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on Econometric Time Series |
| By: | Li, Yushu (CAFO, Växjö University); Shukur, Ghazi (CESIS - Centre of Excellence for Science and Innovation Studies, Royal Institute of Technology) |
| Abstract: | In this paper, we propose a Nonlinear Dickey-Fuller test for unit root against first order Logistic Smooth Transition Autoregressive LSTAR (1) model with time as the transition variable. The Nonlinear Dickey-Fuller test statistic is established under the null hypothesis of random walk without drift and the alternative model is a nonlinear LSTAR (1) model. The asymptotic distribution of the test is analytically derived while the small sample distributions are investigated by Monte Carlo experiment. The size and power properties of the test have been investigated using Monte Carlo experiment. The results have shown that there is a serious size distortion for the Nonlinear Dickey-Fuller test when GARCH errors appear in the Data Generating Process (DGP), which lead to an over-rejection of the unit root null hypothesis. To solve this problem, we use the Wavelet technique to count off the GARCH distortion and to improve the size property of the test under GARCH error. We also discuss the asymptotic distributions of the test statistics in GARCH and wavelet environments. Finally, an empirical example is used to compare our test with the traditional Dickey-Fuller test. |
| Keywords: | Unit root Test; Dickey-Fuller test; STAR model; GARCH; Wavelet method; MODWT |
| JEL: | C32 |
| Date: | 2009–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:cesisp:0184&r=ets |
| By: | Lanne, Markku (Department of Economics, and HECER, University of Helsinki); Saikkonen, Pentti (Department of Mathematics and Statistics, and HECER, University of Helsinki) |
| Abstract: | In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of importance in empirical economic research, which currently uses only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. This is emphasized in the paper by noting that noncausality is closely related to the notion of nonfundamentalness, under which structural economic shocks cannot be recovered from an estimated causal VAR model. As detecting nonfundamentalness is therefore of great importance, we propose a procedure for discriminating between causality and noncausality that can be seen as a test of nonfundamentalness. The methods are illustrated with applications to fiscal foresight and the term structure of interest rates. |
| Keywords: | elliptic distribution; fiscal foresight; maximum likelihood estimation; noncausal; nonfundamentalness; non-Gaussian; term structure of interest rates |
| JEL: | C32 C46 C52 E62 G12 |
| Date: | 2009–08–12 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:bofrdp:2009_018&r=ets |
| By: | Dabo-Niang, Sophie; Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process. We establish consistency and asymptotic normality results for our estimator. A Monte Carlo study and an empirical application on stock market indices suggest that significant gains can be achieved with our approach. |
| Keywords: | ARMA representation; noisy data; Nonparametric regression; optimal prediction |
| JEL: | C14 C22 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:16893&r=ets |
| By: | Ulrich Müller; Mark W. Watson |
| Abstract: | Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust to this potential misspecification. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal in the case of a single cointegrating vector. |
| JEL: | C32 E32 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:15292&r=ets |
| By: | Kuswanto, Heri; Sibbertsen, Philipp |
| Abstract: | We develop a Wald type test to distinguish between long memory and ESTAR nonlinearity by using a directed-Wald statistic to overcome the problem of restricted parameters under the alternative. The test is derived from two basic model specifications where the first is the standard model based on an auxiliary regression and the second allows the parameter to appear as a nuisance parameter in the transition function. A simulation study indicates that both approaches lead to tests with good size and power properties to distinguish between stationary long memory and ESTAR. Moreover, the second approach is shown to have more power. |
| Keywords: | directed-Wald test, ESTAR, long memory |
| JEL: | C12 C22 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-427&r=ets |