strong connection to continuous - time finance models. Y et estimation of ... as a
general method for comple x models in Bayesian spectral analysis. We illustrate.
"!$#%&' # () * + ,- . /10 2436587%9&:8;@?BACEDGF&>
[email protected]=>IU@RTSGRVKHYN@HBUI>@S =ZB[>]\ H^RT_`>ICGSERTD 0
=A.DQ>.a
b
?B?^CGKc_`>IWda
=CIegfhRV[.>jik>@SlD mnN@Cl_PRVSGKC =C@e,pq>rDQ>ICsfZ^t uVuV>IC =C@e,vwCGAHBR6xsRVWyA.[Kc_PRVU =C@egNneBxsRVSEzwAHyA{DQ|yAH
=RTSGSE>@CEDQA.DQRTK`HSGZ / F&R}DGDG>@WRVH?yAClDQRVAunM~ZBu}yuVuTF&>IH1DKMDQ|B> EC >@JZBRTCG>@F>@H1DGSM~K`CDG|B>jWB>@
CG>@>jKM=KPUIDQKCKM8pO|BRTuVK`SEK`?B| 0 RTHDG|B>]=>@?yA.CEDQF>@H1DLKM8NPDQA.DQRTSEDQRTU@SLAH^WX=>IU@RVSERVK`HYNPU@RV>IHBU@>IS RVHDG|B>jCGAWBZyA.DG>]N]\ H^RT_`>ICGSERTD 0 c``
9
7: 236587 7: ; ; ;
9&:8;F&KPWB>@uTSWB#R $ UIZBuTD@e ik>&?BCEK`?oK`SG>b AH %> U@RT>@H1DvA 0 >@SER AH*fXACE[Kc _ w|yARVHkfhKHJDG > A.CGuVKY>@SlDQRTF A.DGRVK`H?^CGKPU@&> WBZ^CG> M~KC A 'K`(
) + * NPDGKIu eik>sWB>r_`>IuVK`?HB>rz SGRVFZBu A.DGRVK`,H / ASE>@W FK@uOWBRVA
`HBK`SlDQRTb U@SjF&>rDQ|BKPWBSjM~K`C]RV-H SQAF?BuV> FKPWB>@u,AW^>@JZyAU 0 U|B>IU[)A.HBW)UIK`F&?BACG>4zLRTDG| DG|B>j?nK`?^ZBu AC . FK@u 0e /Z^CRV-H SQAF?BuV>sWBR A
HBK`SEDGRVUU|^>@U[SG|BKczLS / >rDGDG>@CL[JZBCEDGK`SGRTS ?BCEK`?o>@CEDGRV>IS AHBb WWB!R n>@CE>@H1DN%> n>@UrD
`>@H^>@CQA{DQ>@W /10 DQ|^> NPDQKPU|yASlDQRTUhx,K`uVA.DQRTuVRTD 0 fhKPWB>@u DG|yAHDQ|B1> .g F&KPWB>Iu e*ik>hA.uVSGK WBRTSGUIZBSGSRVSESGZB>ISK.MsDQ|^>YUIK`F?yACGRTSGK`HK.M|BRTSEDQKCGRVU@Au _K`u A.DGRVuTRTD 0 A.HBW)RTF&?BuTRV>IW _K`u A{DQRVuTRTD 0 AHBW*?BCEK`?oK`SG> AhHB>rz FKPWB>@uOzL|BRTU|*U@K`F / RVHB>IS]DG|B> |^RVS DGK`CGRTU Auy_`Ku A.DGRVuVR}D 0 AHBWRTF&?^uVRV>IW_K`u A{DQRVuTRTD 0 Z^HBWB>@CwK`HB>FK@u M~CQAF>Iz K`CG[ 0e |BRTSwHB>rz FKPWB>@u U@AH / >ZBSE>@W M~KC / KDG|M~K`CG>IU ASlDQRVH^
kA.HBWDG>@SlDQRVH^
K.M DG|B>| 0 ?oKDQ|^>@SGRTS&K.M DG|B>&> 2@H^U@>YKM SlDQKPU|yASEDGRVU_`Ku A.DGRVuVR}D 0 e
z K]UIK`FF&K`HF&>rDQ|BKPWBS8> 2^RTSED8M~KCqM~CG>IJZB>@HBU 0 >@SlDQRVF&A.DGRVK`H]RVH U 0 UIuVRTU AuJDQRTF&> SG>@CERV>IS@a?^CGK / R}_
A / RVuVR}D 0 DQ|^>@K`C 0 AH^W KZBCGRT>@C4DQCQA.HBSEM~K`CEFhe >IU@>IHJDz K`CE[ KM`A 0 HB>ISAHBW%vwCE>IDGDG|BK`CESED|yA.S SE|BKczLHDG|B>sUIK`HBHB>IUIDGRVK`HKMDG|B> D z K F>IDQ|^KsDQ|^>@K`CE>IDQRTU AunAW^_.AH1DQA
`>sK.MDQ|B>?^CGK / A / RVuVR}D 0 F>IDG|BKPWde*i)>YWB>r_`>@uTK`? A ZBH^RTy>IWA?^?BCGK1A.U|M~K`C4A.U@U@Z^CQA.DG>YM~CE>@JZB>@H^U 0 >@SlDQRTF A.DGRVK`H ZBH^WB>@CDQ|B>vA 0 >@SER AHf f M~CQAF>Iz K`CE[ M~K`CDG|B>SERVHB
uV&> M~CG>IPZ^>@HBU 0 AHBWF Z^uTDQR M~CE>@JZB>@H^U 0 |yA.CGFK`HBRVUFKPWB>@uBzL|BRTU| U A.H / >
`>IHB>@CGAuV!R @>IWDGKFK`CG>LU@KF&?BuT&> 24FKPWB>@uTS,M~KC,DG|B>LM~CG>@JZB>IHBU 0 e ik>A?B?^u 0 DQ|B>wF&>rDQ|BKPWDQKsCG> A.u^U 0 UIuVRVU@AuPWyA.DA@W /10 DQ|B>SlDQZBW 0 KM / 2 0
`>@H4RTSGKDGK`?n> WyA{DARTH&
>@K`uTK`
0 SlDQZBW 0 m^z >sWBRTSGU@Z^SGS DGRVFRVHB
jRTSGSGZ^>@SwRTH |yA.CGFK`HBRVUAHBAu 0 SGRTS@mJ?yAClDQRTU@ZBuVACGu 0 DQ|^> RTF&?yA.UIDKMqZBHBUI>@ClDARTHDGRVFRVHB
DQK DQ|B>j>ISEDQRTF A{DQRVKH KMM~CG>@JZB>IHBU@RT>@SIegik>jWB>I_>@uVK?XA |yACEF&KHBRVU FK@uwzLR}DQ|ZBHBU@>ICEDQARVHDQRTF&RTHB
XDGKkRTHJ_>@SlDQRV
`A.DQ>DQ|^>YRTF&?BAUID K.MZBHBUI>@ClDARTHDGRVFRVHB
RTHM~CG>& JZB>IHBU 0 >@SlDQRVF&A.DGRVK`HAH^WhDQK&RVuTuVZBSlDQCQA{DQ>sDG|B>ZBSE>K.M,vA 0 >ISGR A.Hf f $SERVF ZBuVA.DQRTK`H F>IDG|BKIHB>@CGAudF>IDG|BK 2FK@uVSwRVHvA 0 >ISGRVAHhSE?n>IUIDGCQAuA.HyAu 0 SERVS@e8ik>jRVuTuVZBSlDQCQA{DQ> K`Z^C RTWB> AjZBSGRTHB
CE> Au / 2 0
`>@H WBA.DAjRVH
`>@KuVK`
0 SEDQZ^W 0 AHBW ?^CGKc_PRVWB> >I_PRVWB>IHBU@> KM6DG|B>sRTF&?BAUID KMqZBHBUI>@ClDARTHYDGRVFRVHB
]DQK4M~CG>@JZB>IHBU 0 >ISEDGRVF&A.DQRTK`Hde
_
sz K`ZBuTWkuTRV[.>4DGKh>2