You state that the data cover 10 years and 39 companies, but you don't state whether that is one measurement per company per year or one measurement in each company in the first year and again in year 10 or something else entirely. Thus, it is hard to gauge the extent to which this is a problem where the residuals should be treated as coming from a time series vs a problem where the residuals covariance matrix can only be treated as being correlated.
I would direct you to the TSCSREG procedure in the ETS module or the MIXED procedure in the STAT module as places to start. The TSCSREG procedure is designed specifically to model time series data for multiple cross-sectional units (companies). The MIXED procedure has some functionality for handling time series data, but has capability for more general modeling of residual covariance structures. One or the other of those ought to handle your data pretty nicely.