The Pacific Decadal Oscillation (PDO) index defines the leading mode of monthly sea surface temperature (SST) anomalies in the North Pacific Ocean. Time series analysis in both the frequency and time domains is applied to 107 years of monthly PDO index values. Simulations of a model fitted to the data are used to estimate p-values associated with particular events observed in the raw data. The simulations are further used to estimate the distribution of various quantities, such as the length (in years) of a positive phase, or the absolute difference between the longest positive and negative phase (in years). The results show that the probability of occurrence of a negative phase surrounded by two positive phases within a 107-year period is approximately 9.9%. The raw data's mean positive phase length is close to the simulation mean and median, while the absolute difference in maximum positive/negative phase lengths corresponds to a p-value of 14.9%. The methodology developed in this paper can be useful to ecologists in assessing the potential ecological effects due to PDO variation, and for estimating the probabilities associated with future phases or other events.