Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets
Identificadores
URI: http://hdl.handle.net/20.500.12020/1247DOI: https://doi.org/10.3390/math11234843
Fecha
2023Tipo de documento
articleÁrea/s de conocimiento
Matemáticas y FísicaResumen
Structural change tests aim to identify evidence of a structural break or change in the
underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks
to test, using the correlation integral, the hypothesis that a time series is generated by an identically
and independently distributed (IID) stochastic process over time. The BDS test is already widely used
as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In
this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate
the hypothesis of structural change in a time series, taking advantage of its ability to test the IID
hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series
and incrementally increasing the number of observations until it is applied to the full sample time
series. A structural change in the unknown underlying generator model is detected when a change in
the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive
BDS test lies in the fact that it does not require making any assumptions about the underlying time
series generator model. We ilustrate the power and potential of this recursive BDS test through an
application to real economic data. In this sense, we apply the test to assess the structural changes
caused by the COVID-19 pandemic in international financial markets. Using daily data from the
world’s top stock indices, we have detected strong and statistically significant evidence of two major
structural changes during the period from June 2018 to June 2022. The first occurred in March 2020,
coinciding with the onset of economic restrictions in the main Western countries as a result of the
pandemic. The second occurred towards the end of August 2020, with the end of the main economic
restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test
for structural changes in a time series is easy to implement and can detect changes in any system
or process behind the time series even when this generating system is not known, and without the
need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could
be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural
change is detected in a time series, rather than estimating a single predictive model for the full-sample
time series, efforts should be made to estimate different predictive models, one for the time before
and one for the time after the detected structural change.