- Introduction
- Early life
- Academic career
- Chronological account of Hannan's contributions
- Appreciation of Hannan's contributions
- Recognition
- Influence on Australian statistics
- The Applied Probability Trust (APT)
- The human dimension
- About this memoir

Ted Hannan died in Canberra after a sudden heart attack on the evening of 7 January 1994. He had been his usual ebullient self during the day, when he had gone to work among his colleagues in the Department of Statistics, The Faculties, at the Australian National University (ANU). On returning home, he told his wife Irene that he felt tired, and retired early. He called out to her at about 9.15 pm during his heart attack, and was promptly driven by ambulance to the Woden Valley Hospital. Despite the care he received, he died before midnight. His death has deprived Australia of one of its most distinguished statisticians, and the world of an eminent time series analyst. This tribute, which can hardly do justice to his life and work, is presented as a record of the achievements of a most unusual, talented and well-loved colleague and friend.

We are fortunate to have access to Adrian Pagan's interview of Hannan for the journal* Econometric Theory *(1985), and to a personal article entitled 'Remembrance of things past' which Hannan published in *The Craft of Probabilistic Modelling *(1986). These, together with the citations for the Lyle Medal of the Australian Academy of Science in 1979 and the Pitman Medal of the Statistical Society of Australia in 1986, have provided us with useful accounts of his life, his research and his many other interests. I have drawn on these and on personal memories for much of my information; for the appreciation of Hannan's work, I have followed Peter Robinson's detailed analysis, which he kindly made available to me before its publication.

Hannan was born in Melbourne, Australia, on 29 January 1921. His father, James Thomas Hannan, was a freelance commercial artist of Irish Catholic parentage, and his mother, Margaret Josephine McEwan was of Anglo-Irish Catholic descent. He had one sibling, his twin sister Josie, a talented artist living in Melbourne.

Hannan attended primary school at St. Fintan's College, St. Kilda, an institution run by Nuns of the Presentation Order. He went on to Xavier College, Kew, a good Jesuit school, for his secondary education; there he excelled in his studies. He left the College at 15, after taking his Leaving Certificate. His father, who had lived through the Great Depression, advised him to take up a safe job, and he went to work as a clerk in the Savings Bank section of the Commonwealth Bank of Australia (CB). He continued in this post until 1941 when he enlisted in the Royal Australian Army Corps of the 2nd AIF. He saw active service as a lieutenant in the infantry in northern New Guinea against the Japanese. He spoke very rarely of his war experiences, and then tried to make light of the dangers he had faced in the New Guinea campaign. He had, in fact, once been wounded in an ambush and evacuated from the front.

At the end of World War II in the Far East, he was repatriated to Melbourne in 1946 and decided to take advantage of the Commonwealth Reconstruction and Training Scheme offered to ex-servicemen to enrol for a degree at the University of Melbourne. Almost by accident, he joined the Faculty of Economics and Commerce in 1946, because it had a minimum of prerequisites. In the course of completing his B.Com. degree, he took 13 subjects, ten in economics (including the Keynesian theory of money and banking, and public finance), two in mathematics (Pure Mathematies I and II, the latter taught by Hans Schwerdtferger) and one in statistics (taught by Maurice Belz). The last three subjects sparked off his enduring interest in mathematical and statistical theory. On completing his degree in December 1948, he decided not to continue with the final Honours year: he and Irene Trott wished to get married and would not have been able to afford it if he had remained a student. They were married in Melbourne on March 1, 1949.

After his graduation, Hannan was offered a job at the CB in Sydney, in what, after an Act of Parliament in 1959, was to become the Reserve Bank of Australia. He and Irene moved to Sydney directly after their marriage in 1949. He worked mainly as a statistician, calculating average interest rates, reconstructing an index of import prices, and building a small model of the Australian economy by Limited Information Maximum Likelihood (LIML) methods to find a consumption function. Partly in connection with his work, but mostly out of personal interest, Hannan read a great deal of modern mathematics and statistics, as some of the textbooks in his library attest.

In 1953, H.C. Coombs, then Governor of the CB and one of the founders of the ANU, chose Hannan to spend a year studying with Professor Trevor Swan at the ANU Department of Economics. There Hannan's exceptional talent in mathematics was recognized by Professor Pat Moran; the story is told that Moran, on one of his visits to the ANU Library, was surprised to find Hannan reading an advanced statistical treatise, Cramér's *Mathematical Methods of Statistics. *He struck up a conversation with him, and soon discovered that Hannan was well versed in both mathematics and statistics. Moran advised Hannan to change his field of study, persuaded Coombs to give him two years' leave without pay, and arranged a Research Fellowship to allow him to work towards a PhD in his Department of Statistics. Hannan never left the ANU; he was awarded his PhD in 1956 for a thesis on *The Theory and Application of Stochastic Processes, *and remained as a Research Fellow in Moran's Department until 1958. Hannan never forgot Moran's initial interest in him, nor his continuing encouragement. He retained a strong, almost filial affection for Moran throughout his life. In 1982, jointly with J. Gani, he edited *Essays in Statistical Science: Papers in honour of P.A.P. Moran*, on the occasion of Moran's 65th birthday.

In 1959, he was appointed to a Professorship in Statistics at the Canberra University College, then a college of the University of Melbourne. This later became the ANU School of General Studies (SGS), the undergraduate section of the ANU now known as The Faculties. Hannan was head of its Department of Statistics until 1970, when it appeared he might have to take up the Deanship of his Faculty. He decided that he could make a more valuable contribution by concentrating on his research, and was appointed the second professor in Moran's Department at the ANU Institute of Advanced Studies (IAS), the postgraduate section of the university. Freed of his teaching duties at the SGS, Hannan made rapid progress in his research, and guided a large number of students working towards their PhDs. When Moran retired in 1982, he succeeded him as Head of the IAS Department of Statistics until the appointment of Chris Heyde in 1985.

In 1986, on Hannan's retirement, the ANU appointed him an Emeritus Professor; he was offered a room and facilities in his old department at the SGS, where he continued to work until the very day of his death. He would usually be at his desk by 8am, and would spend his time reading, writing references, reviewing papers for the many journals with which he was associated, and carrying out research. He often collaborated with past students who had returned to visit him at the ANU. He would leave to catch a bus home shortly before 5pm; occasionally he would ask Irene or me to drive him home.

During 1993, Laimonis Kavalieris of the University of Otago joined him at the ANU in some research on ARMA (autoregressive moving average) models; he also corresponded regularly with David Huang and Barry Quinn on the book he was writing with them. His flow of ideas, many of them pioneering developments in time series analysis, continued unabated over a period of 40 years (1953-1993); he wrote over 130 papers and four very influential books (1).

Hannan's first paper, published in 1955, was concerned with singularities in Sydney rainfall. He retained his interest in hydrological and other climatic factors, as well as in geophysical data throughout his career. He returned to the topic of seasonal variation in 1960, rainfall singularities in 1962, hydrological time series and seasonal patterns in 1964, the analysis of geophysical data in 1966, the effect of weather on sea level in 1968, rainmaking with Moran in 1973, and surface and plane waves in 1975 and 1978. He was a very capable data analyst, with a flair for the interpretation of large tables of numbers, but showed a marked preference for theoretical research.

His major contributions were to be in the field of time series analysis, of which he became one of the recognized authorities. Pat Moran had initially asked him to examine problems of serial correlation; this formed the topic of his second paper in 1955, and led to his third paper on an exact test for correlation between time series. He continued with investigations on tests based on multiple correlations, serial correlation in vector processes, serial correlation in regression with Watson, the estimation of spectral density, and the asymptotic powers of goodness of fit tests in time series until 1960 when his famous monograph *Time Series Analysis* first appeared. It was destined to become a classic.

During the 1960s and early 1970s, Hannan pursued his research in time series modelling, possibly with a greater emphasis on econometric applications. He wrote several papers in this area, some individually, others jointly with Deane Terrell, his PhD student who was appointed Vice-Chancellor of the ANU in January 1994. Spectral inference formed the subject of other papers, some written with another student, Peter Thomson, while he collaborated with Des Nicholls on estimation in ARMA (autoregressive moving average) and other models. In 1965, he published a second book on *Group Representations and Applied Probability*, a mathematical topic in which he drew together group theory and its applications in probability theory.

The book which many consider to be his masterpiece, *Multiple Time Series*, was published in 1970. This is a profound work, whose density sometimes masks the depth of his understanding of time series. Ted himself felt dissatisfied with it: he thought he had devoted too little space to the Kalman filter and to establishing the representation of a system in state-space form. He sometimes spoke of revising it, but unfortunately never got round to it. The 1970s were a period of broadening research into lagged regression with Peter Robinson, limit theorems in discrete time series where the prediction errors are martingale differences with Chris Heyde, rainmaking experiments with Pat Moran, multivariate time series, vector linear time series with Bill Dunsmuir and Manfred Deistler, ARMAX (autoregressive moving average exogenous) models with Katsuto Tanaka, the asymptotics of serial covariances, multivariate ARMA theory, the order of an autoregression with Barry Quinn, and transient signals with Murray Cameron.

A further flowering of his research activities took place in the 1980s, with investigations into the properties of ARMA systems with Manfred Deistler, multivariate ARMA models, Akaike's criterion for determining the order of a regression, autoregression and ARMA estimation with Hong-Zhi An and Zhao-Guo Chen, ARMA processes, autoregressions and multivariate linear time series with Laimonis Kavalieris, a law of the iterated logarithm with Margaret Mackisack, time series and stochastic models, canonical correlation with Don Poskitt, ARMA estimation with Andrew McDougall, rates of convergence with Christian Hesse, spectral windows with Jorma Rissanen, and non-parametric estimation with Peter Hall. In 1988, his last book on *The Statistical Theory of Linear Systems* with Manfred Deistler appeared.

One might have expected that as he approached his 70th year, Hannan would begin to slow down. But he was still brimming over with ideas, though he would often remark that as he grew older, he found the help of younger researchers a stimulus in exploring their details. He collaborated with Bo Wahlberg on convergence rates for inverse Toeplitz matrices, with David Huang on line frequency estimation, and wrote a paper on frequency estimation for the Whittle Festschrift, which appeared in mid-1994. He was in the process of writing a book with David Huang and Barry Quinn during 1993; this work is to be completed by his two younger colleagues.

Of his work, Hannan probably thought most highly of his paper on spectral regression arising from his collaboration with Bruce Hamon of CSIRO on waves, his monograph on *Group Representations and Applied Probability *where he displayed his deep grasp of mathematical theory, his papers on seasonal adjustment, his book on *Multiple Time Series*, and his last book with Manfred Deistler on* The Statistical Theory of Linear Systems*. But his views about his work were difficult to pin down, with his modesty usually getting the better of him. If one asked him to evaluate the impact of his work he would dismiss his renown as being 'a bit generous'. Nevertheless, the corpus of his research indicates a deep approach to problems, backed by a rigorous mathematical technique. He emerges as perhaps the best known international time series analyst of the past 30 years.

Hannan's great strength lay in his mastery of the mathematical methods essential for the analysis of time series. The problems which he considered, however, arose from realistic models in hydrology, climatology, geophysics and econometrics.

His early research between 1955 and 1958 was concerned with testing for zero autocorrelation, against autoregressive alternatives. He soon recognized the inadequacy of finite sample theory, and began to make asymptotic comparisons of the Pitman efficiency (an index of relative performance of two sequences of test statistics). With Watson, he examined the results of mis-specifying the error spectral density, and suggested an asymptotic approximation for studentizing the sample mean of a stationary series. Later, he modified Fisher's test for a jump in the spectral distribution function by considering a non-parametric spectrum under the alternative hypothesis. In 1960 his first book *Time Series Analysis* was published: this was a short monograph on the time and frequency domains in the scalar case. It was immediately popular and was soon translated into Russian and Japanese.

A paper which Hannan always considered to be important was with Hamon. In it they proposed an original frequency domain weighted least squares estimate for combining narrow-band regressions, weighting inversely with smoothed estimates of the nonparametric error spectrum. Later, Hannan showed that this estimate was asymptotically as efficient as the generalized least squares estimate in the presence of nonparametric error autocorrelation. This may be considered as a very early example of adaptive estimation.

It was over a decade later that adaptiveness to regression error heteroscedasticity (difference in error variances) of unknown form with independent observations was finally demonstrated. Hannan, with Groves and Terrell, used the same approach in more elaborate models arising in oceanography and econometrics. In 1963, he introduced the idea of omitting frequencies to cope with the errors-in-variables problem. Hannan justified this view in his paper with Robinson, and the method was further developed subsequently in the econometric context.

Since the early 1960s Hannan had been interested in seasonality. Two early papers, using operators to estimate seasonality, were followed by the modelling of the seasonal component by a cosinusoid whose coefficients were stationary processes, so that its spectrum had smooth leaks. In a similar model in 1967, the roots of the coefficients lay on the unit circle; this was a pioneering idea which was to open up a fertile field of research.

His second book, *Group Representations and Applied Probability* published in 1965, explored the connection between Fourier analysis and group representation. This was followed two years later by a paper in which he presented a deep description of filters, exhibiting his mastery of the mathematical concepts involved. It is difficult to escape the impression that, had Hannan's early training been different, he would have become a distinguished mathematician.

In 1970, his book on *Multiple Time Series* appeared. This is possibly his single most important contribution to the field: it included much of his research over the previous decade, mostly in the multivariate context in both discrete and continuous time. His analysis was, as always, rigorous; but the book was thought difficult to read, containing as it did several unsolved research problems presented in the guise of exercises. It was later translated into Russian.

The next decade was devoted to the solution of several difficult problems in the frequency domain. With his student Thomson, Hannan established a Central Limit Theorem for the discrete Fourier transform of vector time series, while two other papers proposed improved estimates of coherence and group delay. In 1973, he studied a simple cosinusoidal regression with unknown real valued frequency. Later he analysed noise-corrupted measurements recorded at different locations, as well as with Cameron, and considered the properties of periodograms with Zhao-Guo Chen and with Zhao-Guo Chen and Hong-Zhi An.

A proper study of linear ARMA and transfer function models depends on the identification problem, which is difficult because of the presence of lags in the innovations, and possible input as well as output variables. Hannan gave the conditions for identification of stationary vector ARMA and ARMAX models of known order. Their algebraic and topological properties were further clarified through the concept of the McMillan degree, and with Dunsmuir, and with Dunsmuir and Deistler, with Deistler, and with Kavalieris. The McMillan degree may be interpreted as the number of linearly independent linear combinations of present and past vectors in a stationary vector process needed for optimal prediction of all future vectors within the ARMA structure.

The choice of the order of a scalar autoregression is a very practical issue in the use of ARMA and ARMAX models. Hannan proved the consistency of deterministic procedures for obtaining the order of scalar ARMA models, and he estimated the McMillan degree. He went on to discuss Akaike's methods in relation to ARMA models with Kavalieris. Hannan's paper on the subject gives an excellent account of this area.

While Hannan was primarily interested in the mathematical aspects of his research, he had a sharp eye for potential applications. He used an economic asymptotically efficient method in the frequency domain for the estimation of ARMA models. With Nicholls he extended his study to ARMAX models*, *while he and Rissanen developed a recursive ARMA estimation method. This was later modified with Kavalieris.

Hannan brought a variety of mathematical techniques to bear on his problems; of these perhaps Fourier analysis, of which he had a deep understanding, was the most important. He was a pioneer in the application of martingale theory to time series in the early 1970s, as for example in a paper published in 1973, where he improved on earlier asymptotic results. Basic results on the asymptotic properties of sample autocovariances were derived with Heyde, and also with Hong-Zhi An and Zhao-Guo Chen.

His most recent book, *The Statistical Theory of Linear systems *with Deistler published in 1988, collected together a large amount of his work on linear time series models. He continued to work after his retirement in 1986 on the application of stochastic complexity to spectral bandwidth with Rissanen, to nonparametric density estimation with Hall, and parametric signal filtering using Laguerre polynomials with Wahlberg. He was still working actively with Kavalieris on ARMA models, and with Huang and Quinn on frequency estimation at the time of his death.

Hannan's place in time series analysis is well stated by Maurice Priestley, editor of the *Journal of Time Series Analysis, *of which Hannan was an Associate Editor. Priestley writes:

Ted Hannan was a truly great name in the field of Time Series Analysis and over the past 38 years made outstanding fundamental contributions to many areas of the subject. It is true to say that no student of Time Series Analysis could possibly fail to become familiar with his research.

After the publication of his *Time Series Analysis *in 1960, Ted rapidly received international recognition for his research achievements. He was frequently invited to lecture at overseas universities, and address conferences in Europe, Britain, the USA, Japan and China. He gave a series of lectures during his visit to China in 1985, which were later published. He held visiting appointments at the University of North Carolina, The Johns Hopkins University, Brown University, Yale University (The Cowles Foundation), Princeton University MIT, and IBM (The Almaden Research Center at San Jose in California).

In 1970, Hannan was elected to Fellowship of the Australian Academy of Science, and in 1980 to Fellowship of the Academy of Social Sciences in Australia for his contributions to econometrics. He was also a Fellow of the Econometric Society (1967), an Honorary Fellow of the Royal Statistical Society and an elected Member of the International Statistical Institute (1967). He was asked to serve on the editorial boards of numerous journals, among them *Advances in Applied Probability *and the *Journal of Applied Probability, *the *Annals of Statistics, Econometrica, *the *International Economic Review, *the *Journal of Forecasting, *the* Journal of Multivariate Analysis, *and the* Journal of Time Series Analysis. *He was in constant demand as a referee by many more.

In 1979, the Australian Academy of Science awarded Hannan its Lyle Medal; his citation reads: 'Professor Hannan has made many fundamental contributions to the theory of statistical inference, particularly in connection with stationary random processes...His researches are based on a deep mastery of functional analysis and group theory.'

Seven years later, the Statistical Society of Australia presented him with the Pitman Medal, its highest research award, for gaining Australia 'a world-wide reputation as a centre of excellence for time series analysis'. In 1986, on the occasion of his 65th birthday, he was also honoured with a Festschrift entitled *Essays in Time Series and Allied Processes, *edited by J. Gani and M.B. Priestley and published as a Special Volume 23A (1986) of the* Journal of Applied Probability.*

Hannan clearly enjoyed the recognition he received, yet he remained singularly unaffected by it. He was not by nature inclined to reverence; although he had been brought up as a Catholic, he was not at all devout. He would often comment, however, on the profound mystery of life: he thought there was 'something behind it', but would seldom go further than this general expression of faith. He could not abide pretentiousness, and used to poke fun both at pompous colleagues and at himself; in one of his articles, he noted 'how unbearable we can become as we grow old, stressing the obvious, repeating the same advice and telling the same stories!' Eminent though he became, Hannan retained his respect for the fundamental human values; he could never take the importance of himself or others too seriously.

Despite many offers of positions overseas, Hannan was totally committed to remaining in Australia; while he enjoyed his jaunts abroad, he regarded Australia as his much loved permanent home. His research attracted postgraduate students from other Australian universities as well as from overseas, among them Murray Cameron, William Dunsmuir, John Henstridge, Yuzo Hosoya, David Huang, Michael Hune, Laimonis Kavalieris, Andrew McDougall, Margaret Mackisack, Des Nicholls, Barry Quinn, Peter Robinson, Victor Solo, Katsuto Tanaka, Deane Terrell, Peter Thomson and Ian Toft.

Hannan greatly enjoyed collaborating with colleagues on research projects; he wrote jointly on a variety of topics with Hong-Zhi An, Bob Anderssen, Ray Boston, Zhao-Guo Chen, Manfred Deistler, J. Franke, G.W. Groves, Peter Hall, Bruce Hamon, Christian Hesse, Chris Heyde, M. Kanter, Bob Kohn, Pat Moran, Mike Osborne, Don Poskitt, Jorma Rissanen, N.E. Tuckwell, Bo Wahlberg and Geof Watson.

He was generous with his time, and enjoyed discussing statistical problems with friends in Australia and overseas, among them Ted Anderson, Raj Bhansali, Sergio Bittanti, Peter Bloomfield, Harry Cohn, Jim Durbin, Warren Ewens, Chip Heathcote, Paul Kabaila, Don McNeil, Ian MacNeil, Marc Nerlove, Yosi Ogata, Tohru Ozaki, Manny Parzen, Maurice Priestley, Murray Rosenblatt, Eugene Seneta, Ritei Shibata, Terry Speed and Peter Whittle.

This brief list will indicate Hannan's many friendships with professional colleagues, and the central role which stimulating discussions held for him in his research endeavours.

Many of Hannan's students are now themselves influential academics in Australia, Britain, New Zealand, Japan and the USA, exploring and deepening his insights into time series and econometrics and advancing these fields in the directions which he first laid out. If Australia is considered today as a statistics-friendly country, it is in good measure because of Hannan's continued presence at the ANU in Canberra over a period of 40 years. He attracted many visiting statisticians with his scholarship, his insightful research, his good humour and his wit. One of his junior colleagues, now a professor in the USA, described him as having rapidly put him at ease during a shared plane journey 'by his numerous jokes and witty conversation, [he] treated me like an old friend rather than a lowly junior statistician'.

Hannan's technique for research student supervision was challenging: he would be full of suggestions for research problems, sometimes to the initial confusion of his student. When a problem was settled on, he would encourage the student to proceed with its solution, but could not always resist the temptation to do the work himself. He could be occasionally impatient with students' rates of progress, but always maintained his interest in their research and their personal welfare. He directed their projects firmly, yet always knew when to withdraw and let them complete the work on their own. He had the gift of being able to share his enthusiasm for time series with his students, while continuing to draw their attention to interesting unsolved problems in this field. He has left them with a rich legacy of expertise and a wealth of unsolved problems.

Australian statistics owes much to Hannan: he founded one of the major departments of statistics in the country at the SGS, trained a large number of postgraduate students both at the SGS and IAS, and brought Australia to the forefront of research in time series analysis. Together with E.J.G. Pitman, he ranks as one of the two self-trained Australian statisticians who achieved international eminence in their field while working in Australia.

During 1963, Hannan joined with Joe Gani and Norma MacArthur to found the Applied Probability Trust, an Anglo-Australian foundation designed to foster research in mathematics, and more specifically probability theory. The APT's immediate aim was to launch the *Journal of Applied Probability* (JAP), a periodical dedicated to publishing papers in applications of probability theory to the biological, physical, social and technological Sciences. At that time, no such journal existed, and papers in applied probability often failed to find acceptance in either mathematical or statistical journals. The three Australian Trustees raised £stg 2250, half the funds then required to print JAP for one year; with the help of David Kendall, they succeeded in obtaining the other half from the London Mathematical Society who nominated a fourth Trustee, Sir Edward Collingwood. Thus, in 1964 JAP was launched; Hannan was one of its first editors and remained on the editorial board till his death.

In 1969, The APT decided to add *Advances in Applied Probability *(AAP) to JAP; once again Ted became one of its editors. AAP was originally conceived as a medium for the publication of review papers, but it was later reserved for longer papers in applied probability and for Letters to the Editor. The APT also started *Mathematical Spectrum, *a magazine for students in the academic year 1968-69, and took over *The Mathematical Scientist, *a journal for general mathematicians started by CSIRO in 1976. Throughout the APT's years of development, Hannan was intimately involved in its policies and direction; although he did not care for administrative duties, he took his role as Trustee very seriously and would often cut through the complexities of a problem to offer a useful solution.

Hannan's main concern was always the quality of the papers appearing in the JAP and AAP; he saw to it that the papers in time series maintained a standard compatible with his own exacting criteria. As Trustees, we would have regular discussions on the new directions taken over the years by the subject of applied probability, and on its sudden flowering in the biological, environmental, electrical engineering, hydrological and operations research journals. We noted with pleasure the progress of the field over the past 3 decades, as gauged by the number of periodicals now serving applied probabilists, among them the *Annals of Applied Probability, Operations Research *and *Mathematics of Operations Research, Queuing Systems: Theory and Applications, Stochastics, Stochastic Models, Stochastic Processes and their Applications, *and *Transactions of IEEE *as well as the various time series journals such as the *Journal of Time Series Analysis *and *The Journal of Forecasting *on whose editorial boards he served.

Hannan contributed much to the growth of applied probability, partly through his influence as a Trustee of the APT and partly through his lively interest in the applications of probability to the modelling and analysis of natural phenomena. His contributions to the field, and particularly to time series analysis, form an integral part of the tradition of applied probability.

No account of Hannan's life would be complete without mention of his human interests. He was a devoted family man: he and Irene were married for 45 years and raised four children, Christine, Jenny, Patrick and David, of whom he was immensely proud. Hannan and his wife formed an inseparable pair, whose fondness for, and understanding of, each other seemed to require few words or explanations. Hannan relied heavily on his wife's judgment of people; he delighted in her company and would sometimes take the afternoon off to see a film with her. He occasionally felt that he might have neglected his family in an over-emphasis on his work, but nothing was farther from the truth. His feelings of inadequacy were due to the fact that his standards of caring were so high: he was deeply loved by his entire family.

He was much concerned with the health of his twin sister Josie, whom an early attack of polio had left partially crippled. He always spoke of her as 'an indomitable woman' who had made her way in the world, first as an artist in the Victorian Public Service and later as a freelance. He cared greatly for his sister-in-law Marion and her husband Dick Nicolson, who were regular visitors to Canberra and with whom he and Irene would spend occasional holidays. He was particularly fond of his six grandchildren, whose exploits he would retail with relish and with whom he was always very indulgent.

Hannan was a good humoured and totally unpretentious person, despite his immense intelligence and sharp critical sense. He could laugh at himself, as when quoting from his favourite poet W.B. Yeats' lines in 'Youth and Age'

Much did I rage when young

Being by the world oppressed,

But now with flattering tongue

It speeds the parting guest.

He was outspoken, frequently irreverent and occasionally quick-tempered, but always transparently honest and totally lacking in malice. His human qualities, his openness, charm and wit made him many friends in Australia and throughout the world.

Hannan loved literature and read very widely: biography, history, politics and poetry. We would spend much of our time together discussing the latest books we had read, or recent articles in the *New York Review of Books *to which we both subscribed. He finished reading Boorstin's *The Creators* (a history of the creative arts), a book I had lent him, about two weeks before his death, and had launched into Conor Cruise O'Brien's book on Edmund Burke, which he had received as a Christmas present. He described the latter as being somewhat biased in its views.

Hannan had the gift of remembering poetry and quoting it on appropriate occasions. He was particularly fond of Yeats, and would often quote from his poem 'A Prayer for Old Age'

I pray – for fashion's word is out

And prayer comes round again –

That I may seem, though I die old,

A foolish passionate man.

He thought of this as a not inappropriate description of himself.

Hannan was very fond of the Australian landscape. He felt very much at home among gum trees, and loved the skyline of the Brindabella hills near Canberra; he was very proud of Australia's landscape painters. He was equally proud of its scientists and Nobel Prize winners, among them Macfarlane Burnet, John Eccles, Howard Florey and Patrick White. He had an enormous enthusiasm for Australia's sportsmen: he would watch cricket or Australian Rules football on television on Saturday afternoons, and if I visited him at that time, would continue to barrack hilariously for his favourite team. He enjoyed hearing and telling jokes, good company and conviviality, and in the evening a single drink of Scotch whisky; I kept a bottle for him in our drinks cabinet for his occasional visits to our home.

In May 1993, after a lifetime of asthma attacks, which were treated with Ventolin inhalers, Hannan was diagnosed as suffering from a slight cardiac fibrillation. He took medication for this and seemed to have the condition under control. He continued to come to work at the ANU, to collaborate with visitors to the SGS Department of Statistics and the School of Mathematical Sciences, and to hold his usual lively discussions on the economic and political conditions of Australia, the civil war in Bosnia or the unrest in Israel, over lunch. He remained active right up to the afternoon of Friday 7 January 1994, joking with colleagues and remarking on his great good fortune at having enjoyed so full and interesting a life.

Ted Hannan was a distinguished statistician and an exceptional human being, who enriched the lives of all those he touched. He rejoiced in life and all that it had offered him in intellectual achievement and human fulfilment; of him it could truly be said, as in Yeats' poem 'The Apparitions'

When a man grows old his joy

Grows more deep day after day.

His sudden death has left a great gap in our lives: he will be greatly missed by all those who loved him – his wife and family, his friends and his colleagues.

This memoir was originally published in *Historical Records of Australian Science*, vol.10, no.2, 1994. It was written by J.M. Gani, member of the Stochastic Analysis Group, School of Mathematical Sciences, Australian National University.

Shorter and slightly different versions of this account have appeared in *Austral. J. Statist.* and *J. Appl. Prob.*

(1) Hannan, E.J., *Time Series Analysis.* Methuen: London. (1960) (Published in Russian with an Appendix by Yu. B. Rozanov in 1964; published in Japanese.); *Group Representations and Applied Probability.* Methuen: London. (1965) (Published in Russian with introduction by A.M. Yaglom in 1970.); *Multiple Time Series*, Wiley: New York. (1970), (Published in Russian in 1974); (with M. Deistler) *The Statistical Theory of Linear Systems.* (1988) Wiley: New York.

(2) This section relies heavily on Robinson's (1994) comprehensive analysis of Hannan's work.

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