  In a number of environmental studies, relationships between natural processes
are often assessed through regression analyses, using time series data. Such
data are often multi-scale and non-stationary, leading to a poor accuracy of
the resulting regression models and therefore to results with moderate
reliability. To deal with this issue, the present paper introduces the
EMD-regression methodology consisting in applying the empirical mode
decomposition (EMD) algorithm on data series and then using the resulting
components in regression models. The proposed methodology presents a number of
advantages. First, it accounts of the issues of non-stationarity associated to
the data series. Second, this approach acts as a scan for the relationship
between a response variable and the predictors at different time scales,
providing new insights about this relationship. To illustrate the proposed
methodology it is applied to study the relationship between weather and
cardiovascular mortality in Montreal, Canada. The results shed new knowledge
concerning the studied relationship. For instance, they show that the humidity
can cause excess mortality at the monthly time scale, which is a scale not
visible in classical models. A comparison is also conducted with state of the
art methods which are the generalized additive models and distributed lag
models, both widely used in weather-related health studies. The comparison
shows that EMD-regression achieves better prediction performances and provides
more details than classical models concerning the relationship.
