A time-varying effect is an irregularly shaped curve, made up of an infinite number of points. You could measure the p-value at any one point, but that would tell you nothing about the validity of the rest of the curve. Alternately, you could take an average over the whole curve, but this would give you, effectively, no information at all about any single point on the curve.
For a time-invariant parameter, significance can be expressed through either a p-value or a confidence interval (as seen to the left). Because of the variation over time, the p-value is not useful for expressing the significance of time-varying parameters, but a dynamic confidence interval is. So, while journals typically print p-values, a confidence interval provides exactly the same information. That is why the %TVEM macro suite expresses results graphically. An empirical example of the application of the TVEM macro can be found in the article listed below.
Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., & Shiffman, S. (2012). Using the time-varying effect model (TVEM) to examine dynamic associations between negative affect and self confidence on smoking urges: Differences between successful quitters and relapsers. Prevention Science. PMCID: PMC3372905 doi:10.1007/s11121-011-0264-z