The problem of identifying seasonality in published time series is of enduring importance. Many official time series -- such as gross domestic product (GDP) and unemployment rate data -- have an enormous impact on public policy, and are heavily scrutinized by economists and journalists. Obscuring the debate is the lack of universally agreed-upon criteria for detecting seasonality, as well as the different behavior of seasonal patterns in raw versus seasonally adjusted data. We propose the following verbal definition of seasonality: persistency in a time series over seasonal periods that is not explainable by intervening time periods. For a monthly series with a seasonal period equal to twelve, seasonality is indicated by persistency from year to year that is not explained by month-to-month changes. Note that both parts of this definition are crucial: without seasonal persistency from year to year, no seasonal pattern will be apparent, so this facet is clearly necessary; however, any trending time series also has persistency from year to year, which comes through the intervening months -- we need to screen out such cases. If a time series is covariance stationary, it is natural to parse persistency in terms of autocorrelation. The paper shows that we can adapt persistency to non-integer lags of the autocorrelation function via its decomposition in terms of autoregressive (AR) roots, and examine seasonality of arbitrary frequency through the modulus and phase of the root. Whereas under-adjustment would be indicated by the presence of AR roots of near-unit magnitude and seasonal phase, over-adjustment corresponds to a negative form of persistency (i.e., negative seasonal autocorrelations) termed anti-persistency, and can be measured through moving average (MA) roots computed from the inverse autocorrelations, i.e., the autocorrelations of the reciprocal of the spectral density.