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We adjusted the weekly averaged mean temperature using a cross-basis framework (Gasparrini et al. 2010) to account for the combined effects of a 10-week maximum lag structure (stratified at 4 weeks for mean temperature and polynomial for rainfall) and a nonlinear exposure response represented by using natural cubic splines with 5 df for the effect of rainfall and temperature.
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Temp t l is a matrix produced by DLNM to model non-linear and distributed lag effects of ambient temperature over the current day (lag 0) to lag l days, and β is vector of coefficients for Temp t,l ; The maximum lag l was set to 25 days to explore the lag structure of temperature effect [ 17].
We applied linear regressions with Newey-West standard errors with a maximum lag of 2 to be considered in the autocorrelation structure.
The formal testing of the lag structure carried out in this paper is based on the maximum likelihood function and is supported for our data by the Akaike Information Criteria AICC), Schwartz Information Criteria (SIC), Hannan–Quinn Information Criteria (HQIC) and Final Prediction Error (FPE) lag reduction tests (Table 3).
We present only the maximum lag length (see Appendix 2).
Maximum lag is automatically selected based on Schwarz information criterion.
However, causality tests are generally sensitive to lag structure.
This lag structure give us the spatial relationship among locations.
We look to determine maximum lag for which PACF coefficient was statistically significant and the lag gives the minimum AIC.
A maximum lag order of 8 is allowed in the computation of the ADF and WS statistics.
In our application, we take a maximum lag truncation of 12.
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