Identification and Testing Structural Changes at Unknown Locations with Wavelets

点击翻译按钮获取中文摘要

Identification and Testing Structural Changes at Unknown Locations with WaveletsThe primary goal of my research program is to design powerful statistical tests that can be used to identify structural breaks (changes) in the parameters of a linear regression model in small samples. A structural break is an unexpected shift in the mean, persistence and/or in the variance of the underlying statistical process. The presence of such breaks leads to prediction errors and mis-specified models of economic and financial activity. A structural break may affect some or all parameters of a model. Some, for instance, may lead into an altered serial correlation after a certain date, some change in the propensity of a trend and some may lead into a change in the underlying volatility. Institutional changes (reforms), political turmoil, emergence of new economies, economic and financial disasters may account for the presence of such structural breaks in the economic and financial time series. Some breaks may be readily identifiable from raw data, but some may be latent because of the nature of the frictions and volatile nature of the economy. In a regression framework, the breaks account for the change in the nature of the relationship between two or more variables altogether. The wavelet transformation is an ideal toolset for the design of powerful structural change tests because it operates in local time windows and has powerful time/frequency localization features. The mechanism of my original wavelet framework can be described in the following way: The wavelet decomposition yields localized weighted differences (wavelet coefficients) that are equal in number to the number of data points. I square each wavelet coefficient to obtain its magnitude and calculate the sample average of the squared coefficients. I expect this sample average to be equal to one-half of the variance plus one-half of the covariance of the process under the null when there is no structural change. However, the sample average of the squared wavelet coefficients should be significantly deviate from the null average when there are one or more structural breaks. I center and standardize the sample average of the squared wavelet coefficients to obtain the null distribution with no structural change.Structural breaks can be permanent or temporary in nature. If a structural break is permanent, then there is a permanent change of indefinite duration in the mean, persistence or variance of the process. In a temporary break, the mean, persistence or the variance shifts from its null value but eventually reverts to its null value. Whether such breaks are temporary or permanent in nature, they may occur abruptly or gradually. To capture such possibilities, I will allow for abrupt as well as gradual smooth structural breaks. I focus on smooth multiple structural breaks for two reasons. First, most economic and financial data exhibit gradual structural changes in a time window, and the most abrupt structural changes are exceptions rather than the rule. Second, my framework is all-encompassing and allows for abrupt changes. My seed Monte Carlo simulations indicate the presence of minimal empirical size distortions relative to their nominal sizes and significant power improvements compared to the existing structural break tests.Identification of structural changes in an economic activity is a pre-cursor to avoid erroneous policies and to design proper remedies. The diagnosis of such changes requires tests with empirical size close to its nominal counterpart and substantive power, otherwise we may not be able to identify the underlying relationship correctly and in a timely manner. The goal of my research program is to overcome such limitations by providing powerful tests with m