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on Econometric Time Series |
| By: | Michael Ho; Jack Xin |
| Abstract: | Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market microstructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-EM (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to price models that include jumps. We propose two sparse Kalman filtering approaches to this problem. In the first approach we develop a Kalman Expectation Conditional Maximization (KECM) algorithm to determine the unknown covariance as well as detecting the jumps. For this algorithm we consider Laplace and the spike and slab jump models, both of which promote sparse estimates of the jumps. In the second method we take a Bayesian approach and use Gibbs sampling to sample from the posterior distribution of the covariance matrix under the spike and slab jump model. Numerical results using simulated data show that each of these approaches provide for improved covariance estimation relative to the KEM method in a variety of settings where jumps occur. |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1602.02185&r=ets |
| By: | Leopoldo Catania; Anna Gloria Bill\'e |
| Abstract: | We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization. |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1602.02542&r=ets |
| By: | Vikram Krishnamurthy; Elisabeth Leoff; J\"orn Sass |
| Abstract: | Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volatility. In the continuous-time model with switching volatility the underlying Markov chain could be observed due to this stochastic volatility, and no estimation (filtering) of it is needed (in theory), while in the discretized model or the model with constant volatility one has to filter for the underlying Markov chain. The motivations for continuous-time models are explicit computations in finance. To have a realistic model with unobservable Markov chain in continuous time and good econometric properties we introduce a regime-switching model where the volatility depends on the filter for the underlying chain and state the filtering equations. We prove an approximation result for a fixed information filtration and further motivate the model by considering social learning arguments. We analyze its relation to the switching volatility model and present a convergence result for the discretized model. We then illustrate its econometric properties by considering numerical simulations. |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1602.05323&r=ets |
| By: | Stavros Stavroyiannis |
| Abstract: | We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined via application of several statistical tests and risk measures. The results indicate that the APARCH model with the standardized Pearson type IV distribution is accurate, within the general financial risk modeling perspective, providing the financial analyst with an additional skewed distribution for incorporation in the risk management tools. |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1602.05749&r=ets |
| By: | Fiorentini, Gabriele; Galesi, Alessandro; Sentana, Enrique |
| Abstract: | We introduce a frequency domain version of the EM algorithm for general dynamic factor models. We consider both AR and ARMA processes, for which we develop iterative indirect inference procedures analogous to the algorithms in Hannan (1969). Although our proposed procedure allows researchers to estimate such models by maximum likelihood with many series even without good initial values, we recommend switching to a gradient method that uses the EM principle to swiftly compute frequency domain analytical scores near the optimum. We successfully employ our algorithm to construct an index that captures the common movements of US sectoral employment growth rates. |
| Keywords: | Indirect inference; Kalman filter; Sectoral employment; Spectral maximum likelihood; Wiener-Kolmogorov filter |
| JEL: | C32 C38 C51 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10417&r=ets |
| By: | J. Miguel Marín; M. T. Rodríguez-Bernal; E. Romero |
| Abstract: | The analysis of financial series, assuming calendar effects and unequally spaced times over continuous time, can be studied by means of COGARCH models based on Lévy processes. In order to estimate the COGARCH model parameters, we propose to use two different Bayesian approaches. First, we suggest to use a Hamiltonian Montecarlo (HMC) algorithm that improves the performance of standard MCMC methods. Secondly, we introduce an Approximate Bayesian Computational (ABC) methodology which allows to work with analytically infeasible or computationally expensive likelihoods. After a simulation and comparison study for both methods, HMC and ABC, we apply them to model the behaviour of some NASDAQ time series and we discuss the results. |
| Keywords: | Approximate Bayesian Computation methods (ABC) , Bayesian inference , COGARCH model , Continuous-time GARCH process , Hamiltonian Monte Carlo methods (HMC) , Lévy process |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1601&r=ets |
| By: | Aknouche, Abdelhakim |
| Abstract: | This paper proposes a stochastic volatility model (PAR-SV) in which the log-volatility follows a first-order periodic autoregression. This model aims at representing time series with volatility displaying a stochastic periodic dynamic structure, and may then be seen as an alternative to the familiar periodic GARCH process. The probabilistic structure of the proposed PAR-SV model such as periodic stationarity and autocovariance structure are first studied. Then, parameter estimation is examined through the quasi-maximum likelihood (QML) method where the likelihood is evaluated using the prediction error decomposition approach and Kalman filtering. In addition, a Bayesian MCMC method is also considered, where the posteriors are given from conjugate priors using the Gibbs sampler in which the augmented volatilities are sampled from the Griddy Gibbs technique in a single-move way. As a-by-product, period selection for the PAR-SV is carried out using the (conditional) Deviance Information Criterion (DIC). A simulation study is undertaken to assess the performances of the QML and Bayesian Griddy Gibbs estimates. Applications of Bayesian PAR-SV modeling to daily, quarterly and monthly S&P 500 returns are considered. |
| Keywords: | Periodic stochastic volatility, periodic autoregression, QML via prediction error decomposition and Kalman filtering, Bayesian Griddy Gibbs sampler, single-move approach, DIC. |
| JEL: | C11 C15 C51 C58 |
| Date: | 2013–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69571&r=ets |
| By: | Barunik, Jozef; Krehlik, Tomas |
| Abstract: | We propose a general framework for measuring frequency dynamics of connectedness in economic variables based on spectral representation of variance decompositions. We argue that the frequency dynamics is insightful when studying the connectedness of variables as shocks with heterogeneous frequency responses will create frequency dependent connections of different strength that remain hidden when time domain measures are used. Two applications support the usefulness of the discussion, guide a user to apply the methods in different situations, and contribute to the literature with important findings about sources of connectedness. Giving up the assumption of global stationarity of stock market data and approximating the dynamics locally, we document rich time-frequency dynamics of connectedness in US market risk in the first application. Controlling for common shocks due to common stochastic trends which dominate the connections, we identify connections of global economy at business cycle frequencies of 18 up to 96 months in the second application. In addition, we study the effects of cross-sectional dependence on the connectedness of variables. |
| Keywords: | connectedness,frequency,spectral analysis,market risk,business cycles |
| JEL: | C18 C58 G15 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:fmpwps:54&r=ets |
| By: | Barunik, Jozef; Krehlik, Tomas; Vacha, Lukas |
| Abstract: | This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the influence of different timescales on volatility forecasts. The decomposition of volatility into several timescales approximates the behaviour of traders at corresponding investment horizons. The proposed methodology is moreover able to account for impact of jumps due to a recently proposed jump wavelet two scale realized volatility estimator. We propose a realized Jump-GARCH models estimated in two versions using maximum likelihood as well as observation-driven estimation framework of generalized autoregressive score. We compare forecasts using several popular realized volatility measures on foreign exchange rate futures data covering the recent financial crisis. Our results indicate that disentangling jump variation from the integrated variation is important for forecasting performance. An interesting insight into the volatility process is also provided by its multiscale decomposition. We find that most of the information for future volatility comes from high frequency part of the spectra representing very short investment horizons. Our newly proposed models outperform statistically the popular as well conventional models in both one-day and multi-period-ahead forecasting. |
| Keywords: | realized GARCH,wavelet decomposition,jumps,multi-period-ahead volatility forecasting |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:fmpwps:55&r=ets |