How Big is Big Enough? Justifying Results of the iid Test Based on the Correlation Integral in the Non-Normal World
AbstractKocenda (2001) introduced the test for nonlinear dependencies in time series data based on the correlation integral. The idea of the test is to estimate the correlation dimension by integrating over a range of proximity parameter epsilon. However, there is an unexplored avenue if one wants to use the test to identify nonlinear structure in nonnormal data. Using the Monte Carlo studies, we show that non-normality leads to an over-rejection of the null hypothesis due to two reasons: First, the data are not iid, and second, the data are non-normal. It is shown that even a very small deviation from normality could lead to a rejection of the null hypothesis and hence a wrong conclusion. Therefore, the bootstrap method is introduced and it is shown that it helps to avoid the over-rejection problem; moreover the power of the test increases by a significant amount. These findings help us to extend the use of the test into many other fields that deal with nonlinear data that are not necessarily normal, e. g. financial economics, stock price volatility, stock market efficiency, stock exchange, behavior of equity indices, nonlinear dynamics in foreign exchange rates, or interest rates.
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Date of creation: Sep 2006
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Chaos; nonlinear dynamics; correlation integral; Monte Carlo; power tests; high-frequency economic and financial data;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
- F31 - International Economics - - International Finance - - - Foreign Exchange
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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