Supplemental material for “ Space - time modeling of trends in temperature series ”

Let sk (k = 1, . . . , K) denote the locations of theK = 17 temperature series. At each location k we observe M(sk) temperature values z(sk) = (z1(sk), . . . , zM(sk)(sk)) T drawn from the M(sk)-variate random vector (RV) Z(s). Suppose at location k that these observations correspond to times Tt(sk), for t = 1, . . . ,M(sk). Since all sampling in the MCMC algorithm is performed on the wavelet domain, for each k let W Z(sk) denote the vector of wavelet and scaling coefficients of the wavelet transform of Z(sk) analyzed to level Jμ, and partitioned as (5) of the main article. Similarly at each location k let W μ(sk) denote the coefficients of the wavelet transform of the trend {μt(sk)}, W ψ(sk) denote the coefficients of the wavelet transform of the seasonality {ψt(sk)}, and W ζ(sk) denote the coefficients of the wavelet transform of the noise {ζt(sk)}. In our model the latent temperature process is {Yt(s)}. Let Y (sk) denote this process at location sk evaluated at the same M(sk) times point as Z(sk), and let W Y (sk) denote the coefficients