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on Econometric Time Series |
| By: | Giancarlo Bruno (ISAE - Institute for Studies and Economic Analyses) |
| Abstract: | The use of linear parametric models for forecasting economic time series is widespread among practitioners, in spite of the fact that there is a large evidence of the presence of non-linearities in many of such time series. However, the empirical results stemming from the use of non-linear models are not always as good as expected. This has been sometimes associated to the difficulty in correctly specifying a non-linear parametric model. I this paper I cope with this issue by using a more general non-parametric approach, which can be used both as a preliminary tool for aiding in specifying a suitable parametric model and as an autonomous modelling strategy. The results are promising, in that the non-parametric approach achieve a good forecasting record for a considerable number of series. |
| Keywords: | Non-linear Time-Series Models, Non-Parametric Models. |
| JEL: | C52 C53 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:isa:wpaper:98&r=ets |
| By: | Drew Creal (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam); Eric Zivot (University of Washington) |
| Abstract: | In this paper we investigate whether the dynamic properties of the U.S. business cycle have changed in the last fifty years. For this purpose we develop a flexible business cycle indicator that is constructed from a moderate set of macroeconomic time series. The coincident economic indicator is based on a multivariate trend-cycle decomposition model that accounts for time variation in macroeconomic volatility, known as the great moderation. In particular, we consider an unobserved components time series model with a common cycle that is shared across different time series but adjusted for phase shift and amplitude. The extracted cycle can be interpreted as the result of a model-based bandpass filter and is designed to emphasize the business cycle frequencies that are of interest to applied researchers and policymakers. Stochastic volatility processes and mixture distributions for the irregular components and the common cycle disturbances enable us to account for all the heteroskedasticity present in the data. The empirical results are based on a Bayesian analysis and show that time-varying volatility is only present in the a selection of idiosyncratic components while the coefficients driving the dynamic properties of the business cycle indicator have been stable over time in the last fifty years. |
| Keywords: | Bandpass filter; Markov chain Monte Carlo; Stochastic volatility; Trend-cycle decomposition; Unobserved components time series model |
| JEL: | C11 C32 E32 |
| Date: | 2008–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20080069&r=ets |
| By: | Christian Conrad (University of Heidelberg, Department of Economics); Menelaos Karanasos (Brunel University, Dept. of Economics and Finance); Ning Zeng (Brunel University, Dept. of Economics and Finance) |
| Abstract: | Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH speci¯cation of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We ¯nd this multivariate speci¯cation to be generally applicable once power, leverage and long-memory e®ects are taken into consideration. In addition, we ¯nd that both the optimal fractional di®erencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models. |
| Keywords: | Asymmetric Power ARCH, Fractional integration, Stock returns, Volatility forecast evaluation |
| JEL: | C13 C22 C52 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0472&r=ets |
| By: | Christian Conrad (University of Heidelberg, Department of Economics); Enno Mammen (University of Mannheim, Department of Economics) |
| Abstract: | We consider time series models in which the conditional mean of the response variable given the past depends on latent covariates. We assume that the covariates can be estimated consistently and use an iterative nonparametric kernel smoothing procedure for estimating the conditional mean function. The covariates are assumed to depend (non)parametrically on past values of the covariates and of the observations. Our procedure is based on iterative ¯ts of the covariates and nonparametric kernel smoothing of the conditional mean function. An asymptotic theory for the resulting kernel estimator is developed and the estimator is used for testing parametric speci¯cations of the mean function. Our leading example is a semiparametric class of GARCH-in-Mean models. In this set-up our procedure provides a formal framework for testing economic theories that postulate functional relations between macroeconomic or ¯nancial variables and their conditional second moments. We illustrate the usefulness of the methodology by testing the linear risk-return relation predicted by the ICAPM. |
| Keywords: | Speci¯cation test, GARCH-M, semiparametric regression, risk premium, ICAPM. |
| JEL: | C12 C14 C22 C52 G12 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0473&r=ets |
| By: | Yuanhua Feng (Heriot-Watt University, Edinburgh); Jan Beran; Keming Yu |
| Abstract: | A class of semiparametric fractional autoregressive GARCH models (SEMIFARGARCH), which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence, and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term. So that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets. |
| Keywords: | Financial time series, GARCH model, SEMIFAR model, parameter estimation, kernel estimation, asymptotic property. |
| Date: | 2007–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0714&r=ets |
| By: | Jan Beran (University of Konstanz); Mark A. Heiler |
| Abstract: | Estimation of a nonparametric regression spectrum based on the periodogram is considered. Neither trend estimation nor smoothing of the periodogram are required. Alternatively, for cases where spectral estimation of phase shifts fails and the shift does not depend on frequency, a time domain estimator of the lag-shift is defined. Asymptotic properties of the frequency and time domain estimators are derived. Simulations and a data example illustrate the methods. |
| Keywords: | Periodogram, cross spectrum, regression spectrum, phase, wavelets. |
| Date: | 2007–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0712&r=ets |
| By: | Yuanhua Feng (Heriot-Watt University, Edinburgh); Jan Beran |
| Keywords: | Optimal rate of convergence, nonparametric regression, long memory, antipersistence. |
| Date: | 2007–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0715&r=ets |
| By: | Jan Beran (University of Konstanz); Mark A. Heiler |
| Abstract: | We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these quantities is based on wavelet thresholding. The method is illustrated by a simulated example and a three-dimensional time series consisting of ECG, blood pressure and cardiac stroke volume measurements. |
| Keywords: | Nonparametric trend estimation, cross spectrum, wavelets, regression spectrum, phase, threshold estimator |
| Date: | 2008–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0801&r=ets |
| By: | Jan Beran (University of Konstanz) |
| Abstract: | We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth are obtained. In spite of long memory, the optimal bandwidth turns out to be of the order n^(-1/5) and inversely proportional to the square of the second derivative of d. In this sense, local estimation of d is comparable to regression smoothing with iid residuals. |
| Keywords: | long memory, fractional ARIMA process, local stationarity, bandwidth selection |
| Date: | 2007–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0713&r=ets |
| By: | Shamiri, Ahmed; Shaari, Abu Hassan; Isa, Zaidi |
| Abstract: | Being able to choose most suitable volatility model and distribution specification is a more demanding task. This paper introduce an analyzing procedure using the Kullback-Leibler information criteria (KLIC) as a statistical tool to evaluate and compare the predictive abilities of possibly misspecified density forecast models. The main advantage of this statistical tool is that we use the censored likelihood functions to compute the tail minimum of the KLIC, to compare the performance of a density forecast models in the tails. We include an illustrative simulation and an empirical application to compare a set of distributions, including symmetric/asymmetric distribution, and a family of GARCH volatility models. We highlight the use of our approach to a daily index, the Kuala Lumpur Composite index (KLCI). Our results shows that the choice of the conditional distribution appear to be a more dominant factor in determining the adequacy of density forecasts than the choice of volatility model. Furthermore, the results support the Skewed for KLCI return distribution. |
| Keywords: | Density forecast; Conditional distribution; Forecast accuracy; KLIC; GARCH models |
| JEL: | D53 C32 C16 C52 |
| Date: | 2007–08–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:9790&r=ets |