Unfortunately, the global or local Moran's-I is not at all appropriate for multi-temporal data. There is a bivariate version of the statistic, available in GeoDa that can be used to compare two time-periods but not a time-series. Please note that there are some know issues with a bivariate Moran's-I (or by extension LISA) where the matrix is not symmetric and can be non-positive definite. The postulation on the spatial process in Wartenberg is in regard to a lapse rate. This brings up questions regarding the assumption of any given y being correlated at point i through time.
If you want to collapse the time-series data into a single spatial process, for a single evaluation of the spatial structure, I imagine that one would have to meet an assumption of a minimal correlation structure thorough time. Otherwise, resulting spatial clustering would be completely erroneous. For example, say you have one point in the time-series that is considerably different than the others yet you still collapse it into the overall data, how could you adequately be representing a temporally homogeneous spatial process and have relevant clustering?
A better approach may be Kulldorff (1997) scan statistics and its many extensions. Various implementations are available in the software SaTScan, the R interface to SaTScan "rsatscan" and the "kulldorff" function in the SpatialEpi package. This method allows for spatial-temporal models using specified distributional forms (eg., Binomial, Poisson, Gaussian), which provides a distinct advantage in hypothesis testing and inference.
Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics - Theory and Methods. 26(6):1481–1496.