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on Econometric Time Series |
| By: | Chang, C-L.; McAleer, M.J. |
| Abstract: | In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is convenient to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2004) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different effects on conditional volatility of positive and negative effects of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1979). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner showed that leverage was not possible for EGARCH. Surprisingly, the conditions for asymmetry in EGARCH seem to have been ignored in the literature, or have concentrated on the incorrect conditions, with no clear explanation, and hence with associated misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage. |
| Keywords: | Conditional volatility models, random coefficient complex nonlinear moving average process, EGARCH, asymmetry, leverage, regularity condition |
| JEL: | C22 C52 C58 G32 |
| Date: | 2017–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:100416&r=ets |
| By: | Martina Hengge (IHEID, The Graduate Institute of International and Development Studies, Geneva); Seton Leonard (IHEID, The Graduate Institute of International and Development Studies, Geneva) |
| Abstract: | This paper presents a novel dynamic factor model for non-stationary data. We begin by constructing a simple dynamic stochastic general equilibrium growth model and show that we can represent and estimate the model using a simple linear-Gaussian (Kalman) filter. Crucially, consistent estimation does not require differencing the data despite it being cointegrated of order 1. We then apply our approach to a mixed frequency model which we use to estimate monthly U.S. GDP from May 1969 to January 2017 using 171 series with an emphasis on housing related data. We suggest our estimates may, at a quarterly rate, in fact be more accurate than measurement error prone observations. Finally, we use our model to construct pseudo real-time GDP nowcasts over the 2007 to 2009 financial crisis. This last exercise shows that a GDP index, as opposed to real time estimates of GDP itself, may be more helpful in highlighting changes in the state of the macroeconomy. |
| Keywords: | Forecasting; Factor model: Large data sets; Mixed frequency data; Nowcasting; Non-stationarity; Real-time data |
| JEL: | E27 E52 C53 C33 |
| Date: | 2017–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:gii:giihei:heidwp13-2017&r=ets |
| By: | Giorgio Canarella (University of Nevada, Las Vegas); Luis A. Gil-Alaña (University of Navarra); Rangan Gupta (University of Pretoria); Stephen M. Miller (University of Nevada, Las Vegas) |
| Abstract: | This paper estimates the complete historical US price data by employing a relatively new statistical methodology based on long memory. We consider, in addition to the standard case, the possibility of nonlinearities in the form of nonlinear deterministic trends as well as the possibility that persistence exists at both the zero frequency and a frequencies away from zero. We model the fractional nonlinear case using Chebyshev polynomials and model the fractional cyclical structures as a Gegenbauer process. We find in the latter case that that secular (i.e., long-run) persistence and cyclical persistence matter in the behavior of prices, producing long-memory effects that imply mean reversion at both the long-run and cyclical frequencies. |
| Keywords: | Persistence, Cyclicality, Chebyshev polynomials, Gegenbauer processes |
| JEL: | C22 E3 |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:uct:uconnp:2017-13&r=ets |
| By: | Thomas Quistgaard Pedersen (Aarhus University and CREATES); Erik Christian Montes Schütte (Aarhus University and CREATES) |
| Abstract: | We analyze an empirically important issue with the recursive right-tailed unit root tests for bubbles in asset prices. First, we show that serially correlated innovations, which is a feature that is present in most financial series used to test for bubbles, can lead to severe size distortions when using either fixed or automatic (based on information criteria) lag-length selection in the auxiliary regressions underlying the test. Second, we propose a sieve-bootstrap version of these tests and show that this results in more or less perfectly sized test statistics even in the presence of highly autocorrelated innovations. We also find that these improvements in size come at a relatively low cost for the power of the tests. Finally, we apply the bootstrap tests on the housing market of OECD countries, and generally find less strong evidence of bubbles compared to existing evidence. |
| Keywords: | Right-tailed unit root tests, GSADF, Size and power properties, Sieve bootstrap, International housing market |
| JEL: | C58 G12 |
| Date: | 2017–02–16 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-09&r=ets |
| By: | Martina Danielova Zaharieva; Mark Trede; Bernd Wilfling |
| Abstract: | In this paper, we establish a Cholesky-type multivariate stochastic volatility estimation framework, in which we let the innovation vector follow a Dirichlet process mixture, thus enabling us to model highly exible return distributions. The Cholesky decom- position allows parallel univariate process modeling and creates potential for estimating highly dimensional specifications. We use Markov Chain Monte Carlo methods for posterior simulation and predictive density computation. We apply our framework to a five-dimensional stock-return data set and analyze international volatility co-movements among the largest stock markets. |
| Keywords: | Bayesian nonparametrics, Markov Chain Monte Carlo, Dirichlet process mixture, multivariate stochastic volatility |
| JEL: | C11 C14 C53 C58 |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:cqe:wpaper:6217&r=ets |