Inference in the Presence of Stochastic and Deterministic Trends
AbstractThe focus of this paper is inference about stochastic and deterministic trends when both types are present. We show that, contrary to asymptotic theory and the existing literature, the parameters of the deterministic components must be taken into account in finite samples. We analyze the ubiquitous Likelihood Ratio test for the rank of cointegration in vector processes. Here, we directly control the parameters of the data generating process so that a local-asymptotic framework accounts for small sample interactions between stochastic and deterministic trends. We show that the usual corrections are invalid as they take no account of the relative magnitudes of these two types of trends. Block-local models provide an embedding framework which provides a rationale for consistent estimation and testing of the whole set of parameters. In an empirical application to European GDP series, we show that using usual corrections leads to underestimating the number of stochastic trends.
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Bibliographic InfoPaper provided by ESSEC Research Center, ESSEC Business School in its series ESSEC Working Papers with number DR 07021.
Length: 42 pages
Date of creation: Aug 2007
Date of revision:
Block Local Models; Cointegration; Finite Samples; Likelihood Ratio; Weak Trends;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-12-15 (All new papers)
- NEP-ECM-2007-12-15 (Econometrics)
- NEP-ETS-2007-12-15 (Econometric Time Series)
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