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on Econometric Time Series |
| By: | Archil Gulisashvili; Josep Vives |
| Abstract: | In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law. |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1403.5302&r=ets |
| By: | Mike Giles; Yuan Xia |
| Abstract: | We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergence rate for the error introduced by the discrete monitoring of the running supremum of a broad class of L\'{e}vy processes. We use these to obtain upper bounds on the multilevel Monte Carlo variance convergence rate for the Variance Gamma, NIG and $\alpha$-stable processes used in the numerical experiments. We also show numerical results and analysis of a trapezoidal approximation for Asian options. |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1403.5309&r=ets |
| By: | Pan, Li; Politis, Dimitris N |
| Abstract: | In order to construct prediction intervals without the combersome--and typically unjustifiable--assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studies in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the constructuion of bootstrap prediction intervals. Forward and backward bootstrap methods for using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as essimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their acheived coverage level and length of interval. |
| Keywords: | Physical Sciences and Mathematics, Confidence intervals, forecasting, time series |
| Date: | 2014–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt67h5s74t&r=ets |
| By: | Abdelkamel Alj; Rajae Azrak; Guy Melard |
| Keywords: | unconditional Lyapunov condition; conditional Lindeberg condition |
| JEL: | C13 C22 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/154446&r=ets |
| By: | Tobias Kley; Stanislav Volgushev; Holger Dette; Marc Hallin |
| Keywords: | time series; spectral analysis; periodogram; quantiles; copulas; ranks; spearman; blomqvist; gini spectra |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/156105&r=ets |
| By: | Matteo Barigozzi; Marco Lippi; Matteo Luciani |
| Keywords: | dynamic factor models for I (1) variables; cointegration; granger representation theorem |
| JEL: | C00 C01 E00 |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/157568&r=ets |
| By: | Martha Banbura; Domenico Giannone; Michèle Lenza |
| Abstract: | This paper describes an algorithm to compute the distribution of conditional forecasts,i.e. projections of a set of variables of interest on future paths of some othervariables, in dynamic systems. The algorithm is based on Kalman filtering methods andis computationally viable for large vector autoregressions (VAR) and dynamic factormodels (DFM). For a quarterly data set of 26 euro area macroeconomic and financialindicators, we show that both approaches deliver similar forecasts and scenario assessments.In addition, conditional forecasts shed light on the stability of the dynamicrelationships in the euro area during the recent episodes of financial turmoil and indicatethat only a small number of sources drive the bulk of the fluctuations in the euroarea economy. |
| Keywords: | vector autoregression; bayesian shrinkage; dynamic factor model; conditional forecast; large cross-sections |
| JEL: | C11 C13 C33 C53 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/158499&r=ets |
| By: | Heejoon Han; Oliver Linton (Institute for Fiscal Studies and Cambridge University); Tatsushi Oka; Yoon-Jae Whang (Institute for Fiscal Studies and Seoul National University) |
| Abstract: | This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confiÂ…dence intervals we employ the stationary bootstrap procedure; we show the consistency of this bootstrap. Also, we consider the self-normalized approach, which is shown to be asymptotically pivotal under the null hypothesis of no predictability. We provide simulation studies and two empirical applications. First, we use the cross-quantilogram to detect predictability from stock variance to excess stock return. Compared to existing tools used in the literature of stock return predictability, our method provides a more complete relationship between a predictor and stock return. Second, we investigate the systemic risk of individual fiÂ…nancial institutions, such as JP Morgan Chase, Goldman Sachs and AIG. This article has supplementary materials online. |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:06/14&r=ets |
| By: | Stephen Pollock |
| Abstract: | A variety of filters that are commonly employed by econometricians are analysed with a view to determining their effectiveness in extracting well-defined components of economic data sequences. These components can be defined in terms of their spectral structures—i.e. their frequency content—and it is argued that the process of econometric signal extraction should be guided by a careful appraisal of the periodogram of the detrended data sequence. A preliminary estimate of the trend can often be obtained by fitting a polynomial function to the data. This can provide a firm benchmark against which the deviations of the business cycle and the fluctuations of seasonal activities can be measured. The trend-cycle component may be estimated by adding the business cycle estimate to the trend function. In cases where there are evident structural breaks in the data, other means are suggested for estimating the underlying trajectory of the data. Whereas it is true that many annual and quarterly economic data sequences are amenable to relatively unsophisticated filtering techniques, it is often the case that monthly data that exhibit strong seasonal fluctuations require a far more delicate approach. In such cases, it may be appropriate to use filters that work directly in the frequency domain by selecting or modifying the spectral ordinates of a Fourier decomposition of data that have been subject to a preliminary detrending |
| Keywords: | Spectral analysis, Business cycles, Turning points, Seasonality. |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:14/07&r=ets |
| By: | Jean-François Carpantier (CREA, Université de Luxembourg) |
| Abstract: | We propose an estimation method that circumvents the path dependence problem existing in Change-Point (CP) and Markov Switching (MS) ARMA models. Our model embeds a sticky infinite hidden Markov-switching structure (sticky IHMM), which makes possible a self-determination of the number of regimes as well as of the specification : CP or MS. Furthermore, CP and MS frameworks usually assume that all the model parameters vary from one regime to another. We relax this restrictive assumption. As illustrated by simulations on moderate samples (300 observations), the sticky IHMM-ARMA algorithm detects which model parameters change over time. Applications to the U.S. GDP growth and the DJIA realized volatility highlight the relevance of estimating different structural breaks for the mean and variance parameters. |
| Keywords: | Bayesian interference, Markov-switching model, ARMA model, infinite hidden Markov model, Dirichlet Process |
| JEL: | C11 C15 C22 C58 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:14-07&r=ets |
| By: | Chong, Terence Tai Leung; Yan, Isabel K. |
| Abstract: | Conventional threshold models contain only one threshold variable. This paper provides the theoretical foundation for threshold models with multiple threshold variables. The new model is very different from a model with a single threshold variable as several novel problems arisefrom having an additional threshold variable. First, the model is not analogous to a change-point model. Second, the asymptotic joint distribution of the threshold estimators is difficult to obtain. Third, the estimation time increases exponentially with the number of threshold variables. This paper derives the consistency and the asymptotic joint distribution of the threshold estimators. A fast estimation algorithm to estimate the threshold values is proposed. We also develop tests for the number of threshold variables. The theoretical results are supported by simulation experiments. Our model is applied to the study of currency crises. |
| Keywords: | Threshold Model; Multiple Threshold Variables; Currency Crisis; Panel Data |
| JEL: | C12 C13 C33 F3 F31 F37 |
| Date: | 2014–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:54732&r=ets |