On sampling methods for costly multi-objective black-box optimization

February 19th, 2016

Dynamic Algorithm Selection for Pareto Optimal Set Approximation

February 4th, 2016

Forecasting uncertainty in electricity smart meter data by boosting additive quantile regression

January 30th, 2016

Bayesian rank selection in multivariate regressions

January 25th, 2016

Probabilistic Energy Forecasting: Global Energy Forecasting Competition 2014 and Beyond

January 24th, 2016

Long-term forecasts of age-specific participation rates with functional data models

January 1st, 2016

Bagging exponential smoothing methods using STL decomposition and Box-Cox transformation

January 1st, 2016

Fast computation of reconciled forecasts for hierarchical and grouped time series

December 31st, 2015

Measuring forecast accuracy

November 26th, 2015

Forecasting hierarchical and grouped time series through trace minimization

November 2nd, 2015

Forecasting big time series data using R

October 7th, 2015

Optimal forecast reconciliation for big time series data

October 5th, 2015

Google workshop: Forecasting and visualizing big time series data

September 16th, 2015

Unbelievable

August 29th, 2015

Forecasting with temporal hierarchies

August 25th, 2015

New IJF editors

August 17th, 2015

Machine learning bootcamp

August 7th, 2015

Statistical issues with using herbarium data for the estimation of invasion lag-phases

June 30th, 2015

Exploring the feature space of large collections of time series

June 26th, 2015

Exploring the boundaries of predictability: what can we forecast, and when should we give up?

June 25th, 2015

Automatic algorithms for time series forecasting

June 23rd, 2015

MEFM: An R package for long-term probabilistic forecasting of electricity demand

June 19th, 2015

Probabilistic forecasting of peak electricity demand

June 10th, 2015

Do human rhinovirus infections and food allergy modify grass pollen–induced asthma hospital admissions in children?

June 8th, 2015

STR: A Seasonal-Trend Decomposition Procedure Based on Regression

June 4th, 2015

Probabilistic time series forecasting with boosted additive models: an application to smart meter data

June 1st, 2015

Large-scale unusual time series detection

May 26th, 2015

Visualization of big time series data

May 22nd, 2015

Probabilistic forecasting of long-term peak electricity demand

April 20th, 2015

A note on the validity of cross-validation for evaluating time series prediction

April 4th, 2015

Discussion of “High-dimensional autocovariance matrices and optimal linear prediction”

April 1st, 2015

Change to the IJF editors

February 23rd, 2015

Visualization and forecasting of big time series data

January 12th, 2015

Visualizing and forecasting big time series data

December 24th, 2014

Bivariate data with ridges: two-dimensional smoothing of mortality rates

December 17th, 2014

MEFM package for R

October 21st, 2014

Optimally reconciling forecasts in a hierarchy

September 23rd, 2014

Forecasting: principles and practice (UWA course)