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on Econometric Time Series |
| By: | Juan Carlos Cuestas (Department of Economics, The University of Sheffield); Luis A. Gil-Alana (Department of Economics, Universidad de Navarra) |
| Abstract: | This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, we present a procedure that permits us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and an empirical application, using data of real exchange rates, is also carried out at the end of the article. |
| Keywords: | Chebyshev polynomials; long run dependence; fractional integration |
| JEL: | C22 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:shf:wpaper:2012013&r=ets |
| By: | Juan Carlos Cuestas (Department of Economics, The University of Sheffield); Javier Ordóñez (University of Bath) |
| Abstract: | The aim of this paper is to develop a unit root test that takes into account two sources of nonlinearites in data, i.e. asymmetric speed of mean reversion and structural changes. The asymmetric speed of mean reversion is modeled by means of a exponential smooth transition autoregression (ESTAR) function for the autoregressive parameter, whereas structural changes are approximated by a smooth transition in the deterministic components. We find that the proposed test performs well in terms of size and power, in particular when the autoregressive parameter is close to one. |
| Keywords: | unit roots; nonlinear trends; exponential smooth transition; autoregressive model; structural change |
| JEL: | C12 C32 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:shf:wpaper:2012012&r=ets |
| By: | Otavio Ribeiro de Medeiros and Vitor Leone |
| Abstract: | Based on a method developed by Leybourne, Kim and Taylor (2007) for detecting multiple changes in persistence, we test for changes in persistence in the dividend-price ratio of the NASDAQ stocks. The results confirm the existence of the so-called Dotcom bubble around the last turn of the century and its start and end dates. Furthermore, we compare the results with a test for detecting and date-stamping explosive unit-root behaviour developed by Phillips, Wu and Yu’s (2011) also applied to the NASDAQ price and dividend indices. We find that Leybourne, Kim and Taylor’s test is capable of detecting the Dotcom bubble as much as Phillips, Wu and Yu’s test is, but there are significant differences between the bubble start and end dates suggested by both methods and between these and the dates reported by the financial media. We also find an unexpected negative bubble extending from the beginning of the 1970s to the beginning of the 1990s where the NASDAQ stock prices were below their fundamental values as indicated by their dividend yields, which has not been reported in the literature so far. |
| Keywords: | Multiple changes in persistence, Explosive behaviour, Unit roots, Dotcom Bubble, NASDAQ. |
| JEL: | C10 C32 F15 G12 G14 G15 |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbs:wpaper:2012/02&r=ets |
| By: | Li, Dao (Department of Business, Economics, Statistics and Informatics) |
| Abstract: | This paper studies a special class of vector smooth-transition autoregressive (VS- TAR) models containing common nonlinear features (CNFs). To test the existence of CNFs in a VSTAR model, a triangular representation for such a system containing CNFs is proposed. A procedure of testing CNFs in a VSTAR model is consisting of two steps: rst, test unit root in a STAR model against a stable STAR process for each individual time series; secondly, examine if nonlinear features are common in the system by a La- grange Multiplier (LM) test when the null of unit root is rejected in the rst step. The asymptotic distribution of the LM test is derived. Simulation studies of both unit root test and LM test have been carried out to investigate the nite sample properties. In the empirical application, the procedure of testing CNFs is illustrated by analyzing the monthly growth of consumption and income data of United States (1985:1 to 2011:11). The consumption and income system contains CNFs, and an estimated common nonlin- ear factor in VSTAR model is suggested. |
| Keywords: | Vector STAR models; Common features; Lagrange Multiplier test |
| JEL: | C00 C12 C32 C52 |
| Date: | 2012–02–13 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2012_007&r=ets |
| By: | Li, Dao (Department of Business, Economics, Statistics and Informatics) |
| Abstract: | This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system, and nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointe- gration studied by Balke and Fomby (1997). Based on a class of vector ST cointegrating regression models, we develop F-type tests to examine linear cointegration against ST cointegration. The null asymptotic distributions of the tests with choosing various sta- tionary transition variables are derived. Finite-sample distributions of those tests are studied by Monto Carlo simulation. The small-sample performance of the tests are also included and it is shown that our F-type tests have a better power when the system contains a ST cointegration than that when the system is linearly cointegrated. Two empirical examples for the purchasing power parity (PPP) data are illustrated by apply- ing the testing procedures in this paper. It is found that, for each of them, there is no linear cointegration in the system, but there exits a ST cointegration in the system. |
| Keywords: | nonlinear cointegration; smooth transition; F-type test; threshold coin- tegration |
| JEL: | C00 C12 C32 C52 |
| Date: | 2012–02–13 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2012_006&r=ets |
| By: | Gian Piero Aielli |
| Abstract: | We address some issues that arise with the Dynamic Conditional Correlation (DCC) model. We prove that the DCC large system estimator (DCC estimator) can be inconsistent, and that the traditional interpretation of the DCC correlation parameters can lead to misleading conclusions. We then suggest a more tractable dynamic conditional correlation model (cDCC model). A related large system estimator (cDCC estimator) is described and heuristically proven to be consistent. Sufficient stationarity conditions for cDCC processes of interest, including the covariance-return process, are established. The DCC and cDCC estimators are compared by means of applications to simulated and real data. |
| Keywords: | Multivariate GARCH Model, Quasi-Maximum-Likelihood, Two-step Estimation, Integrated Correlation, Generalized Profile Likelihood. |
| JEL: | C13 C32 C51 C52 C53 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0142&r=ets |
| By: | Luis Fernando Melo; Rubén Albeiro Loaiza Maya |
| Abstract: | Typically, when forecasting inflation rates, there are a variety of individual models and a combination of several of these models. We implement a Bayesian shrinkage combination methodology to include information that is not captured by the individual models using expert forecasts as prior information. To take into account two common characteristics in emerging countries’ economies, possible parameter instabilities and non-stationary dynamics, we use a rolling estimation windows technique for series integrated of order one. The empirical results of Colombian inflation show that the Bayesian forecast combination model outperforms the individual models and the random walk predictions for every evaluated forecast horizon. Moreover, these results outperform shrinkage forecasts that consider other priors as equal or zero weights. |
| Date: | 2012–04–22 |
| URL: | http://d.repec.org/n?u=RePEc:col:000094:009511&r=ets |
| By: | Sujin Park; Oliver Linton |
| Abstract: | We propose a new estimator of multivariate ex-post volatility that is robust to microstructure noise and asynchronous data timing. The method is based on Fourier domain techniques, which have been widely used in discrete time series analysis. The advantage of this method is that it does not require an explicit time alignment, unlike existing methods in the literature. We derive the large sample properties of our estimator under general assumptions allowing for the number of sample points for different assets to be of different order of magnitude. The by-product of our Fourier domain based estimator is that we have a consistent estimator of the instantaneous co-volatility even under the presence of microstructure noise. We show in extensive simulations that our method outperforms the time domain estimator especially when two assets are traded very asynchronously and with different liquidity and when estimating the high dimensional integrated covariance matrix. |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:fmg:fmgdps:dp703&r=ets |
| By: | Wolfgang Karl Härdle; Nikolaus Hautsch; Andrija Mihoci |
| Abstract: | We propose a local adaptive multiplicative error model (MEM) accommodating timevarying parameters. MEM parameters are adaptively estimated based on a sequential testing procedure. A data-driven optimal length of local windows is selected, yielding adaptive forecasts at each point in time. Analyzing one-minute cumulative trading volumes of five large NASDAQ stocks in 2008, we show that local windows of approximately 3 to 4 hours are reasonable to capture parameter variations while balancing modelling bias and estimation (in)efficiency. In forecasting, the proposed adaptive approach significantly outperforms a MEM where local estimation windows are fixed on an ad hoc basis. |
| Keywords: | multiplicative error model, local adaptive modelling, high-frequency processes, trading volume, forecasting |
| JEL: | C41 C51 C53 G12 G17 |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2012-031&r=ets |
| By: | Qian, Hang |
| Abstract: | The standard state space model (SSM) treats observations as imprecise measures of the Markov latent states. Our flexible SSM treats the states and observables symmetrically, which are simultaneously determined by historical observations and up to first-lagged states. The only distinction between the states and observables is that the former are latent while the latter have data. Despite the conceptual difference, the two SSMs share the same Kalman filter. However, when the flexible SSM is applied to the ARMA model, mixed frequency regression and the dynamic factor model with missing data, the state vector is not only parsimonious but also intuitive in that low-dimension states are constructed simply by stacking all the relevant but unobserved variables in the structural model. |
| Keywords: | State Space Model; Kalman Filter; ARMA; Mixed Frequency; Factor Model |
| JEL: | C32 C51 |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38455&r=ets |
| By: | Bai, Jushan; Wang, Peng |
| Abstract: | We consider a set of minimal identification conditions for dynamic factor models. These conditions have economic interpretations, and require fewer number of restrictions than when putting in a static-factor form. Under these restrictions, a standard structural vector autoregression (SVAR) with or without measurement errors can be embedded into a dynamic factor model. More generally, we also consider overidentification restrictions to achieve efficiency. General linear restrictions, either in the form of known factor loadings or cross-equation restrictions, are considered. We further consider serially correlated idiosyncratic errors with heterogeneous coefficients. A numerically stable Bayesian algorithm for the dynamic factor model with general parameter restrictions is constructed for estimation and inference. A square-root form of Kalman filter is shown to improve robustness and accuracy when sampling the latent factors. Confidence intervals (bands) for the parameters of interest such as impulse responses are readily computed. Similar identification conditions are also exploited for multi-level factor models, and they allow us to study the spill-over effects of the shocks arising from one group to another. |
| Keywords: | dynamic factor models; multi-level factor models; impulse response function; spill-over effects |
| JEL: | C10 C33 C11 |
| Date: | 2012–04–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38434&r=ets |
| By: | Chambers, Marcus J.; Kyriacou, Maria |
| Abstract: | This paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on non-overlapping sub-samples does not remove fully the first-order bias as intended, but that an ‘optimal’ jackknife estimator can be de- fined that is capable of removing this bias. The results are based on a demonstration that the sub-sample estimators converge to different limiting distributions, and the joint moment generating function of the numerator and denominator of these distributions (which are func- tionals of a Wiener process over a sub-interval of [0,1]) is derived and utilised to extract the optimal weights. Simulations demonstrate the ability of the jackknife estimator to produce substantial bias reductions in the parameter of interest. It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction despite the fact that the distributions of the full-sample and sub-sample estimators have greater bias in this case. Of interest, too, is the fact that the jackknife estimators can also reduce the overall root mean squared error compared to the ordinary least squares estimator, this requiring a larger (though still small) number of sub-samples compared to the value that produces maximum bias reduction (which is typically equal to two). |
| Keywords: | Jackknife; bias reduction; unit root; moment generating function |
| JEL: | C13 C22 C01 |
| Date: | 2012–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38255&r=ets |