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on Econometric Time Series |
| By: | Jentsch, Carsen (TU Dortmund University); Lunsford, Kurt Graden (Federal Reserve Bank of Cleveland) |
| Abstract: | Proxy structural vector autoregressions identify structural shocks in vector autoregressions with external variables that are correlated with the structural shocks of interest but uncorrelated with all other structural shocks. We provide asymptotic theory for this identification approach under mild α-mixing conditions that cover a large class of uncorrelated, but possibly dependent innovation processes, including conditional heteroskedasticity. We prove consistency of a residual-based moving block bootstrap for inference on statistics such as impulse response functions and forecast error variance decompositions. Wild bootstraps are proven to be generally invalid for these statistics and their coverage rates can be badly and persistently mis-sized. |
| Keywords: | External Instruments; Mixing; Proxy Variables; Residual-Based Moving Block Bootstrap; Structural Vector Autoregression; Wild Bootstrap; |
| JEL: | C30 C32 |
| Date: | 2019–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:190800&r=all |
| By: | Martin Burda; Louis Belisle |
| Abstract: | The Copula Multivariate GARCH (CMGARCH) model is based on a dynamic copula function with time-varying parameters. It is particularly suited for modelling dynamic dependence of non-elliptically distributed financial returns series. The model allows for capturing more flexible dependence patterns than a multivariate GARCH model and also generalizes static copula dependence models. Nonetheless, the model is subject to a number of parameter constraints that ensure positivity of variances and covariance stationarity of the modeled stochastic processes. As such, the resulting distribution of parameters of interest is highly irregular, characterized by skewness, asymmetry, and truncation, hindering the applicability and accuracy of asymptotic inference. In this paper, we propose Bayesian analysis of the CMGARCH model based on Constrained Hamiltonian Monte Carlo (CHMC), which has been shown in other contexts to yield efficient inference on complicated constrained dependence structures. In the CMGARCH context, we contrast CHMC with traditional random-walk sampling used in the previous literature and highlight the benefits of CHMC for applied researchers. We estimate the posterior mean, median and Bayesian confidence intervals for the coefficients of tail dependence. The analysis is performed in an application to a recent portfolio of S&P500 financial asset returns. |
| Keywords: | Dynamic conditional volatility, varying correlation model, Markov Chain Monte Carlo |
| JEL: | C11 C15 C32 C63 |
| Date: | 2019–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-638&r=all |
| By: | Feiyu Jiang; Dong Li; Ke Zhu |
| Abstract: | This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data is stationary, and its usefulness is illustrated by simulation studies and one real example. |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1905.01798&r=all |
| By: | Eduardo Abi Jaber (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique); Omar El Euch (X - École polytechnique) |
| Abstract: | Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting. |
| Keywords: | limit theorems,affine Volterra processes,Rough volatility models,rough Heston models,stochastic Volterra equations,fractional Riccati equations |
| Date: | 2019–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01697117&r=all |
| By: | Vanessa Berenguer-Rico (University of Oxford); Søren Johansen (University of Copenhagen and CREATES); Bent Nielsen (University of Oxford) |
| Abstract: | An extended and improved theory is presented for marked and weighted empirical processes of residuals of time series regressions. The theory is motivated by 1-step Huber-skip estimators, where a set of good observations are selected using an initial estimator and an updated estimator is found by applying least squares to the selected observations. In this case, the weights and marks represent powers of the regressors and the regression errors, respectively. The inclusion of marks is a non-trivial extention to previous theory and requires refined martingale arguments. |
| Keywords: | 1-step Huber-skip, Non-stationarity, Robust Statistics, Stationarity |
| JEL: | C13 |
| Date: | 2019–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2019-06&r=all |
| By: | Olivier Ledoit; Michael Wolf |
| Abstract: | Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. In this paper, we review our work in this area going back 15+ years. We have promoted various shrinkage estimators, which can be classified into linear and nonlinear. Linear shrinkage is simpler to understand, to derive, and to implement. But nonlinear shrinkage can deliver another level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models. |
| Keywords: | Dynamic conditional correlations, factor models, large-dimensional asymptotics, Markowitz portfolio selection, rotation equivariance |
| JEL: | C13 C58 G11 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:323&r=all |
| By: | Máximo Camacho; María Dolores Gadea (University of Zaragoza); Ana Gómez Loscos (Banco de España) |
| Abstract: | This paper proposes a new approach to the analysis of the reference cycle turning points, defined on the basis of the specific turning points of a broad set of coincident economic indicators. Each individual pair of specific peaks and troughs from these indicators is viewed as a realization of a mixture of an unspecified number of separate bivariate Gaussian distributions whose different means are the reference turning points. These dates break the sample into separate reference cycle phases, whose shifts are modeled by a hidden Markov chain. The transition probability matrix is constrained so that the specification is equivalent to a multiple changepoint model. Bayesian estimation of finite Markov mixture modeling techniques is suggested to estimate the model. Several Monte Carlo experiments are used to show the accuracy of the model to date reference cycles that suffer from short phases, uncertain turning points, small samples and asymmetric cycles. In the empirical section, we show the high performance of our approach to identifying the US reference cycle, with little difference from the timing of the turning point dates established by the NBER. In a pseudo real-time analysis, we also show the good performance of this methodology in terms of accuracy and speed of detection of turning point dates. |
| Keywords: | business cycles, turning points, finite mixture models |
| JEL: | E32 C22 E27 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:1914&r=all |
| By: | Bruno Deschamps (Nottingham University Business School China); Christos Ioannidis (Aston Business School, Aston University); Kook Ka (Economic Research Institute, Bank of Korea) |
| Abstract: | We examine whether professional forecasters incorporate high-frequency information about credit conditions when revising their economic forecasts. Using Mixed Data Sampling regression approach, we find that daily credit spreads have significant predictive ability for monthly forecast revisions of output growth, at both aggregate and individual forecast levels. The relations are shown to be notably strong during ¡®bad¡¯ economic conditions, suggesting that forecasters anticipate more pronounced effects of credit tightening during economic downturns, indicating the amplification effect of financial developments on macroeconomic aggregates. Forecasts do not incorporate the totality of financial information received in equal measures, implying the presence of information rigidities in the incorporation of credit spread information. |
| Keywords: | Forecast Revision, GDP Forecast, Credit Spread, High-Frequency Data, Mixed Data Sampling (MIDAS) |
| JEL: | C53 E32 E44 |
| Date: | 2019–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:bok:wpaper:1917&r=all |
| By: | Jorge E. Galán (Banco de España) |
| Abstract: | The credit-to-GDP gap computed under the methodology recommended by Basel Committee for Banking Supervision (BCBS) suffers of important limitations mainly regarding the great inertia of the estimated long-run trend, which does not allow capturing properly structural changes or sudden changes in the trend. As a result, the estimated gap currently yields large negative values which do not reflect properly the position in the financial cycle and the cyclical risk environment in many countries. Certainly, most countries that have activated the Countercyclical Capital Buffer (CCyB) in recent years appear not to be following the signals provided by this indicator. The main underlying reason for this might not be only related to the properties of statistical filtering methods, but to the particular adaptation made by the BCBS for the computation of the gap. In particular, the proposed one-sided Hodrick-Prescott filter (HP) only accounts for past observations and the value of the smoothing parameter assumes a much longer length of the credit cycle that those empirically evidenced in most countries, leading the trend to have very long memory. This study assesses whether relaxing this assumption improves the performance of the filter and would still allow this statistical method to be useful in providing accurate signals of cyclical systemic risk and thereby inform macroprudential policy decisions. Findings suggest that adaptations of the filter that assume a lower length of the credit cycle, more consistent with empirical evidence, help improve the early warning performance and correct the downward bias compared to the original gap proposed by the BCBS. This is not only evidenced in the case of Spain but also in several other EU countries. Finally, the results of the proposed adaptations of the HP filter are also found to perform fairly well when compared to other statistical filters and model-based indicators. |
| Keywords: | credit-to-GDP gap, cyclical systemic risk, early-warning performance, macroprudential policy, statistical filters |
| JEL: | C18 E32 E58 G01 G28 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:bde:opaper:1906&r=all |
| By: | Ashley, Richard (Virginia Tech); Verbrugge, Randal (Federal Reserve Bank of Cleveland) |
| Abstract: | We use recently developed econometric tools to demonstrate that the Phillips curve unemployment rate–inflation rate relationship varies in an economically meaningful way across three phases of the business cycle. The first (“bust phase”) relationship is the one highlighted by Stock and Watson (2010): A sharp reduction in inflation occurs as the unemployment rate is rising rapidly. The second (“recovery phase”) relationship occurs as the unemployment rate subsequently begins to fall; during this phase, inflation is unrelated to any conventional unemployment gap. The final (“overheating phase”) relationship begins once the unemployment rate drops below its natural rate. We validate our findings in a forecasting exercise and find statistically significant episodic forecast improvement. Our analysis allows us to provide a unified explanation of many prominent findings in the literature. |
| Keywords: | overheating; recession gap; persistence dependence; NAIRU; |
| JEL: | C22 C32 E00 E31 E5 |
| Date: | 2019–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:190900&r=all |
| By: | Lyudmyla Kirichenko; Vitalii Bulakh; Tamara Radivilova |
| Abstract: | In the work, a comparative correlation and fractal analysis of time series of Bitcoin crypto currency rate and community activities in social networks associated with Bitcoin was conducted. A significant correlation between the Bitcoin rate and the community activities was detected. Time series fractal analysis indicated the presence of self-similar and multifractal properties. The results of researches showed that the series having a strong correlation dependence have a similar multifractal structure. |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1905.01018&r=all |
| By: | Adam Kuèera; Evžen Koèenda; Aleš Maršál (National Bank of Slovakia) |
| Abstract: | We use an affine term structure model with time-varying macro trends and a vector autoregression model to investigate the response of the US Treasury yield curve to changes in fiscal policy. By accounting for the timing of the fiscal policy in the shock identification we can separate the effect of news about future increases in government spending from the effect of innovations in changes of current government expenditures. Further, we use the Baker, Bloom, and Davis (2016) uncertainty index dataset to explain the flight to quality type of events. By controlling for the low frequency movement in yields and the decomposition of yield to risk neutral rates and term premia we show that the news channel is driven by a cautious response of agents to an increase in projected future government spending and leads to a drop in yields. This result contrasts with shock into contemporaneous spending which has no significant impact on bond yields. |
| Keywords: | Government Expenditures, Affine Term Structure Model, Time-varying Macro Trends |
| JEL: | C12 C22 C52 |
| Date: | 2019–03 |
| URL: | http://d.repec.org/n?u=RePEc:svk:wpaper:1060&r=all |
| By: | Milda Norkuté; Vasilis Sarafidis; Takashi Yamagata; Guowei Cui |
| Abstract: | This paper develops two instrumental variable (IV) estimators for dynamic panel data models with exogenous covariates and a multifactor error structure when both crosssectional and time series dimensions, N and T respectively, are large. Our approach initially projects out the common factors from the exogenous covariates of the model, and constructs instruments based on this defactored covariates. For models with homogeneous slope coe_cients, we propose a two-step IV estimator: the _rst step IV estimator is obtained using the defactored covariates as instruments. In the second step, the entire model is defactored by the extracted factors from the residuals of the _rst step estimation and subsequently obtain the _nal IV estimator. For models with heterogeneous slope coe _cients, we propose a mean-group type estimator, which is the cross-sectional average of _rst-step IV estimators of cross-section speci_c slopes. It is noteworthy that our estimators do not require us to seek for instrumental variables outside the model. Furthermore, our estimators are linear hence computationally robust and inexpensive. Moreover, they require no bias correction, and they are not subject to the small sample bias of least squares type estimators. The _nite sample performances of the proposed estimators and associated statistical tests are investigated, and the results show that the estimators and the tests perform well even for small N and T. |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1019r&r=all |
| By: | Valter Di Giacinto (Bank of Italy); Libero Monteforte (Bank of Italy and Ufficio Parlamentare di Bilancio); Andrea Filippone (Bank of Italy); Francesco Montaruli (Bank of Italy); Tiziano Ropele (Bank of Italy) |
| Abstract: | This work documents the construction of the new quarterly indicator of regional economic activity (Indicatore Trimestrale dell’Economia Regionale – ITER), which uses a parsimonious set of regional variables and combines them by means of temporal disaggregation techniques to obtain a quarterly index that is consistent with the official data on national and regional GDP and marked by a small lag compared with the reference period. The methodology was implemented to produce quarterly indicators for the economies of Italy’s four macro-areas in the period 1995-2017. With a view to assessing the performance of the quarterly indicator, a forecasting exercise was conducted regarding annual GDP growth in the four macro-areas for the period 2014-17. The forecasting performance of ITER is in line with that of the indicators developed by other national research institutions. |
| Keywords: | temporal disaggregation by related series, regional economies benchmarking and extrapolation, real time estimates |
| JEL: | C22 C61 C82 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:opques:qef_489_19&r=all |