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StatisticalScience 2012,Vol.27,No.4,594–606 DOI:10.1214/12-STS388 (cid:13)c InstituteofMathematicalStatistics,2012 A Conversation with David Findley Tucker S. McElroy and Scott H. Holan Abstract. David Findley was born in Washington, DC on December 27, 1940. After attending high school in Lyndon, Kentucky, he earned a B.S. 3 (1962)andM.A.(1963)inmathematicsfromtheUniversityofCincinnati. 1 He then lived in Germany, studying functional analysis under Gottfried 0 Ko¨the, obtaining a Ph.D. from the University of Frankfurt in 1967. Re- 2 turning to the United States, he served as a mathematics professor at the n a University of Cincinnati until 1975. Having transitioned from pure math- J ematics to statistical time series analysis, Findley took a new academic 7 position at the University of Tulsa, during which time he interacted fre- quently with the nearby research laboratories of major oil companies and ] E consulted regularly for Cities Service Oil Company (now Citgo). In 1980 M he was invited to lead the seasonal adjustment research effort at the U.S. . Census Bureau, and eventually rose to be a Senior Mathematical Statis- t a tician before his retirement in 2009. In 1966 he married Mary Virginia t s Baker, and they currently live in Washington, DC. [ David Findley has published more than 40 journal articles and book 1 chapters, as well as dozens of technical reports and conference proceed- v ings,manyofwhichareheavilycitedandinfluential.Hehasalsopublished 4 two edited volumes (1978 and 1981) that have had a substantial impact 8 1 on the field of time series analysis. Numerous honors and awards have 1 accrued to him, including ASA Fellow (1987), the Julius Shiskin award . 1 (1996) and the U.S. Department of Commerce Gold Medal (1997). 0 3 Key words and phrases: Census Bureau, diagnostics, model selection, 1 seasonal adjustment, signal extraction, time series. : v i X The initial conversation between David Findley, 1. EDUCATION r a Scott Holan and Tucker McElroy took place on July McElroy: Hello, David. We are thankful to have 13,2010attheU.S.CensusBureau.HolanandMcEl- theopportunitytodiscussyourlifeandcareer.Could roylaterobtainedclarificationsofcertainpointsfrom you describe for us the early influences that led you David Findley during the following year. to pursue a career in mathematics? Findley: In high school I found algebra and geom- Tucker S. McElroy is Principal Researcher, Center for etry enjoyable and interesting. I found out decades Statistical Research and Methodology, U.S. Census later that many of my relatives were mathemat- Bureau, 4600 Silver Hill Road, Washington, DC ics teachers, including one who taught in Suitland 20233-9100, USA e-mail: [email protected]. High School, not far from the U.S. Census Bureau Scott H. Holan is Associate Professor, Department of (USCB). However, my plan was to study physics, Statistics, University of Missouri, Columbia, Missouri and I decided to become a mathematics major only 65211-6100, USA e-mail: [email protected]. when I found out that the mathematics department at the University of Cincinnati would let me take This is an electronic reprint of the original article advanced calculus and linear algebra before com- published by the Institute of Mathematical Statistics in Statistical Science, 2012, Vol. 27, No. 4, 594–606. This pleting the basic calculus sequence, whereas the un- reprint differs from the original in pagination and dergraduate program chair of the Physics Depart- typographic detail. ment would not accept the summer version of the 1 2 T. S. McELROY ANDS. H. HOLAN Beyondmygettingasolidmathematicsbackground, a few other circumstances there also had a large impact. The Math Department’s flexibility continued into graduate school. Because of my interest in physics, I was interested in Hilbert space theory. There was no expert in functional analysis on the faculty,butIandtwomoreseniorgraduatestudents wereallowedtogiveourselvesareadingcourseinthe area with nominal faculty supervision, working our way through the masterful monograph by Riesz and Nagy [25]. Then I was permitted to write a master’s thesis in the area on the topic I chose, expositing a Rus- sian mathematician’s paper on operator representations, generalizing the representation formulas for symmetric and unitary operators, which generalize Fig. 1. David Findley receiving the Commerce Gold Medal the representation formulas for symmetric matrices 1997. David Findley was honored with this award for scien- tific leadership and contributions to the field of time series and unitary matrices. As a consequence, the first analysis, especially seasonal adjustment research. timeIencounteredthebackshiftoperatorintimese- ries analysis and the Cramér integral representation of stationary processes, I recognized them as special general physics course as an adequate prerequisite cases of unitary operator representations. This led for the upper-level physics courses that I wanted to me to conclude that I had an advantageous back- takemysophomoreyear.Bymajoringinmathemat- ground for time series analysis, which led me (years ics, I was able to take the physics courses I wanted, later) to choose this as my area of statistics. including a graduate level electrodynamics course My contacts with Germany also came from UC. my senior year, along with enough graduate mathe- Freshmanphysicsmajors wererequiredtotake Ger- matics courses that I was prepared to complete the man,and—perhapsbecauseof Cincinnati’s German master’s program in mathematics a year later. heritage—therewereoutstandingteachersintheGer- McElroy:Isee;butthiswasinCincinnati,whereas man Department. After three semesters of German you were born in Washington, DC. courses, I felt I had a solid foundation for studying Findley: I spent the first 12 years of my life in inGermany,whenlater theideacametomeofcom- Washington DC, butmoved with my family to Day- biningmy desire to live in Europewith my desire to ton, Ohio, which is close to Cincinnati. get a Ph.D. in mathematics. Holan:Soyourinterests inmathematics primarily Fortunately,forme,theMathematics Department began in high school? in Cincinnati had a professor from Germany named Findley: No, I was interested in physics. I mean, Arno Jaeger, who knew the functional analyst in I enjoyed mathematics, but I was set on physics GermanyIhadwantedtoworkwith,GottfriedKo¨the from an early age. Perhaps because I had been very in Heidelberg. Jaeger also knew a German mathe- impressed by the age of four or five by the atomic matician at the University of Maryland in College bomb, having seen pictures of it on the front page Park, who could offer me a research assistantship of the newspaper. after I learned that Ko¨the would be in College Park Holan: That leads to our next question: why you for the 1963–1964 academic year. chose theUniversity of Cincinnati.Did you consider McElroy: After the University of Cincinnati, you any other schools, such as The Ohio State? held a research assistant position at the University Findley: I only looked at theUniversity of Cincin- of Maryland. What sort of research were you doing nati (UC), because a high school counselor had rec- at the time, and did this have any influence on the ommended it. He knew that its College of Engineer- problems you would later consider in your career? ing had a strong reputation, and assumed that its Findley: The research assistant position had vari- Physics Department would be equally strong, which able duties dependingon who you were working for. it wasn’t at that time. I marked test papers for a first year graduate course A CONVERSATIONWITH DAVIDFINDLEY 3 and proof-read a Ph.D. dissertation. At Professor Findley:Itconcernedthestudyofaquiteabstract Ko¨the’s request, I presented an exposition of a re- generalization—given inpapersin 1963 and1964 by cently publishedpaperbytwo Japanesemathemati- W. A. J. Luxembourg and A. C. Zaanen—of the cians in the Functional Analysis seminar series that general class of vector space of real-valued sequence ran for decades in thehome of Professor John Brace spaces defined by Ko¨the and his Habilitation super- inCollegePark.Theirpaperprovidedacomplicated visor Otto Toeplitz in a 1934 paper. I was able to counter-example to a long-standing open question. prove analogs, in this new abstract setting, of sev- Later in Germany, I learned that seminar presenta- eral results established by Ko¨the in a series of pa- tionslikethiswerethemainfilterusedbyprofessors pers from 1935 to 1951, results that made these se- to select Ph.D. dissertation students. quence spaces quite influential in the development Holan: When you were at the University of Mary- of the theory of locally convex topological vector land (UMD), were there any young professors there spaces. The only part of this work I have been able with whom you came into contact? touseinmytimeseriesresearchisacharacterization Findley: There were two graduate students who I learned then of compact sets in the vector space of showed the rest of us what it was like to be really absolutely summable sequences. This played a mi- gifted! Simon Levin and James Yorke; James has nor clarifying role in a later paper with Benedikt become very well known for his work in chaotic sys- Po¨tscher and Ching-Zong Wei on almost stationary tems theory. He was a graduate student there, and processes [19, 20]. he was then hired after graduation by UMD. I know Holan: So, you decided to go back to the Univer- thetime series analysts at Maryland,butthey came sity of Cincinnati after graduation? Was this your later, and I got to know them by giving seminars first job out of school? at the department. That is where I met my future Findley: Yes, I felt it was an honor to be invited co-authors Ching-Zong Wei and Benedikt Po¨tscher, back. I knew and liked the department, and also my wholaterleftUMD—butwhowerethereatthetime wife, who is a violinist, wanted to continue studying that I started giving seminars. with the violin teacher she previously had at the Holan: At thetime you were a Ph.D. student, was College-Conservatory of Music at the University of it common to go study abroad? Cincinnati. So it suited both of us. Findley: My parents had traveled in Europe, and Holan: So, at the time they just invited you back seemed to enjoy it a lot, and I felt that my German to apply? Today it seems to be much more of an adventure finding a job out of school. language training was solid enough that I probably Findley: It was a slightly different time. Perhaps would survive. In Heidelberg there were a number a year or two after I was back at the University of of foreign students, and also other mathematics stu- Cincinnati, the job market for new Ph.D.s in math- dents from the United States. But, I was the first ematics became quite tight. However, there were US citizen to get a doctorate from the Faculty of many jobs available at the time I applied. In fact, Natural Sciences of the University of Frankfurt. I was also encouraged to apply for a position at the Holan:WereyourclassesinGermanorinEnglish? University of Maryland; so, I wasn’t worried about Findley: German; keep in mind that mathematics opportunities in mathematics. is probably the easiest subject to study in a foreign language. The vocabulary is pretty limited and 2. TRANSITION TO STATISTICS pretty predictable in its forms! McElroy: It seems that during the sequence of Holan: Your return to Cincinnati seems to mark your studies, there was an interval of time between the time you transitioned to time series analysis. HeidelbergandFrankfurt,attheUniversityofCincin- Given your physics interests and the inherent dy- nati. namics of many physical processes, it seems to be Findley: Yes. I came back to the US for various a natural development. Where did you learn time personal reasons, including a death in the family, series analysis? andalsotoearnenoughmoneytomarrymyfiancée. Findley:I was self-taught. I foundthat whenIbe- Also,IwantedsometimetodecidewhetherIwanted gan writing research papers in mathematics that to continue in mathematics, or return to physics. the audience, perhaps because of the area in which McElroy:YourPh.D.workinGermanylastedthree I wrote my dissertation, was very small indeed and years. What was your dissertation about? that the amount of effort necessary to write pa- 4 T. S. McELROY ANDS. H. HOLAN pers that would get into respected journals was so oilcompanyresearchlabsinTulsa.So,IknewIwould great that I became somewhat frustrated.Addition- haveacommunity ofpeopletoworkwith.Addition- ally, I felt that most mathematicians looked to the ally, they were willing to hire someone with no pub- mathematics literature for stimulation for research, lications in time series analysis, because they were rather than anything outside mathematics. Some aware that a mathematician could become a com- were even contemptuous of the mathematical work petent time series analyst. donein,say,econometricsandotherdisciplines.Now Holan: In addition to your colleagues, you also in Frankfurt, through singing together in a chorus, worked as a consultant at Cities Service Oil. Can I had become friends with the young Professor of you tell us a little about your experience there? Stochastics, Hermann Dinges (each Full Professor Findley: I should back up and mention that every had his own Institute then), with whom I had taken mathematics professor there did consulting work, advancedseminarsinMarkov processes;hehadsug- because it was available. The university thought it gested a research problem to me involving Wiener– was a perfectly reasonable thing, as long as they Hopf factorization. So I was interested in stochas- did some other academic things. There were several tics, and therefore also in statistics. So after a year major oil company research labs inTulsaand neigh- or two I started teaching statistics courses for engi- boring cities, and oil companies have been quite at neering students, and knew of the book by Box and the forefront of using new technologies. They were Jenkins [4]. among the first to use radioactivity as a measuring In 1973, at the invitation of the sole mathemat- tool, usinggamma rays in well logs to discover what ical statistician in UC’s Mathematics Department, was down there. So, there were interesting scien- Manny Parzen and Grace Wabha gave a one day tific problems to work on and, in the particular case overview of time series analysis. From this overview of Cities Service, the university had been given a I recognized that time series play an important role building which had belonged to the Carter Oil com- in many disciplines, and that the field uses mathe- pany. Von Neumann had consulted in this building, maticaltoolsthatotherstatisticalfieldsdonot.Ide- and it housed on one end most of the engineering cided to become a time series analyst, and to start college, and at the other end the Cities Service re- by reading books with a probabilist colleague who search laboratories, which the university leased to found the one day overview very stimulating. Grace Cities Service. So I walked out the door at one end Wahba recommended Ted Anderson’s 1971 book to of the building and in the door of the other end, to us [2], which we worked through very thoroughly. consult, which was a very nice arrangement! Later, after I accepted an offer for a time series Also, I helped a geophysicist who was applying positionattheMathematicsDepartmentoftheUni- statespacefilteringmethodology—Kalmanfiltering— versity of Tulsa (TU) in the Spring of 1975, I was tosomegeophysicsproblems.Iworkedonsomeprob- asked to preparea course for the fall semester based lems related to time series methods and seismology. onDavidBrillinger’s1975monograph[5].Afterread- There were pure statistical issues—pure time series ing his powerful presentation of the frequency do- issues of a certain kind, arising from physical rea- main perspective, I decided instead to give a semes- sons. If you calculate wave propagation through a ter-long series of lectures for Mathematics Faculty variety of media and assume everything is happen- membersonitscontents, whilepresentingamoreel- ing in one dimension, autoregressive processes seem ementary two-semester course for the graduate stu- very natural, since partial autocorrelations repre- dents, many of whom worked in exploration seis- sent reflectivity coefficients, and anything that is mology for local oil companies. I taught this two- forecastable represents noise, usually arising from semester course every year at TU, updating it an- echoes of a wave hitting the transition between ge- nually with newmaterial, suchas state–space meth- ologic strata. Thus, anything that was predictable ods. was noise, and hence prediction error filtering was McElroy: What were your reasons for moving to important. I developed some time-varying methods TU? for predicting fifty steps ahead—we were getting Findley: Oh, they advertised the position in time perhapstwenty-fivehundredmeasurementsasecond series analysis, and that was what I wanted to do. in these seismograms, so fifty was a useful forecast Also, they already had three mathematicians on the interval. faculty who had trained themselves in time series Holan: Did any of that consulting work generate analysis—perhaps through consulting work for the mathematical research? A CONVERSATIONWITH DAVIDFINDLEY 5 Findley: The paper on my algorithm for time- Findley: Yes, indeed. When I later left TU and varying forecasting for forecast error analysis was came to the CensusBureau, I lost contact with peo- published in one of the symposium proceedings vol- ple from the geophysics and seismology community, umesfromthetwosymposiaIorganizedinTulsa[8– but I certainly maintained contact with most of the 10]. It had a different approach to looking at Levin- statisticianswhocame.Instatistics,therewasManny son’s algorithm [23]. (Mostly known to statisticians Parzen, Hirotugu Akaike, Henry Gray, G. S. Wat- through the special case independently discovered son,RichardH.Jones,DougMartin,DavidDonoho, by Durbin [7].) I was able to give a geometrical in- WilliamDunsmuir,WillGersch,GenshiroKitagawa, terpretation of it, which seemed possibly new at the Wayne Woodward and Mel Hinich. The electrical time. engineers Alan Oppenheim, Thomas Parks, John McElroy: Can you talk a bit about those sym- Makhoul and Jerry Mendel also attended, as well posia? as the geophysicists Enders Robinson, Sven Treitel Findley: Yes, they were a great opportunity. My and Freeman Gilbert. colleague J. B. Bednar suggested, after I had been WillGerschlater cametoUSCBasanASA/NSF- at TU for a month or two, that I organize a sympo- Census research fellow, with Genshiro Kitagawa as sium on time series analysis. There were now four hisresearchassociate.Akaike,GenshiroandIworked people in the department interested in the subject, together when I visited the Institute of Statistical and I saw this as an opportunity to get in contact Mathematics in Tokyo. My contact with Akaike was with the leading time series researchers in a number verylong-lastingandveryfruitfulforme.Justabout of different fields. This was an idea that was very everyone I mentioned is someone I have benefited exciting to me. I asked J. B. Bednar to contact a substantially from at later times, through contacts very respected electrical engineer at MIT, Alan Op- of one kind or another. Also Enders Robinson can penheim, and ask if he would be willing to speak at be classified as both a time series analyst and a the conference. Once he received an affirmative an- geophysicist; he has written a number of time se- swer, I contacted Manny Parzen, and after he said ries books [26]. His prediction error methods were yes, I contacted Henry Gray. After that we were very important for exploration seismology. Freeman launched, because it began to look very credible! Gilbert was there. Freeman is a very well-known seismologistwhomDavidBrillingerhascollaborated Akaikehappenedtobeonsabbaticalleave atHar- vard; so I contacted him and he agreed to come. with. Sven Treitel, a leading exploration geophysicist, was there from Amoco. So it was a stellar ex- I wound up inviting people from geophysics, electri- perience for me to interact with these people! cal engineering, exploration seismology—or seismol- ogyingeophysics—mathematics,astronomy,andsta- 3. AT THE CENSUS BUREAU tistics. I later discovered that there had been a very successful symposium in 1962 that Murray Rosen- Holan: What led you to leave academia for a fed- blattorganizedatBrownUniversity,whoseproceed- eral career? Maybe you could tell us a little about ings had been published as a book by Wiley, and whattheCensusBureauwaslike; forexample,what that the Tulsa symposium was the first thing like the research environment was like and how your that, bringing people together from so many differ- transition from academia transpired? ent fields. Therefore, there was really great inter- Findley: I knew of the Bureau’s reputation in the est in having such a symposium. Additionally, the field of seasonal adjustment and the influence of its first symposium was successful enough that, when X-11 software. This gave me the sense that any re- three years later I organized another such sympo- search done by me or my group would be noted and sium, things went very well from the beginning! considered by statistical offices and central banks McElroy: Were there any econometricians at the around the world—a larger potential audience than symposium? exists for most academic papers. Also, I was sure Findley: Yes: Clive Granger and Rob Engle, who that there would be support for implementing re- shared the Nobel prize for economics in 2003. They sults of research in software designed for public use, gave very interesting talks,andweredelightful, very making it much more likely that the results would well-informedandinterestingcontactsforlaterwork. be used in practice. This is in contrast to the sit- Holan: Did you keep in contact with many of the uation with software developed in academia, which people at the symposia? usually can only be used by its author. Thus, I felt 6 T. S. McELROY ANDS. H. HOLAN Fig.2. DavidFindley,KunioTanabe,WillGersh,HirotuguAkaike,WallaceLarrimore,andRajBhansali.(US/JapanCon- ference on the Frontiers of Statistical Modeling: An Informational Approach, held at the Department of Statistics, University of Tennessee, Knoxville, to commemorate Akaike’s 65th birthday.) I could have a greater practical impact by working on, that Brian Monsell showed up. Brian has out- at USCB than by staying in academia. standing programming ability, and also a keen in- Finally, I knew from having lived there that the terest in making software usable. Brian was able to Washington, DC area was intellectually stimulating work easily with lots of different operating systems in the field of statistics, because there were a large and write good code, which programmers at SAS number of statisticians there. I was looking forward and other people who have translated his code have to working with Bob Shumway at George Washing- complimented. So, one needs good luck, and Brian’s ton University (GWU), but he was on sabbatical coming along was good luck, as was Bill Bell’s being leave at the University of California, Berkeley, and here, at the time! then accepted a position at Davis. So, Kirk Wolter Bill supervised much of the programming having ofUSCBwrotetoanumberofprominenttimeseries todowithtimeseriesmodeling.But,wedidn’tstart analysts, two of whom recommended me to him. He out programming. I mean, we started out just try- then contacted me, and I came to the Bureau for an ing to respond to whatever the needs seemed to be. interview. Our ultimate goal was to improve the practice of McElroy:Itisinterestingthatyouranswertothat seasonal adjustment at the Census Bureau and else- questionisalmostidenticaltotheanswerthatAgus- where. USCB was still using X-11 then, and hadn’t tin Maravall gives for why he chose a career at the even made the switch to X-11-ARIMA, so working Bank of Spain, namely to develop and maintain a on that transition was important, and other things major software package. came along that also seemed important. Later we Holan: So, in the early development of the soft- realized that there were quite significant things that ware that came out of Census, were you the orig- X-11-ARIMA couldn’t do, namely estimate regres- inal programmer, or did you oversee the program- sion functions jointly with the ARIMA models so ming? that you could estimate level shifts and other out- Findley: No, no; I was not one of the program- liers,aswellasotherkindsofuser-definedregressors mers. They had a programmer already hired when for special effects. I came here. He was someone with a Master’s de- Holan: Given the production needs at the Cen- gree in mathematics, but he had no background sus Bureau, how much time did you spend doing in statistics, and therefore didn’t really understand research? Was it your responsibility to ensure that what he was programming. I was lucky, very early the research have an influence on production? A CONVERSATIONWITH DAVIDFINDLEY 7 Findley: Yes, it was my responsibility. By way of For example, suppose you are sitting at your desk background, in 1978 and then in 1980, the Census and you figure something out, on the topic of con- Bureauhad heldtwo large seasonal adjustmentcon- current adjustment, and you say, “This really looks ferences with many distinguished speakers, includ- like what we need to do.” What was the process for ing Clive Granger. As part of a way of building up getting things implemented in production back in momentum for a new time series center at the Cen- those days? sus Bureau, they had hired two statisticians—one Findley: It was a matter of talking about it, and Master’s degree statistician and one Ph.D. degree presenting results in seminars. Also taking series statistician—in addition to the programmer I men- from each one of the production groups there, and tioned earlier, and already had them working. Kirk giving them the results for each one of their groups. Wolter, who knew time series analysis, as well as Also,therewereotherthingstotalkabout.Thenext samplesurveymethodology,hadbeendirectingsome big project that came along was due to someone work. So, when I arrived, I had to learn about sea- who, without consultation or approval, seasonally sonal adjustment myself! I knew that it existed as a adjusted the January value of a very important se- subject and that it had connections with signal pro- ries,petroleumimports,thathadn’tbeenseasonally cessing, but I had a learning curve to go through. adjusted before because it didn’t exhibit stable sea- But to go back to your question: Kirk Wolter had sonal characteristics. This happened when Shirley established monthly meetings in which all the peo- Kallek, the Associate Director for Economic Statis- ple in the Census Bureau interested in seasonal ad- tics, was out of town, and she decided that the pub- justment attended, and some topic that seemed to lished adjusted number had to be replaced with the be of general interest was discussed. I found out, unadjusted number. This indicated a different di- perhaps in the first week, that Wayne Fuller, who rection, which was embarrassing to the government. did consulting for the Census Bureau, had said that So she asked us to develop diagnostics to correctly he would not work on seasonal adjustment until ascertain when series were not good candidates for they started doing concurrent seasonal adjustment, seasonal adjustment. That set off one of the veins namely using all of the data available every month, of my work that has continued until I left the Cen- rather than forecasting seasonal factors from De- sus Bureau, and is still ongoing. So, diagnostics and cember of the year before. Thus, I had a mandate model selection are the two most continuous veins right away to make a strong case for concurrentsea- of research that I have pursued during my years at sonal adjustment. These monthly meetings, where the Census Bureau. thedivisionsdiscussedproblemsof interest tothem, Holan: So—unusually for a federal employee— also provided an opportunity where we could re- you’ve been able to visit numerous different places, spond to their problems; we could also present the and work with many different people, and spend a research results we were obtaining on the smaller considerable amount of time away from the Census revisions you got to seasonal adjustments—smaller Bureau, sort of like an academic on sabbatical. revisions after you recalculated the adjustment us- Findley: Yes; the thing I was most nervous about inglaterdata—thatcameformostofthetimeseries in leaving academia was giving upsabbatical leaves, when you used all of the data available, rather than because I had already had one and found it very usingforecasted seasonalfactors fromtheDecember fruitful to go away for a number of months to an- before. otherplace,andinteractwithotherpeopleandshare This kind of idea, that you shouldn’tjust usepro- an office with someone doing something completely jected seasonal factors, had been a big stimulus to different, but something that turned out to be in- Estela Dagum to introduce ARIMA models to fore- teresting to me. It was broadening in some way. It cast ahead, so that you could at least use forecasted is the international nature of seasonal adjustment values as replacements forthedatathat you weren’t work that to some extent led to my receiving invi- ready to use, or didn’t even have if it went past tations to go to other places. It was also Bill Bell’s a certain point. So, these monthly meetings, which presencehereonthetimeseriesstaff,beingperfectly continued for several years, built up a rapport with capableoftakingoverformewhenIwasaway,which the other groups in the Census Bureau. I think they was probably more important in making it possible. may have gone on for ten years. Thesevisiting positions have always been produc- Holan: In those times, what was the day-to-day tive for me, usually enabling me to complete re- process like in terms of research versus production? searchrelated tomodelselection thatIcouldn’tfind 8 T. S. McELROY ANDS. H. HOLAN time for at USCB. I have been especially fortunate to have more than one such visit to the Institute of Statistical Mathematics (ISM) in Japan and the In- stitute of Statistical Science of Academia Sinica in Taiwan. Both have strong research groups in many areas of statistics, superb libraries and other research resources, and contacts with other organiza- tions, including statistical offices interested in seasonal adjustment. Genshiro Kitagawa has always been my host at ISM, where Akaike had become director. On my first visit, he provided me with data to try out a slight modification of the order selection procedure for avector autoregressive model-based shipautopi- lot, developed by him in collaboration with marine Fig. 3. Zhao-Guo Chen, David Findley and Ching-Zong Wei at the home of David Findley, April 1989. engineers. I gave an invited presentation on this work at the1988 American ControlConference [11]. My future GWU Ph.D. student Jim Cantor was in ries models, probably including the purely ARIMA the audience, and was stimulated to later ask me to model-basedseasonaladjustmentprocedureofHillmer direct his dissertation work on the recursive estima- and Tiao [22]. George Tiao and his students have tion of incorrect time series models [6]. had a huge impact on the use of models in seasonal I also worked with Yoshinori Kawasaki at ISM, adjustment.WhenIarrivedattheCensusBureauin primarily in conjunction with a series of conferences 1980, his students Steve Hillmer and Bill Bell were relatedtoseasonaladjustmentthatalternatedvenues here.HillmerwasfinishinghisyearasanASA/NSF- between Tokyo and Washington, DC over a six-year Census Research Fellow with Bill Bell as his Re- period. search Associate. Bill was also finishing the writ- At Academia Sinica, I worked mostly with my ing of his dissertation, which had path-breaking re- host and co-author Ching-Zong Wei, whose death sults on nonstationary signal extraction relevant to from a rare disease ended a remarkable research ca- model-based seasonal adjustment. I was able to hire reermuchtoosoon.Ialsointeracted withtheecono- Bill, and with occasional input and contributions metrician Jin-Lung Lin on various topics related to from me, he led the modeling developments for the seasonaladjustment.Hewas attheInstituteofEco- next two decades and more. These efforts resulted nomics there, and is now Dean of the College of in modelinginnovations that were incorporated into Management of Taiwan’s National Dong Hwa Uni- the X-12-ARIMA seasonal adjustment program re- versity in Hualien. leased by USCB in the 1990s [3]. This software is McElroy: Do you feel that themajor goals of time widely used around the world. series research at USCB have been met? Working with Brian Monsell and others, I led the Findley: The major goal has been to improve sea- development of the software’s new seasonal adjust- sonal adjustment practice at USCB and elsewhere. ment quality diagnostics, as well as model selec- This has involved the development of new proce- tion options concerned with transformations (such dures,models,model selection proceduresand diag- as logarithms) and with nonnested choices among nostics. Of course, one must evaluate these proce- candidateregressorsfortradingdayandmovinghol- dures for efficacy and practicality. Finally, it is nec- iday effects. essary to implement successful innovations in soft- The USCB plans to soon release the successor to ware. Much of this work has proceeded incremen- X-12-ARIMA,whichisnamedX-13ARIMA-SEATS. tally, in response to urgently perceived needs or in- Its new capabilities include the option to produce adequacies with existing procedures or tools, or due Hillmer–Tiaomodel-basedadjustments,andtocom- to new opportunities for collaboration with other pare them with X-12-ARIMA adjustments using a seasonal adjusters. common set of diagnostics. This should lead to a Itwasalwaysassumedthatwewould,inthecourse greaterunderstandingofbothtraditionalandmodel- oftime,developanewseasonaladjustmentprogram based adjustments. The model-based adjustments and that we would make greater use of time se- willcomefromitsincorporatedversionoftheSEATS A CONVERSATIONWITH DAVIDFINDLEY 9 seasonal adjustment program, thanks to the collab- needed parameters, they are going to corrupt the orationofitsdesigner,AgustinMaravalloftheBank good results you might have obtained from these of Spain. Equally vital to this undertaking has been models, using an independent replicate of the data. the outstanding software development ability and In this situation, I was able to develop a theory of statistical understandingof BrianMonsell,whonow over-fitting, so that you can take the difference of leadsthetimeseriesgroup.HeandBillBellweremy the likelihood functions and use that as some kind most important hires. of measure of over-fit. Mathematicians and statisticians talk about over-fitting, but here was a case 4. PAST, PRESENT AND FUTURE whereIcouldprovesomeresultsandcomeupwitha RESEARCH rather precise measure—it is pretty theoretical, but at least it’s a handle on the concept of over-fitting, McElroy: Over your career you have made many making it a precise concept. contributions to model selection and seasonal ad- Athirdpaperthat comes to mindis theone I just justment. Of the different projects and papers you completed with Tucker, published in the 2010 JSPI have worked on, are there any favorites that you special issue honoring Manny Parzen [24]; because, have or that particularly stand out in your mind? again, in one case it is another kind of likelihood Findley:This is aquestion I might give a different ratio test for nonnested model comparisons. That answer to every time it is asked! Three papers come paper is generally concerned with the problem of to mind in model selection. I have the feeling that testing the forecasting performance of competing the1991 AISMpaper[12]Ididoncounter-examples models—that is, if you have a statistical test that to BIC and other parsimonious model selection cri- involves saying, “these two models are equally good teria has some value. It has been cited fairly often. at forecasting, one is not better than the other,” What I showed there was that when you are working with models that are not correct, and you are then you would like to have a test of some kind of making nonnested model comparisons, that one un- thishypothesis.Weanalyzeanin-samplemeasureof needed parameter’s estimate can cause problemsfor forecast error, and use as our null hypothesis that forecastingorparameterestimation,ingeneral,that thesetwomodelsforecastequallywell,andwereable are significantly larger than the influence of another to derive a test statistic, in particular an asymp- parameter that is not needed. In other words, we totic distribution for the difference of the two fore- tend to think: if you have p unneeded parameters, cast error measures—and a consistent estimate of then the distribution to describe this is a χ2 distri- the variance of this asymptotic distribution—which p bution or something like this, and there is a kind wecouldusetoformastatistic you couldusetotest of homogeneity to the effects of these unneeded pa- whether one model is better than the other. rameters; but it is not true in the case of nonnested I had started on this topic, in the context of like- incorrect model comparisons. lihood ratio tests, in the early 1980s. I had obtained Much of my research from early on has tried to an asymptotic distribution for the likelihood ratio address the situation of incorrect models, and I rec- in the nonnested model case, having been inspired ommended the use of AIC at the Census Bureau, by the work of the econometrician Quong Vuong, because there is some justification and demonstra- who had done similar things for regression models, blepracticaladvantages formakingcomparisonsbe- but I had never been able to find a consistent vari- tween nonnested models with it. This is something ance estimate for the asymptotic distribution, and that comes up often in seasonal adjustment, and Tucker and I were able to obtain that in our paper. I think in statistics in general. Additionally, there Now, when we find time, we’re at work generalizing aren’treallysystematicwaysofaddressingnonnested this to the vector autoregressive situation. model comparisons. Those are the papers I like that are concerned I’m also very pleased with the 2002 JMVA pa- with model selection. For seasonal adjustment paper [21] I wrote with Ching-Zong Wei on a rigorous pers, I particularly like papers that have had good development of AIC for vector autoregressive mod- expository value. I was invited to write a paper that els. There were some powerful new mathematical would be the Journal of Business and Economics results that others have used, which were in that Statistics invited paper for the 1996 Joint Statisti- paper. But also the paper contains a precise theory calMeetings[17],andIwrotethatwithBillBelland of over-fitting, which says that if you have these un- otherstaffmembers—BrianMonsell,Bor-ChungChen 10 T. S. McELROY ANDS. H. HOLAN and Mark Otto—and we really got a lot of ideas for research, and are you still active in research? about seasonal adjustment and the role of models What sorts of things are you doing? and model selection, and even estimation. It was a Findley:AsImentioned,Iaminterestedinthere- discussion paper, and that brought up a lot of other searchyouandIaredoinginextendingourforecast- ideas. So, I regard that as a valuable paper. ingandlikelihood ratio tests to thevector situation, I would like to mention the 2006 Journal of Of- at least for vector autoregressive models. I should ficial Statistics paper I did with Donald Martin on havementionedthataspecialaspectofthisresearch properties of time-domain filters, seasonal adjust- is that the effect—at least when multi-step ahead ment filters applied to nonstationary series that re- forecasting is involved—of parameter estimation is ally account for the fact that we are working with taken into account in these tests, in a way that has a finite sample, and which examined the effects of not been done before with time series models. So phasedelay [15].Iamalsoverypleasedwithapaper I think the paper’s important for that reason, too— that Catherine Hood and I wrote [14], just setting that it is kind of a breakthrough. out our procedures for seasonally adjusting a bunch I hope someday we will find a way to understand of time series we have never seen before. Specifi- what gain and phase function graphs mean for non- cally, how we go about choosing program settings stationary timeseries: I thinkthereis somehopefor for them, or perhaps even deciding whether they this when only one differencing is involved in trans- should be seasonally adjusted at all. The paper was formingthedatatostationarity.Butwehaven’tseen written for a conference sponsored by the Italian any reason to beoptimistic under morecomplicated Statistical Office, where they gave out a dozen or so differencing operations! I have some other papers time series and asked people to analyze them. Sub- on model selection that I have never written up. sequently, I have been very glad to have that paper I hope I’ll get around to writing those up, in time— available to hand out to people when I have taught mostlyhavingtodowithAIC,butforARIMAmod- seasonal adjustment courses. els rather than AR models.Also I would like to look I like the new trading day regressor that Brian at other situations, say where you’re trying to de- Monsell and I came up with, which is described in cide“shouldIuseaWeibulldistributionoralogistic our 2009 Journal of Official Statistics paper [16]. distribution to model a certain kind of data?” I had It seems to do very well with stock series (e.g., in- a project on that, where I got some pretty formu- ventories), better than the regressors we’ve had be- las, but never quite the theory needed to justify the fore. Akaike stressed to me the importance of mod- formulas. els, and Bill Bell’s concentration on models from his Holan: So, you’ve probably experienced a lot of education under George Tiao and George Box, has changes in statistics over the years. What is your certainly reinforced the power of models to me. To assessment of the state of statistics in general and convey statistical information, and good statistical the future of seasonal adjustment in particular? practice, models are an extremely concentrated way Findley: I don’t feel qualified to comment on the of presenting information to people doing statistical state of statistics in general. But in terms of impact work. on statistics, the internet has been the most impor- Holan: In 1987 you were elected Fellow of the tant development!—for disseminating data, for dis- American Statistical Association. Can you tell us seminating meta-data associated with the data, for a little bit about your award? disseminatingsoftware,fordisseminatingtheresults Findley: Yes, the award had particular meaning of research, and for maintaining contact with users. for me because, while I had had some coursework BrianMonsellgetsmanymessageseverymonthwith in stochastic processes in my Applied Mathematics seasonaladjustmentquestions;TuckerandIgetmes- Ph.D. studies, I had no formal training in statis- sages from people we have taught seasonal adjust- tics or time series analysis. Theaward confirmedfor ment courses to and other places, that sometimes me that I had successfully established myself as a turn into research problems and papers. statistician and time series analyst. I was delighted In seasonal adjustment, with the release of X-13 when Alan Izenman came up to me the day after ARIMA-SEATS, we have just now gotten to the the award with a warm smile and handshake say- pointwhereitis possibleto compare theresults of a ing, “Now no one can say you aren’t a statistician!” model-basedseasonaladjustmentandaseasonalad- McElroy: Well, you are now retired from your po- justment from the older X-11 filter methodologies. sition at the Census Bureau. Are there future plans I think that will be valuable and that, from having