
on Econometric Time Series 
By:  Herwartz, Helmut; Maxand, Simone; Walle, Yabibal M. 
Abstract:  Standard panel unit root tests (PURTs) are not robust to breaks in innovation variances. Consequently, recent papers have proposed PURTs that are pivotal in the presence of volatility shifts. The applicability of these tests, however, has been restricted to cases where the data contains only an intercept, and not a linear trend. This paper proposes a new heteroskedasticityrobust PURT that works well for trending data. Under the null hypothesis, the test statistic has a limiting Gaussian distribution. Simulation results reveal that the test tends to be conservative but shows remarkable power in finite samples. 
Keywords:  panel unit root tests,nonstationary volatility,crosssectional dependence,near epoch dependence,energy use per capita 
JEL:  C23 C12 Q40 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:zbw:cegedp:314&r=ets 
By:  Helmut Lütkepohl; Thore Schlaak 
Abstract:  The performance of information criteria and tests for residual heteroskedasticity for choosing between different models for timevarying volatility in the context of structural vector autoregressive analysis is investigated. Although it can be difficult to find the true volatility model with the selection criteria, using them is recommended because they can reduce the mean squared error of impulse response estimates substantially relative to a model that is chosen arbitrarily based on the personal preferences of a researcher. Heteroskedasticity tests are found to be useful tools for deciding whether timevarying volatility is present but do not discriminate well between different types of volatility changes. The selection methods are illustrated by specifying a model for the global market for crude oil. 
Keywords:  Structural vector autoregression, identification via heteroskedasticity, conditional heteroskedasticity, smooth transition, Markov switching, GARCH 
JEL:  C32 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1672&r=ets 
By:  Dan Pirjol; Lingjiong Zhu 
Abstract:  We consider the stochastic volatility model $dS_t = \sigma_t S_t dW_t,d\sigma_t = \omega \sigma_t dZ_t$, with $(W_t,Z_t)$ uncorrelated standard Brownian motions. This is a special case of the HullWhite and the $\beta=1$ (lognormal) SABR model, which are widely used in financial practice. We study the properties of this model, discretized in time under several applications of the EulerMaruyama scheme, and point out that the resulting model has certain properties which are different from those of the continuous time model. We study the asymptotics of the timediscretized model in the $n\to \infty$ limit of a very large number of time steps of size $\tau$, at fixed $\beta=\frac12\omega^2\tau n^2$ and $\rho=\sigma_0^2\tau$, and derive three results: i) almost sure limits, ii) fluctuation results, and iii) explicit expressions for growth rates (Lyapunov exponents) of the positive integer moments of $S_t$. Under the EulerMaruyama discretization for $(S_t,\log \sigma_t)$, the Lyapunov exponents have a phase transition, which appears in numerical simulations of the model as a numerical explosion of the asset price moments. We derive criteria for the appearance of these explosions. 
Date:  2017–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1707.00899&r=ets 
By:  Jiawen Xu (Shanghai University of Finance and Economics); Pierre Perron (Boston University) 
Abstract:  We present a frequentistbased approach to forecast time series in the presence of insample and outofsample breaks in the parameters of the forecasting model. We first model the parameters as following a random level shift process, with the occurrence of a shift governed by a Bernoulli process. In order to have a structure so that changes in the parameters be forecastable, we introduce two modifications. The first models the probability of shifts according to some covariates that can be forecasted. The second incorporates a builtin mean reversion mechanism to the time path of the parameters. Similar modifications can also be made to model changes in the variance of the error process. Our full model can be cast into a conditional linear and Gaussian state space framework. To estimate it, we use the mixture Kalman filter and a Monte Carlo expectation maximization algorithm. Simulation results show that our proposed forecasting model provides improved forecasts over standard forecasting models that are robust to model misspeciÖcations. We provide two empirical applications and compare the forecasting performance of our approach with a variety of alternative methods. These show that substantial gains in forecasting accuracy are obtained. 
Keywords:  onstabilities; structural change; forecasting; random level shifts; mixture Kalman filter. 
JEL:  C22 C53 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:bos:wpaper:wp2017004&r=ets 
By:  Dukpa Kim (Korea University); Tatsushi Oka (National University of Singapore); Francisco Estrada (Universidad Nacional AutÃ›noma de MÈxico and VU University Amsterdam); Pierre Perron (Boston University) 
Abstract:  What transpires from recent research is that temperatures and forcings seem to be characterized by a linear trend with two changes in the rate of growth. The first occurs in the early 60s and indicates a very large increase in the rate of growth of both temperatures and radiative forcings. This was termed as the "onset of sustained global warming". The second is related to the more recent socalled hiatus period, which suggests that temperatures and total radiative forcings have increased less rapidly since the mid90s compared to the larger rate of increase from 1960 to 1990. There are two issues that remain unresolved. The Örst is whether the breaks in the slope of the trend functions of temperatures and radiative forcings are common. This is important because common breaks coupled with the basic science of climate change would strongly suggest a causal effect from anthropogenic factors to temperatures. The second issue relates to establishing formally via a proper testing procedure that takes into account the noise in the series, whether there was indeed a 'hiatus period' for temperatures since the mid 90s. This is important because such a test would counter the widely held view that the hiatus is the product of natural internal variability. Our paper provides tests related to both issues. The results show that the breaks in temperatures and forcings are common and that the hiatus is characterized by a significant decrease in the rate of growth of temperatures and forcings. The statistical results are of independent interest and applicable more generally. 
Keywords:  ultiple Breaks, Common Breaks, Multivariate Regressions, Joined Segmented Trend. 
JEL:  C32 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:bos:wpaper:wp2017003&r=ets 