A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.
"On Consistency in Time Series Analysis." Ann. Statist. 6 (1) 215 - 223, January, 1978. https://doi.org/10.1214/aos/1176344080