Presence Of Level Shifts Research Articles

Modeling Latin-American stock markets volatility: Varying probabilities and mean reversion in a random level shift model

Following Xu and Perron (2014), I applied the extended RLS model to the daily stock market returns of Argentina, Brazil, Chile, Mexico and Peru. This model replaces the constant probability of level shifts for the entire sample with varying probabilities that record periods with extremely negative returns. Furthermore, it incorporates a mean reversion mechanism with which the magnitude and the sign of the level shift component vary in accordance with past level shifts that deviate from the long-term mean. Therefore, four RLS models are estimated: the Basic RLS, the RLS with varying probabilities, the RLS with mean reversion, and a combined RLS model with mean reversion and varying probabilities. The results show that the estimated parameters are highly significant, especially that of the mean reversion model. An analysis of ARFIMA and GARCH models is also performed in the presence of level shifts, which shows that once these shifts are taken into account in the modeling, the long memory characteristics and GARCH effects disappear. Also, I find that the performance prediction of the RLS models is superior to the classic models involving long memory as the ARFIMA(p,d,q) models, the GARCH and the FIGARCH models. The evidence indicates that except in rare exceptions, the RLS models (in all its variants) are showing the best performance or belong to the 10% of the Model Confidence Set (MCS). On rare occasions the GARCH and the ARFIMA models appear to dominate but they are rare exceptions. When the volatility is measured by the squared returns, the great exception is Argentina where a dominance of GARCH and FIGARCH models is appreciated.

Estimation of the long‐memory stochastic volatility model parameters that is robust to level shifts and deterministic trends

I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short‐memory models, can be used to estimate the long‐memory stochastic volatility model parameters in the presence of additive low‐frequency contamination in log‐squared returns. The types of low‐frequency contamination covered include level shifts as well as deterministic trends. I establish consistency and asymptotic normality in the presence or absence of such low‐frequency contamination under certain conditions on the growth rate of the trimming parameter. I also provide theoretical guidance on the choice of trimming parameter by heuristically obtaining its asymptotic MSE‐optimal rate under certain types of low‐frequency contamination. A simulation study examines the finite sample properties of the robust estimator, showing substantial gains from its use in the presence of level shifts. The finite sample analysis also explores how different levels of trimming affect the parameter estimates in the presence and absence of low‐frequency contamination and long‐memory.

Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends

I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared returns. The types of lowfrequency contamination covered include level shifts as well as deterministic trends. I establish consistency and asymptotic normality in the presence or absence of such lowfrequency contamination under certain conditions on the growth rate of the trimming parameter. I also provide theoretical guidance on the choice of trimming parameter by heuristically obtaining its asymptotic MSE-optimal rate under certain types of lowfrequency contamination. A simulation study examines the finite sample properties of the robust estimator, showing substantial gains from its use in the presence of level shifts. The finite sample analysis also explores how different levels of trimming affect the parameter estimates in the presence and absence of low-frequency contamination and long-memory.

Regression-based, regression-free and model-free approaches for robust online scale estimation

This paper compares the methods for variability extraction from a univariate time series in real time. The online scale estimation is achieved by applying a robust scale functional to a moving time window. Scale estimators based on the residuals of a preceding regression step are compared with regression-free and model-free techniques in a simulation study and in an application to a real time series. In the presence of level shifts or strong non-linear trends in the signal level, the model-free scale estimators perform especially well. However, the investigated regression-free and regression-based methods have higher breakdown points, they are applicable to data containing temporal correlations, and they are much more efficient.

Regression-Based, Regression-Free and Model-Free Approaches for Robust Online Scale Estimation

This paper compares methods for variability extraction from a univariate time series in real time. The online scale estimation is achieved by applying a robust scale functional to a moving time window. Scale estimators based on the residuals of a preceding regression step are compared with regressionfree and model-free techniques in a simulation study and in an application to a real time series. In the presence of level shifts or strong non-linear trends in the signal level, the model-free scale estimators perform especially well. However, the investigated regression-free and regression-based methods have higher breakdown points, they are applicable to data containing temporal correlations, and they are much more efficient.

Forecasting in the Presence of Level Shifts

This article addresses the problem of forecasting time series that are subject to level shifts. Processes with level shifts possess a nonlinear dependence structure. Using the stochastic permanent breaks (STOPBREAK) model, I model this nonlinearity in a direct and flexible way that avoids imposing a discrete regime structure. I apply this model to the rate of price inflation in the United States, which I show is subject to level shifts. These shifts significantly affect the accuracy of out-of-sample forecasts, causing models that assume covariance stationarity to be substantially biased. Models that do not assume covariance stationarity, such as the random walk, are unbiased but lack precision in periods without shifts. I show that the STOPBREAK model outperforms several alternative models in an out-of-sample inflation forecasting experiment.

Forecasting in the presence of level shifts

This article addresses the problem of forecasting time series that are subject to level shifts. Processes with level shifts possess a nonlinear dependence structure. Using the stochastic permanent breaks (STOPBREAK) model, I model this nonlinearity in a direct and flexible way that avoids imposing a discrete regime structure. I apply this model to the rate of price inflation in the United States, which I show is subject to level shifts. These shifts significantly affect the accuracy of out-of-sample forecasts, causing models that assume covariance stationarity to be substantially biased. Models that do not assume covariance stationarity, such as the random walk, are unbiased but lack precision in periods without shifts. I show that the STOPBREAK model outperforms several alternative models in an out-of-sample inflation forecasting experiment. Copyright © 2005 John Wiley & Sons, Ltd.

Detecting Level Shifts in Time Series

This article demonstrates the difficulty that traditional outlier detection methods, such as that of Tsay, have in identifying level shifts in time series. Initializing the outlier/level-shift search with an estimated autoregressive moving average model lowers the power of the level-shift detection statistics. Furthermore, the rule employed by these methods for distinguishing between level shifts and innovation outliers does not work well in the presence of level shifts. A simple modification to Tsay's procedure is proposed that improves the ability to correctly identify level shifts. This modification is relatively easy to implement and appears to be quite effective in practice.