# How to interpret the partial autocorrelation function when non-zero values are preceded by zeros?

I am working with a large number (>500) of partial autocorrelation functions, each for a different time series. I want to be able to quickly identify the likely order of an autoregressive model based on the PACF. In some cases the PACF has a value at a lag (say, lag $$k$$) that is between the confidence intervals (i.e. they are not significantly different from zero), but the PACF has a value at lag $$k+1$$ that is outside of the confidence intervals (i.e. it is non-zero). How should this be interpreted?