
on Econometric Time Series 
By:  AntolinDiaz, Juan (Fulcrum Asset Management); RubioRamirez, Juan F. (Emory University & Federal Reserve Bank of Atlanta) 
Abstract:  We identify structural vector autoregressions (SVARs) using narrative sign restrictions. Narrative sign restrictions constrain the structural shocks and the historical decomposition around key historical events, ensuring that they agree with the established narrative account of these episodes. Using models of the oil market and monetary policy, we show that narrative sign restrictions are highly informative. We highlight that adding a single narrative sign restriction dramatically sharpens and even changes the inference of SVARs originally identified via traditional sign restrictions. Our approach combines the appeal of narrative methods with the popularized usage of traditional sign restrictions. 
Keywords:  narrative information; SVARs; Bayesian approach; sign restrictions; oil market; monetary policy 
JEL:  C32 E52 Q35 
Date:  2016–12–01 
URL:  http://d.repec.org/n?u=RePEc:fip:fedawp:201616&r=ets 
By:  Masafumi Nakano (Graduate School of Ecnonomics, University of Tokyo); Akihiko Takahashi (Faculty of Economics, University of Tokyo); Soichiro Takahashi (Graduate School of Ecnonomics, University of Tokyo) 
Abstract:  This paper proposes a generalized exponential moving average (EMA) model, a new stochastic volatility model with timevarying expected return in financial markets. In particular, we effectively apply a particle filter (PF) to sequential estimation of states and parameters in a state space framework. Moreover, we develop three types of anomaly detectors, which are implemented easily in the PF algorithm to be used for investment decision. As a result, a simple investment strategy with our scheme is superior to the one based on the standard EMA and wellknown traditional strategies such as equallyweighted, minimumvariance and risk parity portfolios. Our dataset is monthly total returns of global financial assets such as stocks, bonds and REITs, and investment performances are evaluated with various statistics, namely compound returns, Sharpe ratios, Sortino ratios and drawdowns. 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cfi:fseres:cf403&r=ets 
By:  Vasily E. Tarasov; Valentina V. Tarasova 
Abstract:  Long and short memory in economic processes is usually described by the socalled discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the GrunwaldLetnikov fractional differences of noninteger order d. Equations of ARIMA(p,d,q) and ARFIMA(p,d,q) models are the fractionalorder difference equations with the GrunwaldLetnikov differences of order d. We prove that the long and short memory with power law should be described by the exact fractionalorder differences, for which the Fourier transform demonstrates the power law exactly. The fractional differencing and the GrunwaldLetnikov fractional differences cannot give exact results for the long and short memory with power law, since the Fourier transform of these discrete operators satisfy the power law in the neighborhood of zero only. We prove that the economic processes with the continuous time long and short memory, which is characterized by the power law, should be described by the fractional differential equations. 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1612.07903&r=ets 
By:  Richard Gerlach; Chao Wang 
Abstract:  A new model framework called Realized Conditional Autoregressive Expectile (RealizedCARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the RealizedGARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed as the dependent variable in the measurement equation and to drive expectile dynamics. The measurement equation here models the contemporaneous dependence between the realized measure and the latent conditional expectile. We also propose employing the quantile loss function as the target criterion, instead of the conventional violation rate, during the expectile level grid search. For the proposed model, the usual search procedure and asymmetric least squares (ALS) optimization to estimate the expectile level and CARE parameters proves challenging and often fails to convergence. We incorporate a fast random walk Metropolis stochastic search method, combined with a more targeted grid search procedure, to allow reasonably fast and improved accuracy in estimation of this level and the associated model parameters. Given the convergence issue, Bayesian adaptive Markov Chain Monte Carlo methods are proposed for estimation, whilst their properties are assessed and compared with ALS via a simulation study. In a real forecasting study applied to 7 market indices and 2 individual asset returns, compared to the original CARE, the parametric GARCH and RealizedGARCH models, onedayahead ValueatRisk and Expected Shortfall forecasting results favor the proposed RealizedCARE model, especially when incorporating the Realized Range and the subsampled Realized Range as the realized measure in the model. 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1612.08488&r=ets 
By:  Abdelkamel Alj; Rajae Azrak; Christophe Ley; Guy Melard 
Abstract:  This paper is about vector autoregressivemoving average (VARMA) models with timedependent coefficients to represent nonstationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series’ length n. Under appropriate assumptions, it is shown that a Gaussian quasimaximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underly ing the theoretical results apply. In the second example the innovations are marginally heteroscedastic with a correlation ranging from −0.8 to 0.8. In the two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finitesample behavior is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory. 
Keywords:  nonstationary process; multivariate time series; timevarying models 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/241623&r=ets 
By:  Abdelkamel Alj; Rajae Azrak; Christophe Ley; Guy Melard 
Abstract:  This technical appendix contains proofs for the asymptotic properties of quasimaximum likelihood (QML) estimators for vector autoregressive moving average (VARMA) models in the case where the coefficients depend on time instead of being constant. We refer to the main theorems of the paper Asymptotic properties of QML estimators for VARMA models with timedependent coefficients" (Alj, Azrak, Ley and M elard, 2016). 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/241626&r=ets 
By:  Christian Kleiber (University of Basel) 
Abstract:  Methods for detecting structural changes, or change points, in time series data are widely used in many fields of science and engineering. This chapter sketches some basic methods for the analysis of structural changes in time series data. The exposition is confined to retrospective methods for univariate time series. Several recent methods for dating structural changes are compared using a time series of oil prices spanning more than 60 years. The methods broadly agree for the first part of the series up to the mid1980s, for which changes are associated with major historical events, but provide somewhat different solutions thereafter, reflecting a gradual increase in oil prices that is not well described by a step function. As a further illustration, 1990s data on the volatility of the Hang Seng stock market index are reanalyzed. 
Keywords:  change point problem, segmentation, structural change, time series 
JEL:  C22 C87 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:bsl:wpaper:2016/06&r=ets 
By:  Manuel GonzalezAstudillo; John M. Roberts 
Abstract:  In this paper, we examine the results of GDP trendcycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the best variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trendcycle correlation coefficient and the cycle. We show that the key feature of unemployment that allows for precise estimates of the cycle of GDP is that its nonstationary component is "small" relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2015:Q4, we obtain the trendcycle decomposition of GDP and find evidence of correlated trend and cycle components and an estimated cycle that is about 2 percent below its trend at the end of the sample. 
Keywords:  Unobserved components model ; Trendcycle decomposition ; Trendcycle correlation 
JEL:  C13 C32 C52 
Date:  2016–12–19 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:201699&r=ets 
By:  Korobilis, Dimitris; Pettenuzzo, Davide 
Abstract:  We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive models (BVARs) and employ it to introduce an "adaptive" version of the Minnesota prior. This flexible prior structure allows each coeffcient of the VAR to have its own shrinkage intensity, which is treated as an additional parameter and estimated from the data. Most importantly, our estimation procedure does not rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods, making it suitable for highdimensional VARs with more predictors that observations. We use a Monte Carlo study to demonstrate the accuracy and computational gains of our approach. We further illustrate the forecasting performance of our new approach by applying it to a quarterly macroeconomic dataset, and find that it forecasts better than both factor models and other existing BVAR methods. 
Keywords:  Bayesian VARs, Minnesota prior, Large datasets, Macroeconomic forecasting 
Date:  2016–08 
URL:  http://d.repec.org/n?u=RePEc:esy:uefcwp:18626&r=ets 
By:  Pierre Guerin; Danilo LeivaLeon; Massimiliano Marcellino 
Abstract:  We introduce a new approach for the estimation of highdimensional factor models with regimeswitching factor loadings by extending the linear threepass regression filter to settings where parameters can vary according to Markov processes. The new method, denoted as MarkovSwitching threepass regression filter (MS3PRF), is suitable for datasets with large crosssectional dimensions since estimation and inference are straightforward, as opposed to existing regimeswitching factor models, where computational complexity limits applicability to few variables. In a Monte Carlo experiment, we study the finite sample properties of the MS3PRF and find that it performs favorably compared with alternative modelling approaches whenever there is structural instability in factor loadings. As empirical applications, we consider forecasting economic activity and bilateral exchange rates, finding that the MS3PRF approach is competitive in both cases. Keywords: Factor model, Markovswitching, Forecasting. JEL Classification Code: C22, C23, C53. 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:591&r=ets 