
on Econometric Time Series 
By:  Nima Nonejad (Aarhus University and CREATES) 
Abstract:  We propose a flexible model to describe nonlinearities and longrange dependence in time series dynamics. Our model is an extension of the heterogeneous autoregressive model. Structural breaks occur through mixture distributions in state innovations of linear Gaussian state space models. Monte Carlo simulations evaluate the properties of the estimation procedures. Results show that the proposed model is viable and flexible for purposes of forecasting volatility. Model uncertainty is accounted for by employing Bayesian model averaging. Bayesian model averaging provides very competitive forecasts compared to any single model specification. It provides further improvements when we average over nonlinear specifications. 
Keywords:  Mixture innovation models, Markov chain Monte Carlo, Realized volatility 
JEL:  C11 C22 C51 C53 
Date:  2013–08–13 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201324&r=ets 
By:  Nima Nonejad (Aarhus University and CREATES) 
Abstract:  This paper proposes a model that simultaneously captures long memory and structural breaks. We model structural breaks through irreversible Markov switching or socalled changepoint dynamics. The parameters subject to structural breaks and the unobserved states which determine the position of the structural breaks are sampled from the joint posterior density by sampling from their respective conditional posteriors using Gibbs sampling and MetropolisHastings. Monte Carlo simulations demonstrate that the proposed estimation approach is effective in identifying and dating structural breaks. Applied to daily S&P 500 data, one finds strong evidence of three structural breaks. The evidence of these breaks is robust to different specifications including a GARCH specification for the conditional variance of volatility. 
Keywords:  Long memory, Structural breaks, Changepoints, Gibbs sampling 
JEL:  C22 C11 C52 G10 
Date:  2013–08–13 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201326&r=ets 
By:  Nima Nonejad (Aarhus University and CREATES) 
Abstract:  This paper details Particle Markov chain Monte Carlo techniques for analysis of unobserved component time series models using several economic data sets. PMCMC combines the particle filter with the MetropolisHastings algorithm. Overall PMCMC provides a very compelling, computationally fast and efficient framework for estimation. These advantages are used to for instance estimate stochastic volatility models with leverage effect or with Studentt distributed errors. We also model changing time series characteristics of the US inflation rate by considering a heteroskedastic ARFIMA model where the heteroskedasticity is specified by means of a Gaussian stochastic volatility process. 
Keywords:  Particle filter, MetropolisHastings, Unobserved components, Bayes 
JEL:  C22 C11 C63 
Date:  2013–08–13 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201327&r=ets 
By:  Kees Jan van Garderen; H. Peter Boswijk 
Abstract:  The maximum likelihood estimator of the adjustment coefficient in a cointegrated vector autoregressive model (CVAR) is generally biased. For the case where the cointegrating vector is known in a firstorder CVAR with no intercept, we derive a condition for the unbiasedness of the maximum likelihood estimator of the adjustment coefficients, and provide a simple characterization of the bias in case this condition is violated. A feasible bias correction method is shown to virtually eliminate the bias over a large part of the parameter space. 
Date:  2013–06–04 
URL:  http://d.repec.org/n?u=RePEc:ame:wpaper:1305&r=ets 
By:  Arturas Juodis 
Abstract:  This paper considers estimation of Panel Vectors Autoregressive Models of order 1 (PVAR(1)) with possible crosssectional heteroscedasticity in the error terms. We focus on fixed T consistent estimation methods in First differences (FD) with or without additional strictly exogenous regressors. Additional results for the Panel FD OLS estimator and the FDLS estimator of Han and Phillips (2010) are provided. In the covariance stationary case it is shown that the univariate moment conditions of the latter estimator are violated for general parameter matrices in the multivariate case. Furthermore, we simplify the analysis of Binder, Hsiao, and Pesaran (2005) by providing analytical results for the _rst two derivatives of the Transformed Maximum Likelihood (TML) function. We extend the original model by taking into account possible crosssectional heteroscedasticity and presence of strictly exogenous regressors. Moreover, we show that in the three wave panel the loglikelihood function of the unrestricted TML estimator violates the global identification assumption. The finitesample performance of the analyzed methods is investigated in a Monte Carlo study. Results indicate that under effect stationarity the TML estimator encounters problems with global identification even for moderate values of T. 
Date:  2013–06–05 
URL:  http://d.repec.org/n?u=RePEc:ame:wpaper:1306&r=ets 
By:  Maurice J.G. Bun; Frank Kleibergen 
Abstract:  We show that Dif(ference), see Arellano and Bond (1991), Lev(el), see Arellano and Bover (1995) and Blundell and Bond (1998), or the N(on)L(inear) moment conditions of Ahn and Schmidt (1995) do not identify the parameters of a firstorder autoregressive panel data model when the autoregressive parameter is equal to one. Combinations of the Dif and Lev, resulting in Sys(tem), moment conditions and the Dif and NL, resulting in A(hn)S(chmidt), moment conditions identify the parameters when there are four or more time periods. The behaviour of one step and two step GMM estimators, however, remains nonstandard. We therefore use size correct GMM statistics, like, the GMMAR, GMMLM or KLM statistic, to conduct inference. We compare their worst case large sample distributions with the power envelope to determine the optimal statistic. The power envelope involves a quartic root convergence rate which further indicates the nonstandard identification issues. The worst case large sample distribution of the KLM statistic coincides with the power envelope whilst the one of the GMMLM statistic only does so when there are four time periods. It shows that the KLM statistic is efficient both when the autoregressive parameter is one or less than one. The power envelopes for the AS and Sys moment conditons are identical so assuming mean stationarity does not help for identification. 
Date:  2013–06–20 
URL:  http://d.repec.org/n?u=RePEc:ame:wpaper:1307&r=ets 
By:  D. S. Grebenkov; J. Serror 
Abstract:  We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both autocorrelation level and transaction costs. Theoretical results are illustrated on the Dow Jones index. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.5658&r=ets 
By:  Roland Langrock; Th\'eo Michelot; Alexander Sohn; Thomas Kneib 
Abstract:  Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. A substantial body of research deals with various techniques for fitting relatively basic SV models, which assume the returns to be conditionally normally distributed or Studenttdistributed, given the volatility. In this manuscript, we consider a frequentist framework for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape. More specifically, we suggest to represent the density of the conditional distribution as a linear combination of standardized Bspline basis functions, imposing a penalty term in order to arrive at a good balance between goodness of fit and smoothness. This allows us to employ the efficient hidden Markov model machinery in order to fit the model and to assess its predictive performance. We demonstrate the feasibility of the approach in a simulation study before applying it to three series of returns on stocks and one series of stock index returns. The nonparametric approach leads to an improved predictive capacity in some cases, and we find evidence for the conditional distributions being leptokurtic and negatively skewed. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.5836&r=ets 
By:  Sucarrat, Genaro; Grønneberg, Steffen; Escribano, Alvaro 
Abstract:  Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when additional exogenous or predetermined variables ("X") are included in the volatility specification. Here, we propose estimation and inference methods for univariate and multivariate Generalised logARCHX (i.e. logGARCHX) models when the conditional density is not known via (V)ARMAX representations. The multivariate specification allows for volatility feedback across equations, and timevarying correlations can be fitted in a subsequent step. Finally, our empirical applications on electricity prices show that the modelclass is particularly useful when the Xvector is highdimensional. 
Keywords:  ARCH, exponential GARCH, logGARCH, ARMAX, Multivariate GARCH 
JEL:  C22 C32 C51 C52 
Date:  2013–08–11 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:49344&r=ets 