
on Econometric Time Series 
By:  Vladimir Filimonov; Guilherme Demos; Didier Sornette 
Abstract:  We present a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterised by a large number of parameters. We apply the general approach to the LogPeriodic Power Law Singularity (LPPLS) model of financial bubbles. This model is particularly relevant because one of its parameters, the critical time $t_c$ signalling the burst of the bubble, is arguably the target of choice for dynamical risk management. However, previous calibrations of the LPPLS model have shown that the estimation of $t_c$ is in general quite unstable. Here, we provide a rigorous likelihood inference approach to determine $t_c$, which takes into account the impact of the other nonlinear (socalled "nuisance") parameters for the correct adjustment of the uncertainty on $t_c$. This provides a rigorous interval estimation for the critical time, rather than a point estimation in previous approaches. As a bonus, the interval estimations can also be obtained for the nuisance parameters ($m,\omega$, damping), which can be used to improve filtering of the calibration results. We show that the use of the modified profile likelihood method dramatically reduces the number of local extrema by constructing much simpler smoother loglikelihood landscapes. The remaining distinct solutions can be interpreted as genuine scenarios that unfold as the time of the analysis flows, which can be compared directly via their likelihood ratio. Finally, we develop a multiscale profile likelihood analysis to visualize the structure of the financial data at different scales (typically from 100 to 750 days). We test the methodology successfully on synthetic price time series and on three wellknown historical financial bubbles. 
Date:  2016–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1602.08258&r=ets 
By:  Dufays, A. (Université catholique de Louvain, CORE, Belgium); Rombouts, V. (ESSEC Business School) 
Abstract:  Changepoint time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an overparametrization issue since typically only one latent state vari able drives the breaks in all parameters. This implies that all parameters have to change when a break happens. We introduce sparse changepoint processes, a new approach for detecting which parameters change over time. We propose shrinkage prior distributions allowing to control model parsimony by limiting the number of parameters which evolve from one structural break to another. We also give clear rules with respect to the choice of the hyper parameters of the new prior distributions. Wellknown applications are revisited to emphasize that many popular breaks are, in fact, due to a change in only a subset of the model parameters. It also turns out that sizeable forecasting improvements are made over recent changepoint models. 
Keywords:  Time series, Shrinkage prior, Changepoint model, Online forecasting 
JEL:  C11 C15 C22 C51 
Date:  2015–07–10 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2015032&r=ets 
By:  BAUWENS, L. (Université catholique de Louvain, CORE, Belgium); BRAIONE, M. (Université catholique de Louvain, CORE, Belgium); STORTI, G. (Université catholique de Louvain, CORE, Belgium) 
Abstract:  The Multiplicative MIDAS Realized DCC (MMReDCC) model of Bauwens et al. [5] decomposes the dynamics of the realized covariance matrix of returns into shortrun transitory and longrun secular components where the latter reflects the effect of the continuously changing economic conditions. The model allows to obtain positivedefinite forecasts of the realized covariance matrices but, due to the high number of parameters involved, estimation becomes unfeasible for large crosssectional dimensions. Our contribution in this paper is twofold. First, in order to obtain a computationally feasible estimation procedure, we propose an algorithm that relies on the maximization of an iteratively recomputed momentbased profile likelihood function. We assess the finite sample properties of the proposed algorithm via a simulation study. Second, we propose a bootstrap procedure for generating multistep ahead forecasts from the MMReDCC model. In an empirical application on realized covariance matrices for fifty equities, we find that the MMReDCC not only statistically outperforms the selected benchmarks insample, but also improves the outofsample ability to generate accurate multistep ahead forecasts of the realized covariances. 
Keywords:  Realized covariance, dynamic component models, multistep forecasting, MIDAS, targeting, model confidence set 
Date:  2016–02–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2016001&r=ets 
By:  Francisco Corona; María Pilar Poncela; Esther Ruiz 
Abstract:  A very common practice when extracting factors from nonstationary multivariate timeseries is to differentiate each variable in the system. As a consequence, the ratiobetween variances and the dynamic dependence of the common and idiosyncraticdifferentiated components may change with respect to the original components. In thispaper, we analyze the effects of these changes on the finite sample properties of somepopular procedures to determine the number of factors. In particular, we consider theinformation criteria of Bai and Ng (2002), the edge distribution of Onastki (2010) andthe ratios of eigenvalues proposed by Ahn and Horenstein (2013). The performance ofthese procedures when implemented to differentiated variables depend on both theratios between variances and dependences of the differentiated factor and idiosyncraticnoises. Furthermore, we also analyze the role of the number of factors in the originalnonstationary system as well as of its temporal and crosssectional dimensions. 
Keywords:  Dynamic Factor Model , Eigenvalue ratios , Edge distribution , Information criteria , Principal Components factor extraction 
URL:  http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1602&r=ets 
By:  BOUSALAM, Issam; HAMZAOUI, Moustapha; ZOUHAYR, Otman 
Abstract:  In this paper we decompose the realized volatility of the GARCHRV model into continuous sample path variation and discontinuous jump variation to provide a practical and robust framework for nonparametrically measuring the jump component in asset return volatility. By using 5minute highfrequency data of MASI Index in Morocco for the period (January 15, 2010  January 29, 2016), we estimate parameters of the constructed GARCH and EGARCHtype models (namely, GARCH, GARCHRV, GARCHCJ, EGARCH, EGARCHRV, and EGARCHCJ) and evaluate their predictive power to forecast future volatility. The results show that the realized volatility and the continuous sample path variation have certain predictive power for future volatility while the discontinuous jump variation contains relatively less information for forecasting volatility. More interestingly, the findings show that the GARCHCJtype models have stronger predictive power for future volatility than the other two types of models. These results have a major contribution in financial practices such as financial derivatives pricing, capital asset pricing, and risk measures. 
Keywords:  GARCHCJ; Jumps variation; Realized volatility; MASI Index; Morocco. 
JEL:  C22 F37 F47 G17 
Date:  2016–01–20 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:69636&r=ets 
By:  Jiang Liang (Singapore Management University); Wang Xiaohu (The Chinese University of Hong Kong); Jun Yu (Singapore Management University) 
Abstract:  Based on the Girsanov theorem, this paper rst obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and trimodal, indicating that the estimator is seriously biased. These two properties are also found in the nite sample distribution of the least squares estimator of structural break point in the discrete time model. The paper then builds a continuous time approximation to the discrete time model and develops an in ll asymptotic theory for the least squares estimator. The obtained in ll asymptotic distribution is asymmetric and trimodal and delivers good approximations to the nite sample distribution. In order to reduce the bias in the estimation of both the continuous time model and the discrete time model, a simulationbased method based on the indirect estima tion approach is proposed. Monte Carlo studies show that the indirect estimation method achieves substantial bias reductions. However, since the binding function has a slope less than one, the variance of the indirect estimator is larger than that of the original estimator. 
Keywords:  Structural break, Bias reduction, Indirect estimation, Exact distribution, In ll asymptotics 
JEL:  C11 C46 
Date:  2016–01 
URL:  http://d.repec.org/n?u=RePEc:siu:wpaper:012016&r=ets 