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on Econometric Time Series |
| By: | Dinghai Xu (Department of Economics, University of Waterloo) |
| Abstract: | This paper investigates the “spurious almost integration” effect of volatility under a threshold GARCH structure with realized volatility measures. To closely examine the effect, the realized persistence of volatility is proposed to be used as a threshold trigger for volatility regimes. Under the threshold framework, general closed-form solutions of moment conditions are derived, which provide a convenient way to theoretically examine the “spurious almost integration” effect and its associated impacts. We find that introducing the volatility persistence-driven threshold can capture regime-specific characteristics well. It performs better than the traditional GARCH-type models in terms of both in-sample fitting and out-of-sample forecasting. Based on our Monte Carlo and empirical results, in general we find that overlooking the relatively low persistence regime(s) could lead to some misleading conclusions. |
| JEL: | C01 C58 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:wat:wpaper:1903&r=all |
| By: | Simon Hetland (Department of Economics, University of Copenhagen, Denmark); Rasmus Søndergaard Pedersen (Department of Economics, University of Copenhagen, Denmark); Anders Rahbek (Department of Economics, University of Copenhagen, Denmark) |
| Abstract: | In this paper we consider a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models where the eigenvalues of the conditional covariance matrix are time-varying. The proposed dynamics of the eigenvalues is based on applying the general theory of dynamic conditional score models as proposed by Creal, Koopman and Lucas (2013) and Harvey (2013). We denote the obtained GARCH model with dynamic conditional eigenvalues (and constant conditional eigenvectors) as the ?-GARCH model. We provide new results on asymptotic theory for the Gaussian QMLE, and for testing of reduced rank of the (G)ARCH loading matrices of the time-varying eigenvalues. The theory is applied to US data, where we ?find that the eigenvalue structure can be reduced similar to testing for the number in factors in volatility models. |
| Keywords: | Multivariate GARCH; GO-GARCH; Reduced Rank; Asymptotic Theory |
| JEL: | C32 C51 C58 |
| Date: | 2019–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1913&r=all |
| By: | Maurizio Daniele; Julie Schnaitmann |
| Abstract: | We propose a regularized factor-augmented vector autoregressive (FAVAR) model that allows for sparsity in the factor loadings. In this framework, factors may only load on a subset of variables which simplifies the factor identification and their economic interpretation. We identify the factors in a data-driven manner without imposing specific relations between the unobserved factors and the underlying time series. Using our approach, the effects of structural shocks can be investigated on economically meaningful factors and on all observed time series included in the FAVAR model. We prove consistency for the estimators of the factor loadings, the covariance matrix of the idiosyncratic component, the factors, as well as the autoregressive parameters in the dynamic model. In an empirical application, we investigate the effects of a monetary policy shock on a broad range of economically relevant variables. We identify this shock using a joint identification of the factor model and the structural innovations in the VAR model. We find impulse response functions which are in line with economic rationale, both on the factor aggregates and observed time series level. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.06049&r=all |
| By: | Mark Bognanni; John Zito |
| Abstract: | We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VAR-SV). The algorithm builds particle approximations to the sequence of the model’s posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm’s computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a medium-scale VAR-SV model. |
| Keywords: | Vector autoregressions; sequential Monte Carlo; Rao-Blackwellization; particle filter; stochastic volatility |
| JEL: | E17 C11 C51 C32 |
| Date: | 2019–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:86647&r=all |
| By: | Igor Kheifets (Instituto Tecnologico Autonomo de Mexico); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Multicointegration is traditionally deï¬ ned as a particular long run relationship among variables in a parametric vector autoregressive model that introduces links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modiï¬ ed least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in ï¬ nite samples. We illustrate our ï¬ ndings by analyzing ï¬ scal sustainability of the US government over the post-war period. |
| Keywords: | Cointegration, Multicointegration, Fully modified regression, Singular long run variance matrix, Degenerate Wald test, Fiscal sustainability |
| JEL: | C12 C13 C22 |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2210&r=all |
| By: | Mohamed CHIKHI; Claude DIEBOLT; Tapas MISHRA |
| Abstract: | Despite an inherent share of unpredictability, asset prices such as in stock and Bitcoin markets are naturally driven by significant magnitudes of memory; depending on the strength of path dependence, prices in such markets can be (at least partially) predicted. Being able to predict asset prices is always a boon for investors, more so, if the forecasts are largely unconditional and can only be explained by the series’ own historical trajectories. Although memory dynamics have been exploited in forecasting stock prices, Bitcoin market pose additional challenge, because the lack of proper financial theoretic model limits the development of adequate theory-driven empirical construct. In this paper, we propose a class of autoregressive fractionally integrated moving average (ARFIMA) model with asymmetric exponential generalized autoregressive score (AEGAS) errors to accommodate a complex interplay of ‘memory’ to drive predictive performance (an out-of-sample forecasting). Our conditional variance includes leverage effects, jumps and fat tail-skewness distribution, each of which affects magnitude of memory both the stock and Bitcoin price system would possess enabling us to build a true forecast function. We estimate several models using the Skewed Student-t maximum likelihood and find that the informational shocks in asset prices, in general, have permanent effects on returns. The ARFIMA-AEGAS is appropriate for capturing volatility clustering for both negative (long Value-at-Risk) and positive returns (short Value-at-Risk). We show that this model has better predictive performance over competing models for both long and/or some short time horizons. The predictions from this model beats comfortably the random walk model. Accordingly, we find that the weak efficiency assumption of financial markets stands violated for all price returns studied over longer time horizon. |
| Keywords: | Asset price; Forecasting; Memory; ARFIMA-AEGAS; Leverage effects and jumps; Market Efficiency. |
| JEL: | C14 C58 C22 G17 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2019-43&r=all |