A robust Cusum test for SETAR‐type nonlinearity in time series

As a part of an effective self‐exciting threshold autoregressive (SETAR) modeling methodology, it is important to identify processes exhibiting SETAR‐type nonlinearity. A number of tests of nonlinearity have been developed in the literature. However, it has recently been shown that all these tests perform poorly for SETAR‐type nonlinearity detection in the presence of additive outliers. In this paper, we develop an improved test for SETAR‐type nonlinearity in time series. The test is an outlier‐robust test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits. A Monte Carlo study confirms that the proposed test is competitive with existing tests for data from uncontaminated SETAR models and superior to them for SETAR data contaminated with additive outliers. Copyright © 2008 John Wiley & Sons, Ltd.     

A Robust Test for Threshold‐Type Nonlinearity in Multivariate Time Series Analysis

There is growing interest in exploring potential forecast gains from the nonlinear structure of multivariate threshold autoregressive (MTAR) models. A least squares‐based statistical test has been proposed in the literature. However, previous studies on univariate time series analysis show that classical nonlinearity tests are often not robust to additive outliers. The outlier problem is expected to pose similar difficulties for multivariate nonlinearity tests. In this paper, we propose a new and robust MTAR‐type nonlinearity test, and derive the asymptotic null distribution of the test statistic. A Monte Carlo experiment is carried out to compare the power of the proposed test with that of the least squares‐based test under the influence of additive time series outliers. The results indicate that the proposed method is preferable to the classical test when observations are contaminated by outliers. Finally, we provide illustrative examples by applying the statistical tests to two real datasets. Copyright © 2015 John Wiley & Sons, Ltd.     

Robustness of alternative non‐linearity tests for SETAR models

In recent years there has been a growing interest in exploiting potential forecast gains from the non‐linear structure of self‐exciting threshold autoregressive (SETAR) models. Statistical tests have been proposed in the literature to help analysts check for the presence of SETAR‐type non‐linearities in an observed time series. It is important to study the power and robustness properties of these tests since erroneous test results might lead to misspecified prediction problems. In this paper we investigate the robustness properties of several commonly used non‐linearity tests. Both the robustness with respect to outlying observations and the robustness with respect to model specification are considered. The power comparison of these testing procedures is carried out using Monte Carlo simulation. The results indicate that all of the existing tests are not robust to outliers and model misspecification. Finally, an empirical application applies the statistical tests to stock market returns of the four little dragons (Hong Kong, South Korea, Singapore and Taiwan) in East Asia. The non‐linearity tests fail to provide consistent conclusions most of the time. The results in this article stress the need for a more robust test for SETAR‐type non‐linearity in time series analysis and forecasting. Copyright © 2004 John Wiley & Sons, Ltd.     

On robust estimation of threshold autoregressions

We investigate the effects of additive outliers on the least squares (LS) estimation of threshold autoregressive models. The class of generalized-M (GM) estimates for linear time series is modified and applied to non-linear threshold processes. A Monte Carlo experiment is carried out to study the robust properties of these estimates. Their relative forecasting performances are also examined. The results indicate that the GM method is preferable to the LS estimation when the observations are contaminated by additive outliers. A real example is also given to illustrate the proposed method.     

Robust forecasting with exponential and Holt–Winters smoothing

Robust versions of the exponential and Holt–Winters smoothing method for forecasting are presented. They are suitable for forecasting univariate time series in the presence of outliers. The robust exponential and Holt–Winters smoothing methods are presented as recursive updating schemes that apply the standard technique to pre‐cleaned data. Both the update equation and the selection of the smoothing parameters are robustified. A simulation study compares the robust and classical forecasts. The presented method is found to have good forecast performance for time series with and without outliers, as well as for fat‐tailed time series and under model misspecification. The method is illustrated using real data incorporating trend and seasonal effects. Copyright © 2009 John Wiley & Sons, Ltd.     

Guaranteed‐content prediction intervals for non‐linear autoregressions

In this paper we present guaranteed‐content prediction intervals for time series data. These intervals are such that their content (or coverage) is guaranteed with a given high probability. They are thus more relevant for the observed time series at hand than classical prediction intervals, whose content is guaranteed merely on average over hypothetical repetitions of the prediction process. This type of prediction inference has, however, been ignored in the time series context because of a lack of results. This gap is filled by deriving asymptotic results for a general family of autoregressive models, thereby extending existing results in non‐linear regression. The actual construction of guaranteed‐content prediction intervals directly follows from this theory. Simulated and real data are used to illustrate the practical difference between classical and guaranteed‐content prediction intervals for ARCH models. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust modelling of ARCH models

The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the conditional scale. We examine the L₁‐estimation of ARCH models and derive the limiting distributions of the estimators. A robust standardized absolute residual autocorrelation based on least absolute deviation estimation is proposed. Then a robust portmanteau statistic is constructed to test the adequacy of the model, especially the specification of the conditional scale. We obtain their asymptotic distributions under mild conditions. Examples show that the suggested L₁‐norm estimators and the goodness‐of‐fit test are robust against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright © 2001 John Wiley & Sons, Ltd.     

On SETAR non‐linearity and forecasting

We compare linear autoregressive (AR) models and self‐exciting threshold autoregressive (SETAR) models in terms of their point forecast performance, and their ability to characterize the uncertainty surrounding those forecasts, i.e. interval or density forecasts. A two‐regime SETAR process is used as the data‐generating process in an extensive set of Monte Carlo simulations, and we consider the discriminatory power of recently developed methods of forecast evaluation for different degrees of non‐linearity. We find that the interval and density evaluation methods are unlikely to show the linear model to be deficient on samples of the size typical for macroeconomic data. Copyright © 2003 John Wiley & Sons, Ltd.     

Outlier Detection in Regression Models with ARIMA Errors using Robust Estimates

A diagnostic procedure for detecting additive and innovation outliers as well as level shifts in a regression model with ARIMA errors is introduced. The procedure is based on a robust estimate of the model parameters and on innovation residuals computed by means of robust filtering. A Monte Carlo study shows that, when there is a large proportion of outliers, this procedure is more powerful than the classical methods based on maximum likelihood type estimates and Kalman filtering. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust exponential smoothing

The paper is devoted to robust modifications of exponential smoothing for time series with outliers or long-tailed distributions. Classical exponential smoothing applied to such time series is sensitive to the presence of outliers or long-tailed distributions and may give inadequate smoothing and forecasting results. First, simple and double exponential smoothing in the L₁ norm (i.e. based on the least absolute deviations) are discussed in detail. Then, general exponential smoothing is made robust, replacing the least squares approach by M-estimation in such a way that the recursive character of the final formulas is preserved. The paper gives simple algorithmic procedures which preserve advantageous features of classical exponential smoothing and, in addition, which are less sensitive to outliers. Robust versions are compared numerically with classical ones.     

Real‐time or current vintage: does the type of data matter for forecasting and model selection?

In this paper we investigate the impact of data revisions on forecasting and model selection procedures. A linear ARMA model and nonlinear SETAR model are considered in this study. Two Canadian macroeconomic time series have been analyzed: the real‐time monetary aggregate M3 (1977–2000) and residential mortgage credit (1975–1998). The forecasting method we use is multi‐step‐ahead non‐adaptive forecasting. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Simultaneously High‐Dimensional Time Series: A Robust Model‐Based Clustering Approach

This paper considers the problem of forecasting high‐dimensional time series. It employs a robust clustering approach to perform classification of the component series. Each series within a cluster is assumed to follow the same model and the data are then pooled for estimation. The classification is model‐based and robust to outlier contamination. The robustness is achieved by using the intrinsic mode functions of the Hilbert–Huang transform at lower frequencies. These functions are found to be robust to outlier contamination. The paper also compares out‐of‐sample forecast performance of the proposed method with several methods available in the literature. The other forecasting methods considered include vector autoregressive models with ∕ without LASSO, group LASSO, principal component regression, and partial least squares. The proposed method is found to perform well in out‐of‐sample forecasting of the monthly unemployment rates of 50 US states. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecast Combinations in a DSGE‐VAR Lab

We explore the benefits of forecast combinations based on forecast‐encompassing tests compared to simple averages and to Bates–Granger combinations. We also consider a new combination algorithm that fuses test‐based and Bates–Granger weighting. For a realistic simulation design, we generate multivariate time series samples from a macroeconomic DSGE‐VAR (dynamic stochastic general equilibrium–vector autoregressive) model. Results generally support Bates–Granger over uniform weighting, whereas benefits of test‐based weights depend on the sample size and on the prediction horizon. In a corresponding application to real‐world data, simple averaging performs best. Uniform averages may be the weighting scheme that is most robust to empirically observed irregularities. Copyright © 2016 John Wiley & Sons, Ltd.     

The variance ratio and trend stationary model as extensions of a constrained autoregressive model

This paper shows that a constrained autoregressive model that assigns linearly decreasing weights to past observations of a stationary time series has important links to the variance ratio methodology and trend stationary model. It is demonstrated that the proposed autoregressive model is asymptotically related to the variance ratio through the weighting schedules that these two tools use. It is also demonstrated that under a trend stationary time series process the proposed autoregressive model approaches a trend stationary model when the memory of the autoregressive model is increased. These links create a theoretical foundation for tests that confront the random walk model simultaneously against a trend stationary and a variety of short‐ and long‐memory autoregressive alternatives. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting volatility with outliers in GARCH models

In this paper, we detect and correct abnormal returns in 17 French stocks returns and the French index CAC40 from additive‐outlier detection method in GARCH models developed by Franses and Ghijsels (1999) and extended to innovative outliers by Charles and Darné (2005). We study the effects of outlying observations on several popular econometric tests. Moreover, we show that the parameters of the equation governing the volatility dynamics are biased when we do not take into account additive and innovative outliers. Finally, we show that the volatility forecast is better when the data are cleaned of outliers for several step‐ahead forecasts (short, medium‐ and long‐term) even if we consider a GARCH‐t process. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting volatility by means of threshold models

The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out‐of‐sample forecasting ability of the SETAR‐Threshold GARCH (SETAR‐TGARCH) and the SETAR‐Threshold Stochastic Volatility (SETAR‐THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ‘true’ underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR‐THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd.     

A forecasting procedure for nonlinear autoregressive time series models

Forecasting for nonlinear time series is an important topic in time series analysis. Existing numerical algorithms for multi‐step‐ahead forecasting ignore accuracy checking, alternative Monte Carlo methods are also computationally very demanding and their accuracy is difficult to control too. In this paper a numerical forecasting procedure for nonlinear autoregressive time series models is proposed. The forecasting procedure can be used to obtain approximate m‐step‐ahead predictive probability density functions, predictive distribution functions, predictive mean and variance, etc. for a range of nonlinear autoregressive time series models. Examples in the paper show that the forecasting procedure works very well both in terms of the accuracy of the results and in the ability to deal with different nonlinear autoregressive time series models. Copyright © 2005 John Wiley & Sons, Ltd.     

Bicorrelations and cross‐bicorrelations as non‐linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross‐bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non‐linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high‐frequency exchange rate returns, and their out‐of‐sample forecasting performance is compared to that of other time series models. Copyright © 2001 John Wiley & Sons, Ltd.     

Can urban coffee consumption help predict US inflation?

Motivated by the importance of coffee to Americans and the significance of the coffee subsector to the US economy, we pursue three notable innovations. First, we augment the traditional Phillips curve model with the coffee price as a predictor, and show that the resulting model outperforms the traditional variant in both in‐sample and out‐of‐sample predictability of US inflation. Second, we demonstrate the need to account for the inherent statistical features of predictors such as persistence, endogeneity, and conditional heteroskedasticity effects when dealing with US inflation. Consequently, we offer robust illustrations to show that the choice of estimator matters for improved US inflation forecasts. Third, the proposed augmented Phillips curve also outperforms time series models such as autoregressive integrated moving average and the fractionally integrated version for both in‐sample and out‐of‐sample forecasts. Our results show that augmenting the traditional Phillips curve with the urban coffee price will produce better forecast results for US inflation only when the statistical effects are captured in the estimation process. Our results are robust to alternative measures of inflation, different data frequencies, higher order moments, multiple data samples and multiple forecast horizons.     

Detection of outliers and level shifts in time series: an evaluation of two alternative procedures

A unified method to detect and handle innovational and additive outliers, and permanent and transient level changes has been presented by R. S. Tsay. N. S. Balke has found that the presence of level changes may lead to misidentification and loss of test‐power, and suggests augmenting Tsay's procedure by conducting an additional disturbance search based on a white‐noise model. While Tsay allows level changes to be either permanent or transient, Balke considers only the former type. Based on simulated series with transient level changes this paper investigates how Balke's white‐noise model performs both when transient change is omitted from the model specification and when it is included. Our findings indicate that the alleged misidentification of permanent level changes may be influenced by the restrictions imposed by Balke. But when these restrictions are removed, Balke's procedure outperforms Tsay's in detecting changes in the data‐generating process. Copyright © 2000 John Wiley & Sons, Ltd.