Since the PDO series starts at year 1900, the period 1900-1953 will be considered the training period since all time series are available during this time span.
An ARIMA model was fitted to the PDO series  for the training period (1900-1953). An autoregressive model of order 1 (AR(1) ) was adequate for the series. Figures \ref{586715} presents the sample crosscorrelation function (CCF) between the PDO series  (X) and the PDSI series (Y) , and the sample CCF between the pre-whitened  X series (residuals after fitting an ARIMA model)  and the filtered Y series (after applying the AR(1) filter).