Testing for Threshold Effect in ARFIMA Models: Application to US Unemployment Rate Data

Statistics and Its Interface, 2011

Since the pioneering work by Tong (1978, 1983), threshold time series modelling and its applications have become increasingly important for research in economics and finance. A number of books and a vast number of research papers published in this area have been motivated by Tong's threshold models. The goal of this paper is to give a through review on the development of the family of threshold time series model in finance and to provide a streamlined approach to financial time series analysis. It covers threshold modeling, nonlinearity tests, statistical inference, diagnostic checking, and model selection, as well as applications of the threshold autoregressive model and its generalizations in finance.

Studies in Nonlinear Dynamics & Econometrics, 2004

Practical aspects of likelihood-based inference and forecasting of series with long memory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact first-order asymptotic methods are compared. The analysis is extended using modified profile likelihood analysis, which is a higher-order asymptotic method suggested by . The relevance of the differences between the methods is investigated for models and forecasts of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK.

Statistics and Its Interface, 2011

This paper generalizes Ling's (2007) double AR(p) model by considering a threshold effect in the mean equation. Provided the threshold is known, consistency and asymptotic normality of the quasi maximum likelihood estimators for the model are proved under weak conditions. Based on the Lagrange Multiplier principle, a threshold effect test is studied and its asymptotic null distribution is shown to be a functional of a zero-mean Gaussian process. Approximate methods are given to compute the upper percentage points and simulation results show that they perform well. From the empirical studies, we know that the original model can be improved when the threshold effect is considered.

2003

The aim of this paper is to identify permanent and transitory shocks. This identification is done according to the size of the shocks or the size of some other important economic variable. In order to be able to carry this identification scheme on, we introduce a new class of threshold models: threshold integrated moving average models (TIMA). These are integrated models with a threshold structure in the moving average part. In one of the regimes the moving average has a unit root and in the other an invertible one. The former regime corresponds to transitory shocks, while the latter corresponds to permanent shocks. The paper analyzes the impulse response function generated by TIMA models and their invertibility. Consistency and asymptotic normality of least squares estimators are established and hypothesis tests for TIMA models are developed. The paper concludes with an application to exchange rates and stock market prices

2011

Over recent years several methods to deal with high-frequency data (economic, …nancial and other) have been proposed in the literature. An interesting example is for instance intervalvalued time series described by the temporal evolution of high and low prices of an asset. In this paper a new class of threshold models capable of capturing asymmetric e¤ects in interval-valued data is introduced as well as new forecast loss functions and descriptive statistics of the forecast quality proposed. Least squares estimates of the threshold parameter and the regression slopes are obtained; and forecasts based on the proposed threshold model computed. A new forecast procedure based on the combination of this model with the k nearest neighbors method is introduced. To illustrate this approach, we report an application to a weekly sample of S&P500 index returns. The results obtained are encouraging and compare very favorably to available procedures.

2011

Financial instruments are known to exhibit abrupt and dramatic changes in behaviour. This paper investigates the relative efficacy of two-regime threshold autoregressive (TAR) models and smooth threshold autoregressive (STAR) models, applied successfully to econometric dynamics, in the finance domain. The nature of this class of models is explored in relation to the conventional linear modeling approach, with reference to simulated data and real stock return indices.

The Econometrics Journal, 2004

Recent research has focused on the links between long memory and structural breaks, stressing the memory properties that may arise in models with parameter changes. In this paper, we question the implications of this result for forecasting. We contribute to this research by comparing the forecasting abilities of long memory and Markov switching models. Two approaches are employed: the Monte Carlo study and an empirical comparison, using the quarterly Consumer Price inflation rate in Portugal in the period 1968-1998. Although long memory models may capture some in-sample features of the data, we find that their forecasting performance is relatively poor when shifts occur in the series, compared to simple linear and Markov switching models.

Future Business Journal

Background Inflation is the industrious and non-stop ascent in the overall prices of any given commodity in an economy. During the global food crisis, Ethiopia experienced an unprecedented increase in inflation ranked the highest in Africa. It is among the most macroeconomic variable described nonlinear behavior. Objective The main purpose of this study was intended to modeling inflation rate factors on present consumption price index (CPI) in Ethiopia: using the threshold autoregressive (TAR) models. Methods The study was utilized the secondary data collected from monthly data of CPI for inflation rate from January 1994 to December 2020 which was obtained from central statistical Agency. The forecast was applied between the nonlinear and linear ARMA models using different techniques. The unit root test of Dickey–Fuller test was made for each variables and applied lag length transformation for the variables that had unit root. A threshold autoregressive models was utilized for data ...

Communications in Statistics - Simulation and Computation, 2015

We introduce a Bayesian approach to test linear autoregressive movingaverage (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.

Mathematics and Computers in Simulation, 2005

In recent years, research in nonlinear time series analysis has grown rapidly. Substantial empirical evidence of nonlinearities in economic time series fluctuations has been reported in the literature. Nonlinear time series models have the advantage of being able to capture asymmetries, jumps, and time irreversibility which are characteristics of many observed financial and economic time series. As compared to the linear models, the nonlinear time series models provide a much wider spectrum of possible dynamics for the economic time series data. In this paper, we explore the use of nonlinear time series models to analyze Australian interest rates. In particular, we concentrate on the class of bivariate threshold autoregressive (BTAR) models. Monthly Australian interest rates from 1957.1 to 2002.8 are considered. The series under study are 2-year and 15-year government bonds, representing short-term and long-term series in the term structure of interest rates. A BTAR model is fitted to the observed vector series and the results show that the dynamic structure of the two interest rate series depends heavily on the status (expansion versus contraction) of the economy.