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on Econometric Time Series |
| By: | HAFNER Christian, (Université catholique de Louvain); KYRIAKOPOULOU Dimitra, (Université catholique de Louvain, CORE, Belgium) |
| Abstract: | One of the implications of the intertemporal capital asset pricing model (CAPM) is that the risk premium of the market portfolio is a linear function of its variance. Yet, estimation theory of classical GARCH-in-mean models with linear-in-variance risk premium requires strong assumptions and is incomplete. We show that exponential-type GARCH models such as EGARCH or Log-GARCH are more natural in dealing with linear-in-variance risk premia. For the popular and more difficult case of EGARCH-in-mean, we derive conditions for the existence of a unique stationary and ergodic solution and invertibility following a stochastic recurrence equation approach. We then show consistency and asymptotic normality of the quasi maximum likelihood estimator under weak moment assumptions. An empirical application estimates the dynamic risk premia of a variety of stock indices using both EGARCH-M and Log-GARCH-M models. |
| Keywords: | GARC H-in-Mean, EGARCH, Log-GARCH, CAPM, risk premium, maximum likelihood, stochastic recurrence equation |
| JEL: | C71 C78 |
| Date: | 2019–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2019013&r=all |
| By: | Wang, Xiaohu (The Chinese University of Hong Kong); Xiao, Weilin (Zhejiang University); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper proposes a two-stage method for estimating parameters in a para-metric fractional continuous-time model based on discrete-sampled observations. In the first stage, the Hurst parameter is estimated based on the ratio of two second-order differences of observations from different time scales. In the second stage, the other parameters are estimated by the method of moments. All estimators have closed-form expressions and are easy to obtain. A large sample theory of the pro-posed estimators is derived under either the in-fill asymptotic scheme or the double asymptotic scheme. Extensive simulations show that the proposed theory performs well in finite samples. Two empirical studies are carried out. The first, based on the daily realized volatility of equities from 2011 to 2017, shows that the Hurst parameter is much lower than 0.5, which suggests that the realized volatility is too rough for continuous-time models driven by standard Brownian motion or fractional Brownian motion with Hurst parameter larger than 0.5. The second empirical study is of the daily realized volatility of exchange rates from 1986 to 1999. The estimate of the Hurst parameter is again much lower than 0.5. Moreover, the proposed frac-tional continuous-time model performs better than the autoregressive fractionally integrated moving average (ARFIMA) model out-of-sample. |
| Keywords: | Rough Volatility; Hurst Parameter; Second-order Difference; Different Time Scales; Method of Moments; ARFIMA |
| JEL: | C15 C22 C32 |
| Date: | 2019–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2019_017&r=all |
| By: | Sven Schreiber |
| Abstract: | As applied cointegration analysis faces the challenge that (a) potentially relevant variables are unobservable and (b) it is uncertain which covariates are relevant, partial systems are often used and potential (stationary) covariates are ignored. Recently it has been argued that a nominally significant cointegration outcome using the bootstrapped rank test (Cavaliere, Rahbek, and Taylor, 2012) in a bivariate setting might be due to test size distortions when a larger data-generating process (DGP) with covariates is assumed. This study reviews the issue systematically and generally finds noticeable but only mild size distortions, even when the specified DGP includes a large borderline stationary root. The previously found drastic test size problems in an application of a long-run Phillips curve (inflation and unemployment in the euro area) appear to hinge on the particular construction of a time series for the output gap as a covariate. We conclude that the problems of the bootstrapped rank test are not severe and that it is still to be recommended for applied research. |
| Keywords: | bootstrap, cointegration rank test, empirical size |
| JEL: | C32 C15 E31 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:imk:wpaper:199-2019&r=all |
| By: | Lijuan Huo (Beijing Institute of Technology); Jin Seo Cho (Yonsei Univ) |
| Abstract: | This study aims to directly test for the sandwich-form asymptotic covariance matrix entailed by conditional heteroskedasticity and autocorrelation in the regression error. Given that none of the conditional heteroskedastic or autocorrelated regression errors yield the sandwich-form asymptotic covariance matrix for the least squares estimator, it is not necessary to estimate the asymptotic covariance matrix using the heteroskedasticity-consistent (HC) or heteroskedasticity and autocorrelation-consistent (HAC) covariance matrix estimator. Because of this fact, we first examine testing for the sandwich-form asymptotic covariance matrix before applying the HC or HAC covariance matrix estimator. For this goal, we apply the testing methodologies proposed by Cho and White (2015) and Cho and Phillips (2018) to fit the context of this study by extending the scope of their maximum test statistic to have greater power and further establishing a methodology to sequentially detect the influence of heteroskedastic and autocorrelated regression errors on the asymptotic covariance matrix. We affirm the theory on the test statistics of this study through a simulation and further apply our test statistics to economic and energy price growth rate data for illustrative purposes. |
| Keywords: | Information matrix equality; sandwich-form covariance matrix; heteroskedasticity-consistent covariance matrix estimator; heteroskedasticity and autocorrelation-consistent covariance matrix estimator; economic growth rate; energy price growth rate. |
| JEL: | C12 C22 O47 G17 Q47 |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2019rwp-152&r=all |
| By: | Pfarrhofer, Michael (University of Salzburg) |
| Abstract: | This paper investigates the time-varying impacts of international macroeconomic uncertainty shocks. We use a global vector autoregressive (GVAR) specification with drifting coefficients and factor stochastic volatility in the errors to model six economies jointly. The measure of uncertainty is constructed endogenously by estimating a scalar driving the innovation variances of the latent factors, and is included also in the mean of the process. To achieve regularization, we use Bayesian techniques for estimation, and introduce a set of hierarchical global local shrinkage priors. The adopted priors center the model on a constant parameter specification with homoscedastic errors, but allow for time-variation if suggested by likelihood information. Moreover, we assume coefficients across economies to be similar, but provide sufficient flexibility via the hierarchical prior for country-specific idiosyncrasies. The results point towards pronounced real and financial effects of uncertainty shocks in all countries, with differences across economies and over time. |
| Keywords: | Bayesian global vector autoregressive model; state space modeling; hierarchical priors; factor stochastic volatility; stochastic volatility in mean |
| JEL: | C11 C55 E32 E66 G15 |
| Date: | 2019–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:ris:sbgwpe:2019_003&r=all |
| By: | Boriss Siliverstovs (KOF Swiss Economic Institute, ETH Zurich, Switzerland); Daniel Wochner (KOF Swiss Economic Institute, ETH Zurich, Switzerland) |
| Abstract: | This article re-examines the findings of Stock and Watson (2012b) who assessed the predictive performance of dynamic factor models (DFM) over autoregressive (AR) bench-marks for hundreds of target variables by focusing on possible business cycle performance asymmetries in the spirit of Chauvet and Potter (2013) and Siliverstovs (2017a, 2017b, 2019). Our forecasting experiment is based on a novel big macroeconomic dataset (FRED-QD) comprising over 200 quarterly indicators for almost 60 years (1960-2018; cf. e.g. McCracken & Ng, 2019b). Our results are consistent with this nascent state-dependent evaluation literature and generalize their relevance to a large number of indicators: We document systematic model performance differences across business cycles (longitudinal) as well as variable groups (cross-sectional). While the absolute size of prediction errors tend to be larger in busts than in booms for both DFMs and Arts, DFMs relative im-provement over Arts is typically large and statistically significant during recessions but not during expansions (cf. e.g. Chauvet & Potter, 2013). Our findings further suggest that the widespread practice of relying on full sample forecast evaluation metrics may not be ideal: For at least two thirds of all 216 macroeconomic indicators full sample relative RMSFEs systematically over-estimate performance in expansionary subsamples and under-estimate it in recessionary subsamples (cf. e.g. Siliverstovs, 2017a, 2019). These findings are robust to several alternative specifications and have high practical relevance for both consumers and producers of model-based economic forecasts. |
| Keywords: | Forecast Evaluation, Dynamic Factor Models, Business Cycle Asymmetries, Big Macroeconomic Datasets, United States |
| JEL: | C32 C45 C52 E17 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:kof:wpskof:19-463&r=all |
| By: | Eraslan, Sercan; Schröder, Maximilian |
| Abstract: | We propose a novel time-varying parameters mixed-frequency dynamic factor model which is integrated into a dynamic model averaging framework for macroeconomic nowcasting. Our suggested model can efficiently deal with the nature of the real-time data flow as well as parameter uncertainty and time-varying volatility. In addition, we develop a fast estimation algorithm. This enables us to generate nowcasts based on a large factor model space. We apply the suggested framework to nowcast German GDP. Our recursive out-of-sample forecast evaluation results reveal that our framework is able to generate forecasts superior to those obtained from a naive and more competitive benchmark models. These forecast gains seem to emerge especially during unstable periods, such as the Great Recession, but also remain over more tranquil periods. |
| Keywords: | dynamic factor model,forecasting,GDP,mixed-frequency,model averaging,time-varying-parameter |
| JEL: | C11 C32 C51 C52 C53 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:412019&r=all |
| By: | Florian, Huber (University of Salzburg); Kaufmann, Daniel (Université de Neuchâtel) |
| Abstract: | We estimate a multivariate unobserved components stochastic volatility model to explain the dynamics of a panel of six exchange rates against the US Dollar. The empirical model is based on the assumption that both countries’ monetary policy strategies may be well described by Taylor rules with a time-varying inflation target, a time-varying natural rate of unemployment, and interest rate smoothing. Compared to the existing literature, our model simultaneously provides estimates of the latent components included in a typical Taylor rule specification and the model-based real exchange rate. Our estimates closely track major movements along with important time series properties of real and nominal exchange rates across all currencies considered, outperforming a benchmark model that does not account for changes in trend inflation and trend unemployment. More precisely, the proposed approach improves upon competing models in tracking the actual evolution of the real exchange rate in terms of simple correlations while it appreciably improves upon simpler competitors in terms of matching the persistence of the real exchange rate. |
| Keywords: | Exchange rate models; trend inflation; natural rate of unemployment; Taylor rule; unobserved components stochastic volatility model |
| JEL: | E31 E52 F31 F41 |
| Date: | 2019–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:ris:sbgwpe:2019_004&r=all |
| By: | Juan Carlos Cuestas (Department of Economics, Universitat Jaume I, Castellón, Spain) |
| Abstract: | In this paper we contribute to the long literature on determining the real exchange rate by using models that incorporate structural breaks and nonlinearities. We estimate cointegrated dynamic ordinary least squares regressions, Bayesian vector autoregressions (VAR), and interactive panel VARs. We find that the estimated coefficients for the CEECs and for the other member states differ from each other. We also find that the models are different before and after the crisis, and appreciations and depreciations of the RER seem to condition the long run equations for the EU15+2. |
| Keywords: | Real exchange rates, competitiveness, quantile regression, Bayesian, asymmetric model, structural breaks, European integration |
| JEL: | C22 F15 F32 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:jau:wpaper:2019/09&r=all |
| By: | Melolinna, Marko (Bank of England); Tóth, Máté (European Central Bank) |
| Abstract: | This paper presents a range of unobserved components models to study productivity dynamics in the United Kingdom. We introduce a set of univariate and bivariate models that allow for shocks between the trend and the cycle to be correlated, and use Bayesian sampling techniques to estimate the models. We show that the size of the priors on the trend and cycle shock has an effect on the results, suggesting that a range of priors need to be considered for policy-making purposes. If the prior is set to a smooth trend, then models with little correlation between the trend and cycle shocks are the likeliest to fit the data. On the other hand, if there is a prior belief that the trend shock is allowed to vary relatively freely, the results suggest that there is a negative correlation between trend and cycle shocks to LIK productivity. This is consistent with real-business cycle type narratives, where trend shocks are the main driver of productivity dynamics. Finally, our evidence suggests that the trend productivity growth rate in the UK has been weaker since the financial crisis. There is also a significant positive correlation between shocks to UK trend productivity and those of other advanced economies. |
| Keywords: | Business cycle; Markov Chain Monte Carlo; productivity puzzle |
| JEL: | C11 C32 E32 |
| Date: | 2019–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0826&r=all |