NON-LINEAR MODELING OF DAILY EXCHANGE RATE RETURNS, VOLATILITY, AND NEWS IN A SMALL DEVELOPING ECONOMY. José R. Sánchez-Fung Kingston University

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1 NON-LINEAR MODELING OF DAILY EXCHANGE RATE RETURNS, VOLATILITY, AND NEWS IN A SMALL DEVELOPING ECONOMY José R. Sánchez-Fung Kingson Universiy Absrac This paper models daily reurns, volailiy, and news in he parallel foreign exchange marke of a small developing economy, namely he Dominican Republic, during he period The research adops a non-linear specificaion ha encompasses several members of he GARCH family. A lefward iled news impac reveals ha posiive shocks (depreciaions) have a higher impac han negaive ones (appreciaions) on he volailiy of exchange rae reurns. JEL classificaion numbers: G2; F3. Keywords: daily exchange rae reurns; non-linear GARCH models; news impac ; developing counries. Acknowledgemens: I am especially graeful o Seffen Sørensen for useful commens on previous versions of he paper. I also hank Alan Carruh and Peer A. Prazmowski. All remaining errors are mine alone. Correspondence address: José R. Sánchez-Fung, School of Economics, Kingson Universiy, Penrhyn Road, Kingson upon Thames, KT 2EE, England, UK. j.sanchez-fung@kingson.ac.uk.

2 Modelling he reurns and volailiy of financial variables such as, for example, sock markes indexes and exchange raes has been amongs he main areas of curiosiy wihin he empirical finance lieraure, given heir forefron role in economic agens decision making processes. Noably, a garganuan lieraure has been spearheaded by he auoregressive condiional heeroscedasiciy ( ARCH ) model advanced by Engle (982) and generalised ( GARCH ) by Bollerslev (986). However, his lieraure has chiefly focused on advanced and, more recenly, emerging marke economies. This gap in he research program under consideraion probably arises due o a lack of sysemaically colleced high frequency ime series daa for less developed counries and o he idiosyncraic phenomena driving asse-pricing mechanisms in hese economies. The objecive of his paper is o conribue o his branch of he empirical asse pricing lieraure in a case sudy basis. Paricularly, he projec aemps o do so by inquiring ino daily observaions on he Dominican Republic s (DR) nominal parallel marke exchange ( ask ) spo rae for he span ranging from January 989 o February 200, i.e. a oal of 3,045 observaions. The source of he saisical informaion is he Cenral Bank of he Dominican Republic (CBDR). As is sandard in he lieraure, he variable o be modelled is he percenage daily exchange rae reurn, which can be expressed as The DR s exchange rae sysem is composed of he official, banking sysem, and parallel markes. In he ligh of he fac ha he price of foreign currency in he parallel marke is expeced o be deermined mainly by marke forces, he presen sudy focuses on his marke. Throughou he paper refers o he exchange rae of Dominican Republic Pesos (DR$) per Unied Saes Dollars (US$), since he US is by far he DR s main rading parner. Noe ha he way in which i has been defined implies ha increases (decreases) in he exchange rae are depreciaions (appreciaions) of he domesic currency.

3 r 00 [ln e ln e ] () where r is he daily percenage reurn o he exchange rae ( e ) described above. Par A of Table provides relevan descripive saisics on r. The baseline economeric specificaion o be implemened can be expressed as n 2 i i h i r, (2a) q h D h 2 2 p 0 i ( i ) ( ) i i i i. (2b) Equaions (2a) and (2b) are he mean and condiional variance equaions, respecively. In equaion (2a) sands for he consan erm, and are explanaory variables and heir corresponding coefficiens, respecively, and is a coefficien o capure he variance-in-mean effec (Engle e al, 987), or risk-reurn rade-off. Also, he paper will assume ha in (2a), (3) i.e. he residuals are esimaed assuming a sandardised -disribuion wih degrees of freedom, as suggesed by Bollerslev (987). Equaion (2b) proposes a condiional variance ( h ) specificaion ha accouns for asymmeric ( ) and hreshold ( ) effecs, i.e. an ATGARCH ( q, p), wih if D 2

4 , and zero oherwise. I is worhy o noe ha he ATGARCH model encompasses several members of he GARCH family (see Henschel, 995, for a deailed exposiion on he opic). The resuls of esimaing equaions (2a) and (2b) using he maximum likelihood echnique are displayed in Table s equaion (4), along wih a baery of diagnosic saisics 2. The resuls, which allow for five lags, i.e. informaion on he previous rading week, of he dependen variable o ener he mean equaion, and a sandard GARCH (,) in he variance equaion, seem sensible. In he mean equaion mos of he coefficiens are saisically significan, and display reasonable magniudes. Addiionally, he coefficien, which is posiive and saisically well deermined, unveils he presence of a non-negligible risk-reurn rade-off. Also, he variance equaion s fi is adequae, wih all coefficiens significan a he 5% level, exceping he one inended o capure asymmeric effecs 3. A salien fac porrayed by he esimaions is ha boh and are pushing he news impac schedule (Pagan and Schwer, 990; Engle and Ng, 993) in he same direcion, implying ha volailiy rises more for posiive han for negaive shocks. Such a relaionship can be clearly perceived by inspecing he news impac plo exhibied in Figure. Economically, his graph conveys ha depreciaions (a posiive r ) increase he condiional volailiy of he exchange rae o a greaer exen han appreciaions (a negaive r ). In a small developing economy where foreign currency is a scarce asse 2 All he economeric resuls presened in his paper were compued using he GARCH module in PcGive 0 (see Doornik and Hendry, 200). 3 Dropping his coefficien, however, only mildly improves he fi according o he AIC es, which goes from o In conras, he likelihood is when he asymmeric effec is presen and oherwise. Henceforh, he asymmeric effec is accouned for in subsequen esimaions. 3

5 hese resuls are compelling. Finally, he ess for he presence of ARCH and auocorrelaion are no acceped, supporing he model s adequacy. Having esimaed a sensible model for daily exchange reurns in he DR, assessing he relevance of addiional facors ha are expeced o impinge on such a marke should prove a valuable exercise. The subsequen modelling will consider () marke opening effecs, (2) he repercussion of a momenous IMF sabilisaion program, and (3) seasonal inflows of foreign currency. In order o gauge he impac of opening days on he DR s exchange rae marke, a dummy variable was included for Mondays, or he firs rading day of he week, as in Bollerslev and Ghysels (996). Specifically, Frade akes a value of for Mondays or he firs rading day of he week, and 0 oherwise. The resuls displayed in equaion (5) reflec negligible changes in relaion o he mean and variance equaions coefficiens in (4), and saisfacory diagnosic saisics. However, he consan erm in he variance equaion is now saisically insignifican, whereas he added Frade dummy is significan a roughly he 9% level. The reader should noe ha afer he inclusion of Frade he consan erm in he variance equaion is given by 0 Frade. Therefore, i seems ha opening days have a more significan impac on exchange rae reurns han he res of he week. Also, boh he loglikelihood and informaion crierion model comparison saisics suppor model (5) over (4). Beween 989 and 99 a series of adverse domesic and inernaional economic and poliical evens (e.g. a domesic banking crisis and he Gulf War) undermined he credibiliy of he DR s exchange rae regime, as well as ha of he economy as whole. Given he ime span under scruiny, i is sraighforward o ask: Did he Augus 99 agreemen he DR signed wih he IMF had a significan impac on he foreign 4

6 exchange marke? Equaion (6) shows ha he coefficien affecing he variable IMF 99 (included in he mean equaion and aking a value of afer Augus 99 and 0 before ha dae) has he expeced negaive sign, suggesing ha he 99 agreemen wih he IMF was indeed successful in pulling down he Dominican currency 4. However, he coefficien affecing IMF 99 is no saisically well deermined. In spie of ha, he likelihood saisic displayed in Table is slighly higher for equaion (6) han for equaion (5), alhough he informaion crierion is minimised for he laer. A furher characerisic of he DR s exchange rae marke o be invesigaed is he high seasonal inflow of foreign currency recurrenly occurring during he Chrismas period 5. Dominican emigrans who massively reurn o he counry (mainly) during his ime of he year generae his paern. The phenomenon a hand is proxied by a dummy variable ( December ) added o he mean equaion of he model, aking a value of during he monh of December and 0 oherwise. Equaion (7) porrays he resuls of accouning for he December effec. Once more, he overall characerisics of he general ATGARCH M (,) specificaion are mosly invarian. The seasonal effec spel ou above seems o have a negaive effec on exchange rae reurns ha can be read as a supply shock. However, December s coefficien is no saisically well deermined. In spie of ha, noe ha he 4 In a recen IMF repor, Young e al (999, page 8) sae ha Since 992, he Dominican Republic has experienced an exended period of robus economic growh, declining unemploymen raes, modes consumer price inflaion, and a generally manageable exernal posiion. 5 Remiances are a key variable in he DR s foreign exchange marke, due o he large amoun of Dominicans living abroad, mainly in he US. For example, in 999 ne foreign ransfers oalled almos 2% of GDP, according o calculaions made using numbers from he World Bank (2000). 5

7 loglikelihood saisic is higher for model (7) han for model (6), whereas he informaion crierion is minimised for model (6). References Bollerslev, Tim (986) Generalised auoregressive condiional heerocedasiciy, Journal of Economerics, 3, Bollerslev, Tim (987) A condiional heeroskedasic ime series model for speculaive prices and raes of reurn, Review of Economics and Saisics, 69, Bollerslev, Tim, and Eric Ghysels (996) Periodic auoregressive condiional heerocedasiciy, Journal of Business and Economic Saisics, 4, Doornik, Jurgen A., and David F, Hendry (200) Economeric modelling using PcGive 0, Volume III, Timberlake Consulans LTD, UK. Engle, Rober F. (982) Auoregressive condiional heeroscedasicy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 50, Engle, Rober F., D.M. Lilien and R.P. Robins (987) Esimaing ime varying risk premia in he erm srucure: he ARCH-M model, Economerica, 55, Engle, Rober F., and Vicor K. Ng (993) Measuring and esing he impac of news on volailiy, Journal of Finance, 48, Henschel, Ludger (995) All in he family: Nesing symmeric and asymmeric GARCH models, Journal of Financial Economics, 39, Pagan, Adrian R, and G.William Schwer (990) Alernaive models for condiional sock volailiy, Journal of Economerics, 45, The World Bank (2000) World Developmen Repor 2000/200, Washingon, D.C. Young, P., D. Dunn, A. Giusiniani, F. Nadal De-Simone, E. Tanner, and J. McHugh (999) Dominican Republic: seleced issues, IMF Saff Repor No. 99/7, Inernaional Moneary Fund, Washingon, D.C., Ocober. 6

8 Table Descripive saisics for r and ATGARCH - M - (,) (Equaions 2a and 2b) maximum likelihood esimaion based on daily daa for he period January 989-February 200 Mean Sandard deviaion A. Descripive saisics r Skewness Kurosis Minimum Maximum B. ATGARCH - M - (,) (Equaions 2a and 2b) maximum likelihood esimaion I. Mean equaion Variables Coefficiens Equaion (4) (5) (6) (7) numbers (2.02) (.48) (.03) (.03) (3.3) (3.07) (3.06) (3.00) 0.0 (6.07) 0.0 (6.4) 0.0 (6.3) 0.099(6.04) (2.64) (2.65) (2.64) 0.04 (2.60) (.67) (.70) (.70) (.63) (.9) (.89) (.90) (.88) 0.06 (2.99) (2.8) (2.82) (2.88) IMF (0.592) (0.37) December (.0) II. Variance equaion (2.38) 0.00 (0.580) 0.00 (0.579) 0.00 (0.57) Frade (.72) 0.03 (.7) 0.03 (.73).379 (2.7).329 (2.8).327 (2.7).294 (2.23) (7.) (7.2) (7.2) (7.2) (.45) (.49) (.52) -0.0 (.64) (3.75) (3.70) (3.68) (3.73) III. Diagnosic and model comparison saisics N 3,039 3,039 3,039 3, (4.6) (4.2) (4.) (4.) l AIC ARCH 2 F P. maneau

9 Noes on Table. Coefficiens absolue -raios are included in parenheses. N denoes he number of observaions used in he esimaion of each equaion. Esimaions are based on -suden disribued errors, as suggesed by Bollerslev (987); denoes he coefficien of such errors. l is he log-likelihood of he esimaed model. AIC is an informaion crierion calculaed as AIC 2l 2s, where s denoes he number of parameers esimaed. ARCH and P. maneau are ess of he null of residual auoregressive 2 condiional heeroscedasicy and auocorrelaion, wih F and disribuions, respecively. For boh ess probabiliy values are provided, wih * and ** denoing significance a he % and 5% levels, respecively. Figure News impac plo from ATGARCH M (,) model Equaion (4), Table 70 Condiional variance () Residuals (-)