He then moved to Uppsala, Sweden in 1950 to study for his PhD with Herman Wold (at Uppsala University). His thesis, "Hypothesis Testing in Time Series", generalised Wold's autoregressive representation theorem for univariate stationary processes to multivariate processes. Whittle's thesis was published in 1951. A synopsis of Whittle's thesis also appeared as an appendix to the second edition of Wold's book on time-series analysis. He remained in Uppsala at the Statistics Institute as a docent until 1953, when Whittle returned to New Zealand.