Hong Kong Statistical Society

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1 香港統計學會 Hong Kong Saisical Sociey c/o Deparmen of Saisics & Acuarial Science, The Universiy of Hong Kong, Pokfulam Road, Hong Kong hp://www.hkss.org.hk Bullein Volume 6 No.

1 1 香港統計學會 Hong Kong Saisical Sociey c/o Deparmen of Saisics & Acuarial Science, The Universiy of Hong Kong, Pokfulam Road, Hong Kong hp:// Bullein Volume 6 No. December 003 Edior's Foreword There is a good news in he sociey of Saisics. The 003 Nobel prize in Economics was awarded o wo disinguished economericians Professor C.W.J. Granger of he Universiy of California, San Diego and Professor R.F. Engle of New York Universiy. I is a significan evidence ha Saisics is a very useful subjec. In order o le members know he conribuions of hese wo Nobel Laureaes, Prof. W.K. Li kindly wroe an aricle regarding heir major works on ime series analysis. Korean Saisical Sociey and submied a repor on his rip. Finally, I urge members o submi aricles o his Bullein. The Saisical Projec Compeiion (SPC) for Secondary School Sudens is one of he more successful aciviies organized by he Sociey. Leers of inviaion have been sen ou and briefing sessions have been held. A repor on he even was wrien by he organizing commiee his year. Profs. W.K. Li and Philip Yu aended he conference organized by he P.S. Chan Edior : Chan, Ping-shing, CUHK Tel Fax Associae Ediors : Chan, Wai, CUHK Chan, Wai-sum, HKU Ms Ng, Teresa, CiyU Secreary : Lam, John Hon-kwan, C&SD

2 CONTENTS (Vol. 6/No., December 003) Page Presiden s Forum 1 Tony W.K. Fung The Nobel Laureaes in Economics: 003 : heir conribuions W.K. Li The 003 Auumn Conference of he Korean Saisical Sociey 9 W.K. Li and Philip Yu Saisical Projec Compeiion for Secondary School Sudens 11 Organizing Commiee for he 003/04 Saisical Projec Compeiion News 13

3 Presiden s Forum Professor Tony W.K. FUNG I is wih regre ha we have o repor he deah of Professor Hu Hsiao-Sheng, he oldes member of our Sociey. Professor Hu was born in He was Head of organise a session on risk managemen in heir Auumn Conference. On behalf of he Sociey, Professor W.K. Li and Dr. Philip Yu aended he Conference during 31 Deparmen of Economics of he Chinese Ocober 1 November, 003. Boh of Universiy of Hong Kong and Bapis College. The Sociey would like o send condolences o Professor Hu s family. hem presened heir research findings in he session. I may visi Korea oo in he nex few monhs for furher exchange/collaboraion beween he KSS As menioned in he las issue of he and HKSS. Bullein, I expeced ha a HKSS member would submi an aricle on he conribuions of he Nobel Laureaes in The Saisical Projec Compeiion for Secondary School Sudens has been Economics 003. Professor W.K. Li has running smoohly. I am hankful o he submied his aricle, and I am indebed o his kind assisance. Organising Commiee for heir hard work. The Commiee will need many adjudicaors for he even, and your Las year, he Korean Saisical Sociey (KSS) invied our Sociey o assisance o become he adjudicaors is very much appreciaed

4 The Nobel Laureaes in Economics: 003: heir conribuions W.K. Li The Universiy of Hong Kong The 003 Nobel prize in Economics was awarded o wo disinguished economericians Professor C.W.J. Granger of he Universiy of California, San Diego and Professor R.F. Engle of New York Universiy. R.F. Engle was also associaed wih UC San Diego earlier. Acually one may regard boh Nobel Laureaes as saisicians since he Nobel prize was awarded o hem based on heir conribuions o ime series analysis. I will briefly summarize broadly below wha conribuions hese wo genlemen have made o ime series analysis and financial economerics. variables are affecing he volailiy of an asse? and wha is he fuure price of an opion on an asse, which according o he famous Black-Scholes formula depends on he volailiy of he underlying asse? Le R be he reurn of an asse which is usually defined as he log-difference of he asse price, i.e., R = ln P - ln P -1, where P is he asse price a ime. (For simpliciy, he mean of R is assumed o be zero and ha R is uncorrelaed over ime.) Specifically, an ARCH model of order one (an ARCH(1) model) akes he form Firs, hose of R.F. Engle. In he press release of he Nobel award i is noed ha he major conribuion of R.F. Engle is o he modeling of ime-varying volailiy in financial ime series. As is well known, here are many ways o define volailiy and he variance of he sock reurn is one possible way. In 198, Engle published in Economerica he firs paper on he so-called, auoregressive condiional heeroscedasiciy (ARCH) model which can model he ime-varying feaures of volailiy which is presen in many financial ime series. This model can help one o undersand beer he behaviour of financial series especially in answering quesions like: wha is he fuure risk associaed wih an invesmen porfolio?, wha R =σ ε where ε is independen sandard normal wih mean 0 and variance Noe ha = α0 + αr 1 σ (1) given R -1. σ is he condiional variance of R Subsequen o he 198 paper here has been an explosion of papers on generalizaions of he ARCH model and applicaions of hese models o financial daa. An imporan generalizaion is ha of Bollerslev (1986) where he condiional - -

5 variance a ime -1 is also involved in he equaion forσ, i.e., = + + α0 αr 1 β1σ 1 σ () Equaion () is called a generalized ARCH (GARCH) model of order (1,1) or simply a GARCH(1,1) model. The GARCH family and is generalizaions can model he following sylized facs of financial reurns: (1) he disribuion of financial reurns usually have a faer ail han ha given by a normal disribuion; () clusering of high volailiy periods and (3) volailiy is higher during a bear marke han in a bull marke (See e.g. Nelson, 1991 and Li & Li, 1996). As an example, consider he daily closing Hang Seng Index (1980) (Figure 1). he corresponding reurns by R. Denoe A so-called ARCH in he mean model for R is given by R = 0.16σ + a, (0.06) where (3) Var ( a a 1 ) = σ = a (0.0001) (0.1170) 1 Tha is, a is an uncorrelaed noise process wih an ARCH(1) specificaion (a saisfies equaion (1)). Noe ha here he condiional variance σ also serves as an explanaory variable for he reurn series R. The figures in parenhesis are he sandard errors. Model (3) is called an ARCH-M or ARCH in he mean (Engle, Lilien & Robins, 1987) model as 0.16 σ is he condiional mean of R given R -1. In oher words, using (3) one can predic omorrow's reurn based on oday's closing reurn of he HSI. Engle and his collaboraors are able o derive a whole series of models and mehodologies, like he ARCH-M model, for handling volailiy changes. Bollerslev e al. (1994) consiss of a comprehensive review. Because of space, we now urn o he conribuion of Professor C.W.J. Granger. The press release for he 003 Nobel prize award recognized ha, Clive Granger demonsraed ha he saisical mehods used for saionary ime series could yield wholly misleading resuls when applied o he analysis of nonsaionary daa. His significan discovery was ha specific combinaions of nonsaionary ime series may exhibi saionariy, hereby allowing for correc saisical inference. Granger called his phenomenon coinegraion. He developed mehods ha have become invaluable in sysems where shor-run dynamics are affeced by large random disurbances and long-run dynamics are resriced by economic equilibrium relaionships. Examples include he relaions beween wealh and consumpion, exchange raes and price levels, and shor and long-erm ineres raes. Back in 1974, Granger and Newbold noiced dubious resuls could exis when fiing regression relaionship of he form - 3 -

6 Y = β X + a. (4) where X and Y are wo (possibly nonsaionary) economic ime series and a is zero mean independen idenically disribued (i.i.d.) noise process. Specifically, a high R could be observed even if Y and X should be independen. Noe ha if (4) is rue hen Y and X on boh sides mus exhibi similar feaures. (Oherwise, (4) does no make sense.) For example, if X has a (random) rend hen Y mus also have a (random) rend. Equivalenly, (4) holds means ha here is a β such ha Granger has in fac made many oher conribuions o ime series analysis. Some of he major ones include he idea of fracional differencing or long memory ime series (Granger and Joyeux, 1980). A ime series has long memory if he absolue value of is auocovariances sum o infiniy. In conras, he popular saionary auoregressive moving-average models have shor memory. The simples non-rivial long memory ime series can be defined as a fracionally differenced process as follows. Le B be he lag operaor, BX = X -1 and a an i.i.d. noise process. A long memory ime series X is given by Y β X = a. d ( 1 B ) X = a (5) Tha is, he common feaure, he random rend in Y and X has been removed by he regression (4) because a is an i.i.d. sequence wih no rend. If his is he case we say ha X and Y are coinegraed. An example of coinegraion is given in Figures and 3 where he wo ineres rae series appear o rend ogeher and herefore coinegraed. Granger wen furher o propose an appropriae model for ime series exhibiing coinegraion. See for example, Engle and Granger (1987). Such a model is called an error-correcion model and has found imporan applicaions in esing economic heories such as he hypohesis of purchasing power pariy; he permanen income hypohesis; presen value heory and he erm srucure of ineres raes. where d <1/ and he L.H.S. is inerpreed as a power series expansion in B. Granger shows ha long memory process can arise as a resul of aggregaing a large number of heerogenous bu shor memory auoregressive processes of order one. The possibiliy of a long memory componen in financial ime series has been picked up by many researchers resuling in long memory GARCH or Fracionally Inegraed GARCH (FIGARCH) models. Anoher conribuion made by Granger is he concep of Granger causaliy. Of course, wha is causaliy? is a big philosophical quesion since he ime of Plao. Granger's approach is by means of addiive predicion power. According o Granger (1969), a ime series X causes anoher ime series Y if Y can be beer prediced by using pas observaion of - 4 -

The ile of he paper by Hendry and Mizon (1999), The pervasiveness of Granger causaliy suggesed clearly he imporance and impac of he concep of Granger causaliy.

7 X in addiion o pas observaions of Y hen by using only pas observaions of Y. Clearly, he concep of Granger causaliy can be easily exended o sudy causaliy relaionships of volailiy in financial ime series. The ile of he paper by Hendry and Mizon (1999), The pervasiveness of Granger causaliy suggesed clearly he imporance and impac of he concep of Granger causaliy. Oher conribuions of Granger include he inroducion of bilinear ime series models in a 1978 monograph co-auhored by A.P. Andersen; improving forecas performances by combining several differen forecass (Granger & Baes, 1969) and specral analysis of economic ime series (Granger & Haanaka, 1964). The Deparmen of Saisics and Acuarial Science of he Universiy of Hong Kong is also paricularly graeful for having Professor C.W.J. Granger as a keynoe speaker in wo of he major evens organized by he Deparmen back in July, The firs one was he Hong Kong Inernaional Workshop on Saisics and Finance (a proceedings was published in 000 Cerainly Nobel well Granger and his collaboraors conribued wo Economics. aricles.) The second one is he Symposium been given, via hese wo awardees, he on Financial Risk and Saisics which was held recogniion for is conribuions o he Sociey. a he Conrad Hoel, Hong Kong, July We look forward o seeing more saisicians Finally, his auhor is also graeful for having receiving recogniions of his kind in fuure are deserved examiner back in he genlemen by he Imperial College Press where Professor Professor C.W.J. Granger as his Ph.D. hesis for boh prize in The saisics profession has also

8 References Bollerslev, T.: 1986, Generalized auoregressive condiional heeroskedasiciy, Journal of Economerics 31, Bollerslev, T., Engle, R.F. and Nelson, D.B.: 1994, ARCH models, in R.F. Engle and D.L. McFadden (eds), Handbook of Economerics, Vol. 4, Norh-Holland, Amserdam, Engle, R.F.: 198, Auoregressive condiional heeroscedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica 50, Engle, R.F. and Granger, C.W.J.: 1987, Co-inegraion and error-correcion: Represenaion, esimaion and esing, Economerica 55, Engle, R.F., Lilien, D.M. and Robins, R.P.: 1987, Esimaing ime-varying risk premia in he erm srucure: The ARCH-M model, Economerica 55, Granger, C.W.J.: 1969, Invesigaing causal relaions by economeric models and cross-specral mehods, Economerica 37, Granger, C.W.J. and Andersen, A.P.: 1978, Inroducion o Bilinear Time Series Models, Vandenhoeck and Ruprech, Gőingen. Granger, C.W.J. and Baes, J.: 1969, The combinaion of forecass, Operaions Research Quarerly 0, Granger, C.W.J. and Haanaka, M.: 1964, Specral Analysis of Economic Time Series, Princeon Universiy Press, Princeon, NJ. Granger, C.W.J. and Joyeux, R.: 1980, An inroducion o long-memory ime series models and fracional differencing, Journal of Time Series Analysis 1, Granger, C.W.J. and Newbold, P.: 1974, Spurious regressions in economerics, Journal of Economerics, Hendry, D.F. and Mizon, G.E.: 1999, The Pervasiveness of Granger Causaliy in Economerics, in R.F. Engle and H. While (Eds.), Coinegraion, Causaliy and Forecasing, Oxford Universiy Press, pp Li, C.W. and Li, W.K.: 1996, On a double hreshold auoregressive heeroscedasic ime series model, Journal of Applied Economerics 11, Nelson, D.B.: 1991, Condiional heeroskedasiciy in asse reurns: A new approach, Economerica 59,

9 Figure 1. HSI 1980 log of daily closing Figure. Cenered Logarihms of US Federal Fund Rae - 7 -

10 Figure 3. Cenered Logarihms of 90-day US Treasury Bill Rae - 8 -

The 003 Auumn Conference of he Korean Saisical Sociey W.K. Li and Philip Yu The Universiy of Hong Kong As a major saisical sociey in Asia he Korean Saisical Sociey holds a Spring and an Auumn conference in Korea each year.

11 The 003 Auumn Conference of he Korean Saisical Sociey W.K. Li and Philip Yu The Universiy of Hong Kong As a major saisical sociey in Asia he Korean Saisical Sociey holds a Spring and an Auumn conference in Korea each year. In 003, he Auumn conference was held a he Seoul Naional Universiy from Ocober 31 s o November 1 s. This ime here were wo inernaional sessions in addiion o he 1 oher local sessions. One of he inernaional sessions was focused on mulivariae saisics and he oher was focused on saisical risk managemen. The Hong Kong Saisical Sociey was invied o organise he session on risk managemen. Three speakers were arranged in ha session. Dr. Philip Yu of HKU delivered a paper on esimaing value-a-risk using GARCH models (a join paper wih Dr. Mike So of HKUST); Dr. S. Kim of Chung-Ang Universiy, Korea, delivered a paper on modelling hreshold-asymmeric ARCH ime series via random power ransformaion, and Professor W.K. Li of HKU delivered a paper on value-a-risk models (a join paper wih S. Jin and P. Yu). The conference also feaured he Ilsong Lecure which was delivered by Professor Fujikoshi of he Hiroshima Universiy of Japan. Professor Fujikoshi is a world renowned saisician and he spoke on mulivariae analysis for he case when he dimension is large compared o he sample size. As is presiden, Professor Fujikoshi also represened he Japan Saisical Sociey. There were some 300 paricipans from Korea and he risk managemen session was well received. Unforunaely, he local sessions were mosly delivered in Korean. Neverheless, a few of hese had been very well prepared so ha we had no difficulies in undersanding he speakers. Our Korean hoss were very kind and ook very good care of us. We were given a warm welcome by Professor Woochul Kim, he Presiden of he Korean Saisical Sociey, Professor Young Il Kim, he Direcor of Planning and Business, and oher members of he Board of Direcors of he Sociey. We have made many Korean friends and we expec ha here will be more exchanges beween HKSS and KSS in he fuure. We ook his opporuniy o hank he Korean Saisical Sociey for heir inviaion and hospialiy. Afer he session on risk managemen - 9 -

12 Two aliens in Seoul A he Conference dinner

Saisical Projec Compeiion for Secondary School Sudens Organizing Commiee for he 003/04 Saisical Projec Compeiion Since 1986/87, he Saisical Projec Compeiion (SPC) for Secondary School Sudens has been

The SPC aims a promoing a sense of civic awareness and encouraging sudens o undersand he local communiy in a scienific and objecive manner hrough he proper use of saisics.

13 Saisical Projec Compeiion for Secondary School Sudens Organizing Commiee for he 003/04 Saisical Projec Compeiion Since 1986/87, he Saisical Projec Compeiion (SPC) for Secondary School Sudens has been an annual even of he Hong Kong Saisical Sociey (HKSS). The SPC aims a promoing a sense of civic awareness and encouraging sudens o undersand he local communiy in a scienific and objecive manner hrough he proper use of saisics. All sudens aending Secondary 3 o 7, or sudying a equivalen educaional levels, in schools are eligible o ener. The SPC is divided ino wo Secions, namely, "Junior Secion for Secondary 3 o 5 sudens" and "Senior Secion for Secondary 6 and 7 sudens". pas winning projecs were held on November 003 a he Ciy Universiy of Hong Kong. More han 600 eachers and sudens aended he even. In each briefing session, Prof. Tony FUNG, he HKSS Presiden / Mr. K C LEUNG, he HKSS Vice-Presiden presened an opening address and briefed paricipans of he SPC. Ms Teresa NG of he Ciy Universiy of Hong Kong, he Chief Adjudicaor of his year s SPC, explained deails abou he adjudicaion process/crieria, and highlighed some remarks based on repors submied in pas years. Represenaives from he Census and Saisics Deparmen inroduced major issues in daa analysis and presenaion, sources and channels of obaining official saisics. A he end of each session, winning eams of he 00/03 SPC were invied o share wih paricipans heir valuable experience in preparing for heir saisical repors. Briefing seminar and exhibiion of pas winning projecs This year's SPC is is 18 h round. To help paricipans prepare for he SPC, hree idenical sessions of briefing seminar and exhibiion of

14 Seleced opic of he hemaic projec for he 003/04 SPC Submission of repors and announcemen of resuls Paricipans may op o work on a special heme in order o compee for he "Hang Seng Bank Prize for he Bes Themaic Projec". The seleced opic of he hemaic projec for his round is "Hong Kong is a knowledge-based sociey". For his round of SPC, he deadline for submission of enries is 8 February 004. All paricipans will be informed of he resuls of he SPC in April 004. The prize presenaion ceremony will be held on 4 April 004. Furher deails of he 003/04 SPC can be found a he HKSS websie (hp://

15 News Universiy of Hong Kong The Universiy of Hong Kong has decided o re-locae is Deparmen of Saisics and Acuarial Science from he Faculy of Social Sciences o he Faculy of Science, effecive from July 1, 004. The Deparmen however will coninue is eaching commimen in, and research collaboraion wih, he Social Sciences Faculy. The Acuarial Science sudens of all years will be enrolled in he Faculy of Science, saring form July 1. The curren saisics sudens will complee heir BSS(Sa) degree in he Faculy of Social Sciences. c) B.Soc.Sc. in Social Sciences Faculy, and choosing Saisics or Risk Managemen as one of he Majors. Professor Hu Hsiao-Sheng ( ) Professor Hu Hsiao-Sheng passed away on 7 February, 004, a he age of eighy-five. He was one of he oldes members of he Sociey. Professor Hu was born in Fu Zhou, China. He graduaed a Xia Men Universiy, China and finished his posgraduae sudy in USA. Professor Hu was Head of Deparmen of Economics a he Chinese Universiy of Hong Kong and Bapis College. From , sudens will be able o sudy saisics a HKU hrough differen programmes as follows: a) B.Sc. - Saisics programme, wih he opion of selecing he Risk Managemen Theme afer admission. b) B.Sc. - Saisics programme, wih a Major in eiher (i) Saisics or (ii) Risk Managemen, and wih a complemening Major or Minor in he Faculy of Science, Social Sciences, or any oher faculy where Major/Minor opions are available

On the disappearance of Tuesday effect in Australia

On the disappearance of Tuesday effect in Australia Edih Cowan Universiy Research Online ECU Publicaions Pre. 2011 2001 On he disappearance of Tuesday effec in Ausralia Chien-Ting Lin Lee Kian Lim Lin, C., & Lim, L. (2001). On he disappearance of Tuesday