FINANCIALENGINEERING
Themostcomprehensivedefinitionoffinancialengineeringisthefollowing: Financialengineering involvesthedesign,development,andimplementationofinnovative financialinstrumentsandprocesses,andtheformulationofcreativesolutionsto problemsoffinance(Finnerty,1988).Fromthedefinitionitisclearthatfinancial engineeringislinkedtoinnovation.Ageneraldefinitionoffinancialinnovation includesnotonlythecreationofnewtypesoffinancialinstruments,butthedevelopmentandevolutionofnewfinancialinstitutions(Masonetal.,1995).Financial innovationisthedrivingforcebehindthefinancialsysteminfulfillingitsprimary
function:themostefficientpossibleallocationoffinancialresources(Ζαπράνης, 2005).Investors,organizations,andcompaniesinthefinancialsectorbenefitfrom financialinnovation.Thesebenefitsarereflectedinlowerfundingcosts,improved yields,bettermanagementofvariousrisks,andeffectiveoperationwithinchanging regulations.
Inrecentdecadestheuseofmathematicaltechniquesandprocesses,derived fromoperationalresearch,hasincreasedsignificantly.Thesemethodsareusedin variousaspectsoffinancialengineering.Methodssuchasdecisionanalysis,statistical estimation,simulation,stochasticprocesses,optimization,decisionsupportsystems, neuralnetworks,waveletnetworks,andmachinelearningingeneralhavebecome indispensableinseveraldomainsoffinancialoperations(Mulveyetal.,1997).
AccordingtoMarshallandBansal(1992),manyfactorshavecontributedtothe developmentoffinancialengineering,includingtechnologicaladvances,globalizationoffinancialmarkets,increasedcompetition,changingregulations,theincreasing abilitytosolvecomplexfinancialmodels,andtheincreasedvolatilityoffinancial markets.Forexample,theoperationofthederivativesmarketsandriskmanagement systemsissupporteddecisivelybycontinuousadvancesinthetheoryofthevaluation ofderivativesandtheiruseinhedgingfinancialrisks.Inaddition,thecontinuous increaseincomputationalpowerwhileitscostisbeingreducedmakesitpossibleto monitorthousandsofmarketpositionsinrealtimetotakeadvantageofshort-term anomaliesinthemarket.
Inadditiontotheirknowledgeofeconomicandfinancialtheory,financialengineers arerequiredtopossessthequantitativeandtechnicalskillsnecessarytoimplement engineeringmethodstosolvefinancialproblems.Financialengineeringisaunique fieldoffinancethatdoesnotnecessarilyfocusonpeoplewithadvancedtechnical backgroundswhowishtomoveintothefinancialareabut,isaddressedtothose whowishtogetinvolvedininvestmentbanking,investmentmanagement,orrisk management.
Thereisamistakenpointofviewthatfinancialengineeringisaccessibleonlyby peoplewhohaveastrongmathematicalandtechnicalbackground.Theusefulnessof afinancialinnovationshouldbemeasuredonthebasisofitseffectontheefficiencyof thefinancialsystem,notonthedegreeofnoveltythatintroduces.Similarly,thepower offinancialengineeringshouldnotbeconsideredinthelightofthecomplexityofthe modelsthatareusedbutfromtheadditionaladministrativeandfinancialflexibility thatitoffersitsusers.Hence,financialengineeringisaddressedtoalargeaudience andshouldbeconsideredwithinthebroadercontextoftheadministrativedecisionmakingsystemthatitsupports.
FINANCIALENGINEERINGANDRELATEDRESEARCHAREAS
Financialengineeringisaverylargemultidisciplinaryfieldofresearch.Asaresult, researchersareoftenfocusedonsmallersubfieldsoffinancialengineering.There aretwomainbranchesoffinancialengineering: quantitativefinance and financialeconometrics.Quantitativefinanceisacombinationoftwoveryimportantand
popularsubfieldsoffinance: mathematicalfinance and computationalfinance.Onthe otherhand,financialeconometricsarisesfrom financialeconomics.Researchareas relatedtofinancialengineeringareillustratedinFigure1.1.
Thescientificfieldoffinancialengineeringiscloselyrelatedtotherelevantdisciplinaryareasofmathematicalfinanceandcomputationalfinance,asallfocuson theuseofmathematics,algorithms,andcomputerstosolvefinancialproblems.It canbesaidthatfinancialengineeringisamultidisciplinaryfieldinvolvingfinancial theory,themethodsofengineering,thetoolsofmathematics,andthepracticeof programming.However,financialengineeringisfocusedonapplications,whereas mathematicalfinancehasamoretheoreticalperspective.
Mathematicalfinance,afieldofappliedmathematicsconcernedwithfinancial markets,beganinthe1970s.Itsprimaryfocuswasthestudyofmathematicsappliedto financialconcerns.Today,mathematicalfinanceisanestablishedandveryimportant autonomousfieldofknowledge.Ingeneral,financialmathematiciansstudyaproblem andtrytoderiveamathematicalornumericalmodelbyobservingtheoutputvalues: forexample,marketprices.Theiranalysisdoesnotnecessarilyhavealinkback tofinancialtheory.Moreprecisely,mathematicalconsistencyisrequired,butnot necessarilycompatibilitywitheconomictheory.
Mathematicalfinanceiscloselyrelatedtocomputationalfinance.Moreprecisely, thetwofieldsoverlap.Mathematicalfinancedealswiththedevelopmentoffinancial models,andcomputationalfinanceisconcernedwiththeirapplicationinpractice. Computationalfinanceemphasizespracticalnumericalmethodsratherthanmathematicalproofs,andfocusesontechniquesthatapplydirectlytoeconomicanalyses.In additiontoagoodknowledgeoffinancialtheory,thebackgroundofpeopleworking inthefieldofcomputationalfinancecombinesfluencyinfieldssuchasalgorithms, networks,databases,andprogramminglanguages(e.g.,C/C++,Java,Fortran).
Today,thedisciplinaryareaofmathematicalfinanceandcomputationalfinance constitutespartofalarger,established,andmoregeneralareaoffinancecalled
Figure1.1 Researchareasrelatedtofinancialengineering.
quantitativefinance.Ingeneral,therearetwomainareasinwhichadvancedmathematicalandcomputationaltechniquesareusedinfinance.Onetriestoderivemathematicalformulasforthepricesofderivatives,theotheronedealswithriskand portfoliomanagement.
Financialeconometrics isanotherfieldofknowledgecloselyrelated(although moreremote)tofinancialengineering.Financialeconometricsisthebasicmethodof inferenceinthebranchofeconomicstermedfinancialeconomics.Moreprecisely,the focusisondecisionsmadeunderuncertaintyinthecontextofportfoliomanagement andtheirimplicationstothevaluationofsecurities(HuangandLitzenberger,1988). Theobjectiveistoanalyzefinancialmodelsempiricallyundertheassumptionof uncertaintyinthedecisionsofinvestorsandhenceinmarketprices.Forexample,the martingalemodelforcapitalassetpricingisrelatedtomathematicalfinance.However, theempiricalanalysisofthebehavioroftheautocorrelationcoefficientoftheprice changesgeneratedbythemartingalemodelisthesubjectoffinancialeconometrics.
Weillustratethevarioussubfieldsoffinancialengineeringbythefollowingexample.Afinancialeconomiststudiesthestructuralreasonsthatacompanymayhave acertainshareprice.Afinancialmathematician,ontheotherhand,takestheshare priceasagivenandmayuseastochasticmodelinanattempttoderivethecorrespondingpriceofaderivativewiththestockasanunderlyingasset.Thefundamental theoremofarbitrage-freepricingisoneofthekeytheoremsinmathematicalfinance, whilethedifferentialBlack–Scholes–Mertonapproach(BlackandScholes,1973) findsapplicationsinthecontextofpricingoptions.However,toapplythestochastic model,acomputationaltranslationofthemathematicstoacomputingandnumerical environmentisnecessary.
FUNCTIONSOFFINANCIALENGINEERING
Financialengineersareinvolvedinmanyimportantfunctionsinafinancialinstitution. AccordingtoMulveyetal.(1997),financialengineeringisusedwidelyinfourmajor functionsinfinance:(1)corporatefinance,(2)trading,(3)investmentmanagement, and(4)riskmanagement(Figure1.2).Incorporatefinance,large-scalebusinesses areinterestedinraisingfundsfortheiroperation.Financialengineersdevelopnew instrumentsorenhanceexistingonesinordertosecurethesefunds.Also,theyare involvedintakeoversandbuyouts.Intradingofsecuritiesorderivatives,theobjective ofafinancialengineeristodevelopnewdynamictradingstrategies.Ininvestment managementtheaimistodevelopnewinvestmentvehiclesforinvestors.
ExamplespresentedbyMulveyetal.(1997)includehigh-yieldmutualfunds, moneymarketfunds,andtherepomarket.Inaddition,theydevelopsystemsfor transforminghigh-riskinvestmentinstrumentstolow-riskinstrumentsbyapplying techniquessuchasrepackagingandovercollaterization.Finally,inriskmanagement, afinancialengineermust,ontheonehand,assessthevarioustypesofriskofa rangeofsecuritiesand,ontheotherhand,usetheappropriatemethodologiesand toolstoconstructportfolioswiththedesiredlevelsofriskandreturn.Thesemethodologicalapproachesrelateprimarilytoportfolioinsurance,portfolioimmunization
• New instruments to secure funds • Engineering takeovers and buyouts
ALM
FinancialengineeringactivitiesaccordingtoMulveyetal.(1997).
againstchangesincertainfinancialvariables,hedging,andefficientassets/liability management.
Riskmanagementisacrucialpartofcorporatefinancialmanagement.Theinterrelatedareasofriskmanagementandfinancialengineeringfinddirectapplications inmanyproblemsofcorporatefinancialmanagement,suchasassessmentofdefault risk,creditrisk,portfolioselectionandmanagement,sovereignandcountryrisk,and financialprograming,tonameafew.
Duringthepastthreedecades,aseriesofnewscientifictoolsderivedfromthe widerfieldofoperationsresearchandartificialintelligencehasbeendevelopedfor themostrealisticandcomprehensivemanagementoffinancialrisks.Techniquesthat havebeenproposedandimplementedincludemulticriteriadecisionanalysis,expert systems,neuralnetworks,geneticandevolutionaryalgorithms,fuzzynetworks,and waveletnetworks.AtypicalexampleistheuseofneuralnetworksbyZapranisand Sivridis(2003)toestimatethespeedofinversionwithintheVasicekmodel,usedto derivethetermstructureofshort-terminterestrates.
APPLICATIONSOFMACHINELEARNINGINFINANCE
Neuralnetworksandmachinelearningingeneralareemployedwithconsiderable successinprimarilythreetypesofapplicationsinfinance:(1)modelingforclassificationandprediction,(2)associativememory,and(3)clustering(Hawleyetal., 1990).TheuseofwaveletnetworksisshowninFigure1.3.
Figure1.2
Types of applications of wavelet networks
ModelingClustering Associative memory
Typesofapplicationsofwaveletnetworks.
Classification includesassignmentofunitsinpredefinedgroupsorclasses,based onthediscoveryofregularitiesthatexistinthesample.Generally,nonlinearnonparametricpredictorssuchaswaveletnetworksareabletoclassifytheunitscorrectly evenifthesampleisincompleteoradditionalnoisehasbeenadded.Typicalexamplesofsuchapplicationsarethevisualrecognitionofhandwrittencharactersandthe identificationofunderwatertargetsbysonar.Infinance,anexampleofaclassification applicationcouldbethegroupingofbonds,basedonregularitiesinfinancialdata oftheissuer,intocategoriescorrespondingtotheratingassignedbyaspecialized company.Otherexamplesaretheapprovalofcreditgranting(thedecisionastowho receivescreditandhowmuch),stockselection(classificationbasedontheanticipated yield),andautomatedtradingsystems.
Theterm prediction referstothedevelopmentofmathematicalrelationships betweentheinputvariablesofthewaveletnetworkandusuallyone(althoughit canbemore)outputvariable.Artificialnetworksexpandthecommontechniques thatareusedinfinance,suchaslinearandpolynomialregressionandautoregressive movingaverages(ARMAandARIMA).Infinance,machinelearningisusedmainly inclassificationandpredictionapplications.Whenawaveletnetworkistrained,it canbeusedforthepredictionofafinancialtimeseries.Forexample,awavelet networkcanbeusedtoproducepointestimatesofthefuturepricesorreturnsofa particularstockorindex.However,financialanalystsareusuallyalsointerestedin confidenceandpredictionintervals.Forexample,ifthepriceofastockmovesoutside thepredictioninterval,afinancialanalystcanadjustthetradingstrategy.
In associativememory applicationsthegoalistoproduceanoutputcorresponding totheclassorgroupdesired,basedononeinputvectorpresentedintheneuralnetwork thatdetermineswhichoutputistobeproduced.Forexample,theinputvectormay beadigitizedimageofafingerprint,andtheoutputdesiredmaybereconstructionof theentirefingerprint.
Figure1.3
MACHINELEARNINGANDFINANCIALENGINEERING
Clustering isusedtogroupalargenumberofdifferentinputvariables,eachof which,however,hassomesimilaritieswithotherinputs.Clusteringisusefulforcompressionorfilteringofdatawithoutthelossofasubstantialpartoftheinformation. Afinancialapplicationcouldbethecreationofclustersofcorporatebondsthatcorrespondtouniformriskclassesbasedondatafromfinancialstatements.Thenumber andcompositionoftheclasseswillbedeterminedbythemodel,notbytheuser.In thiscase,incontrasttotheuseofclassification,thecategoriesarenotpredetermined. Thismethodcouldprovideaninvestorwithadiversifiedportfolio.
FROMNEURALTOWAVELETNETWORKS
Inthissectionthebasicnotionsofwaveletanalysis,neuralnetworks,andwavelet networksarepresented.Ourpurposeistopresentthebasicmathematicalandtheoreticalbackgroundthatisusedinsubsequentchapters.Also,thereasonsthatmotivated thecombinationofwaveletanalysisandneuralnetworkstocreateanewtool,wavelet networks,arediscussed.
WaveletAnalysis
Waveletanalysisisamathematicaltoolusedinvariousareasofresearch.Recently, waveletshavebeenusedespeciallytoanalyzetimeseries,data,andimages.Time seriesarerepresentedbylocalinformationsuchasfrequency,duration,intensity,and timeposition,andbyglobalinformationsuchasthemeanstatesoverdifferenttime periods.Bothglobalandlocalinformationisneededforthecorrectanalysisofa signal.Thewavelettransform(WT)isageneralizationoftheFouriertransform(FT) andthewindowedFouriertransform(WFT).
FourierTransform
Theattempttounderstandcomplicatedtimeseriesbybreaking themintobasicpiecesthatareeasiertounderstandisoneofthecentralthemesin Fourieranalysis.IntheframeworkofFourierseries,complicatedperiodicfunctions arewrittenasthesumofsimplewavesrepresentedmathematicallybysinesand cosines.Moreprecisely,Fouriertransformbreaksasignaldownintoalinearcombinationofconstituentsinusoidsofvariousfrequencies;hence,theFouriertransform isdecompositiononafrequency-by-frequencybasis.
Let f : R → C beaperiodicfunctionwithperiod T > 0thatsatisfies
anditsFouriercoefficientsaregivenby
InacommoninterpretationoftheFTgivenbyMallat(1999),theperiodicfunction f (t )isconsideredasamusicaltonethattheFTdecomposestoalinearcombination ofdifferentnotes cn withfrequencies ��n .Thismethodallowsustocompressthe originalsignal,inthesensethatitisnotnecessarytostoretheentiresignal;onlythe coefficientsandthecorrespondingfrequenciesarerequired.Knowingthecoefficients cn ,onecansynthesizetheoriginalsignal f (t ).Thisprocedure,called reconstruction, isachievedbytheinverseFT,givenby
TheFThasbeenusedsuccessfullyinavarietyofapplications.Themostcommon useofFTisinsolvingpartialdifferentialequations(Bracewell,2000),inimage processingandfiltering(Lim,1990),indataprocessingandanalysis(Oppenheim etal.,1999),andinoptics(Wilson,1995).
Short-TimeFourierTransform(WindowedFourier) Fourieranalysisperforms extremelywellintheanalysisofperiodicsignals.However,intransformingtothe frequencydomain,timeinformationislost.WhenlookingattheFouriertransformofa signal,itisimpossibletotellwhenaparticulareventtookplace.Thisisaseriousdrawbackifthesignalpropertieschangealotovertime:thatis,iftheycontainnonstationaryortransitorycharacteristics:drift,trends,abruptchanges,orbeginningsandends ofevents.Thesecharacteristicsareoftenthemostimportantpartofatimeseries,and Fouriertransformisnotsuitedtodetectingthem(ZapranisandAlexandridis,2006). TryingtoovercometheproblemsofclassicalFouriertransform,Gaborapplied theFouriertransforminsmalltime“windows”(Mallat,1999).Toachieveasort ofcompromisebetweenfrequencyandtime,Fouriertransformwasexpandedin windowedFouriertransformorshort-timeFouriertransform(STFT).WFTusesa windowacrossthetimeseriesandthenusestheFTofthewindowedseries.Thisisa decompositionoftwoparameters,timeandfrequency.WindowFouriertransformis anextensionoftheFouriertransformwhereasymmetricwindow, g(u) = g( u),is usedtolocalizesignalsintime.If t ∈ R,wedefine
Expression(1.6)revealsthat ft (u)isalocalizedversionof f thatdependsonly onvaluesof f (u).AgainfollowingthenotationofKaiser(1994),theSTFTof f is givenby
Itiseasytoseethatbysetting g(u) = 1,theSFTFisreducedtoordinaryFT. Becauseofthesimilarityofequations(1.2)and(1.7),theinverseSFTFcanbe definedas
Asmentionedearlier,FTcanbeusedtoanalyzeaperiodicmusicaltone.However, ifthemusicaltoneisnotperiodicbutratherisaseriesofnotesoramelody,theFourier seriescannotbeuseddirectly(Kaiser,1994).Ontheotherhand,theSTFTcananalyze themelodyanddecomposeittonotes,butitcanalsogivetheinformationwhena givennoteendsandthenextonebegins.TheSTFThasbeenusedsuccessfullyina varietyofapplications.Commonusesareinspeechprocessingandspectralanalysis (Allen,1982)andinacoustics(Nawabetal.,1983),amongothers.
ExtendingtheFourierTransform:TheWaveletAnalysisParadigm
Asmentionedearlier,Fourieranalysisisinefficientindealingwiththelocalbehavior ofsignals.Ontheotherhand,windowedFourieranalysisisaninaccurateandinefficienttoolforanalyzingregulartimebehaviorthatiseitherveryrapidorveryslow relativetothesizeofthewindow(Kaiser,1994).Moreprecisely,sincethewindowsize isfixedwithrespecttofrequency,WFTcannotcaptureeventsthatappearoutsidethe widthofthewindow.Manysignalsrequireamoreflexibleapproach:thatis,onewhere wecanvarythewindowsizetodeterminemoreaccuratelyeithertimeorfrequency. InsteadoftheconstantwindowusedinWFT,waveformsofshorterduration athigherfrequenciesandwaveformsoflongerdurationatlowerfrequencieswere usedaswindowsbyGrossmannandMorlet(1984).Thismethod,called wavelet analysis,isanextensionoftheFT.Thefundamentalideabehindwaveletsisto analyzeaccordingtoscale.Lowscalerepresentshighfrequency,whilehighscales representlowfrequency.Thewavelettransform(WT)notonlyislocalizedinboth timeandfrequencybutalsoovercomesthefixedtime–frequencypartitioning.The newtime–frequencypartitionislongintimeatlowfrequenciesandlonginfrequency athighfrequencies.ThismeansthattheWThasgoodfrequencyresolutionforlowfrequencyeventsandgoodtimeresolutionforhigh-frequencyevents.Also,theWT adaptsitselftocapturefeaturesacrossawiderangeoffrequencies.Hence,theWT canbeusedtoanalyzetimeseriesthatcontainnonstationarydynamicsatmany differentfrequencies(Daubechies,1992).
Infinance,waveletanalysisisconsideredanewpowerfultoolfortheanalysis offinancialtimeseries,anditisappliedinawiderangeoffinancialproblems. Oneexampleisthedailyreturnstimeseries,whichisrepresentedbylocalinformationsuchasfrequency,duration,intensity,andtimeposition,andbyglobal informationsuchasthemeanstatesoverdifferenttimeperiods.Bothglobalandlocal informationisneededforacorrectanalysisofthedailyreturntimeseries.Wavelets havetheabilitytodecomposeasignaloratimeseriesondifferentlevels.Asaresult, thisdecompositionbringsoutthestructureoftheunderlyingsignalaswellastrends, periodicities,singularities,orjumpsthatcannotbeobservedoriginally.
Waveletanalysisdecomposesageneralfunctionorsignalintoaseriesof(orthogonal)basisfunctionscalled wavelets,whichhavedifferentfrequencyandtimelocations.Moreprecisely,waveletanalysisdecomposestimeseriesandimagesinto componentwavesofvaryingdurationscalledwavelets,whicharelocalizedvariationsofasignal(Walker,2008).AsillustratedbyDonohoandJohnstone(1994), thewaveletapproachisveryflexibleinhandlingveryirregulardataseries.Ramsey (1999)alsocommentsthatwaveletanalysishastheabilitytorepresenthighlycomplexstructureswithoutknowingtheunderlyingfunctionalform,whichisofgreat benefitineconomicandfinancialresearch.Aparticularfeatureofthesignalanalyzed canbeidentifiedwiththepositionsofthewaveletsintowhichitisdecomposed.
Recently,anincreasingnumberofstudiesapplywaveletanalysistoanalyzefinancialtimeseries.WaveletanalysiswasusedbyAlexandridisandHasan(2013)to estimatethesystematicriskofCAPMusingwaveletanalysistoexaminethemeteor showereffectsoftheglobalfinancialcrisis.Similarly,onerecentresearchstrandof CAPMhasbuiltanempiricalmodelingstrategycenteringontheissueofthemultiscalenatureofthesystematicriskusingaframeworkofwaveletanalysis(Fernandez, 2006;Genc¸ayetal.,2003,2005;Masihetal.,2010,Norsworthyetal.,2000;Rabeh andMohamed,2011).Waveletanalysishasalsobeenusedtoconstructamodeling andpricingframeworkinthecontextoffinancialweatherderivatives(Alexandridis andZapranis2013a,b;ZapranisandAlexandridis,2008,2009).
Moreover,waveletanalysiswasusedbyInandKim(2006a,b)toestimatethe hedgeratio,anditwasusedbyFernandez(2005),andInandKim(2007)toestimate theinternationalCAPM.Maharajetal.(2011)madeacomparisonofdevelopedand emergingequitymarketreturnvolatilityatdifferenttimescales.Therelationship betweenchangesinstockpricesandbondyieldsintheG7countrieswasstudied byKimandIn(2007),whileKimandIn(2005)examinedtherelationshipbetween stockreturnsandinflationusingwaveletanalysis.Heetal.(2012)studiedthevalueat-riskinmetalmarkets,whileawavelet-basedassessmentoftheriskinemerging marketswaspresentedbyRuaandNunes(2012).Finally,awavelet-basedmethod formodelingandpredictingoilpriceswaspresentedbyAlexandridisandLivanis (2008),Alexandridisetal.(2008),andYousefietal.(2005).Finally,asurveyofthe contributionofwaveletanalysisinfinancewaspresentedbyRamsey(1999).
Wavelets Awavelet �� isawaveformofeffectivelylimiteddurationthathasan averagevalueofzero.TheWAprocedureadoptsaparticularwaveletfunctioncalled a motherwavelet.A waveletfamily isasetoforthogonalbasisfunctionsgenerated
bydilationandtranslationofacompactlysupported scalingfunction �� (or father wavelet),anda waveletfunction �� (ormotherwavelet). Thefatherwavelets �� andmotherwavelets �� satisfy
Thewaveletfamilyconsistsof waveletchildren whicharedilatedandtranslated formsofamotherwavelet:
where a isthe scale or dilationparameter and b isthe shift or translationparameter. Thevalueofthescaleparameterdeterminesthelevelofstretchorcompression ofthewavelet.Theterm1/√a normalizes ‖ ‖��
‖ ‖ = 1.Inmostcaseswelimit ourchoiceof a and b valuesbyusingadiscreteset,becausecalculatingwavelet coefficientsateverypossiblescaleiscomputationallyintensive.Temporalanalysis isperformedwithacontractedhigh-frequencyversionofthemotherwavelet,while frequencyanalysisisperformedwithadilated,low-frequencyversionofthesame motherwavelet.Inotherwords,whereasFourieranalysisconsistsofbreakingasignal upintosinewavesofvariousfrequencies,waveletanalysisisthebreakupofasignal intoshiftedandscaledversionsoftheoriginal(ormother)wavelet(Misitietal., 2009).WaveletdecompositionisillustratedinFigure1.4. TwoversionsoftheWTcanbedistinguished:thecontinuouswavelettransform (CWT)andthediscretewavelettransform(DWT).Thedifferencebetweenthem liesinthesetofscalesandpositionsatwhicheachtransformoperates.TheCWT canoperateateveryscale.However,anupperboundisdeterminedsinceCWTis extremelycomputationallyexpensive.Also,inCWTtheanalyzingwaveletisshifted
Constituent wavelets of different scales and positions Original signal
Wavelet transform
Figure1.4 Waveletdecomposition.
smoothlyoverthefulldomainofthefunctionanalyzed.Toreducethecomputational burden,waveletcoefficientsarecalculatedonlyonasubsetofscales.Thismethodis calledtheDWT.
Ingeneral,waveletscanbeseparatedinorthogonalandnonorthogonalwavelets. Theterm waveletfunction isusedgenericallytorefertoeitherorthogonalor nonorthogonalwavelets.Anorthogonalsetofwaveletsiscalleda waveletbasis, andasetofnonorthogonalwaveletsistermeda waveletframe.TheuseofanorthogonalbasisimpliestheuseoftheDWT,whereasframescanbeusedwitheitherthe discreteorthecontinuoustransform.
Overtheyearsasubstantialnumberofwaveletfunctionshavebeenproposedinthe literature.TheGaussian,theMorlet,andtheMexicanhatwaveletsarecrudewavelets thatcanbeusedonlyincontinuousdecomposition.ThewaveletsintheMeyerwavelet familyareinfinitelyregularwaveletsthatcanbeusedinbothCWTandDWT. ThewaveletsintheDaubechies,symlet,andcoifletfamiliesareorthogonaland compactlysupportedwavelets.ThesewaveletfamiliescanalsobeusedinCWTand DWT.TheB-splinesandbiorthogonalwaveletfamiliesarebiorthogonal,compactly supportedwaveletpairsthatcanalsobeusedinbothCWTandDWT.Finally,the complexGaussian,complexMorlet,complexShannon,andcomplex-frequencyBsplinewaveletfamiliesarecomplexwaveletsthatcanbeusedinthecomplexCWT.
Generally,theDWTisusedfordatacompressionifthesignalisalreadysampled, andtheCWTisusedforsignalanalysis.InthenextsectionstheCWTandthe DWTareexaminedindetail.InFigure1.5theMexicanhatwaveletispresented,
Wavelet function
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S , John, in prison after the Revolution, 13; a creditor punished for imprisoning him, 27.
Small-pox (1713), 387; inoculation for introduced, 530.
S of Whitehill’s plans for introducing water into towns, 238.
Soldiers, recruiting of, by nefarious means, 43; from criminals, 64; recruits kept in jails, 79; mutinies of recruits in Canongate Tolbooth, 182, 601.
Spirits, young man troubled with, at Glencorse, 555.
Spott church communion-cups, 335; witch of Spott, 275.
Stage-coach from Edinburgh to Glasgow (1758), 612; from London to Glasgow, 613; from Edinburgh to London, 407.
Stair church burnt, 355.
S , Viscountess of, death of; her coffin placed in an upright position; bon mot of, 74.
Stang, riding of the, a punishment for cruel husbands, 589.
Staving of Irish victual, proclamation regarding, 241.
S , Sir R., visits Scotland, as a commissioner on forfeited estates, 409, 426; anecdotes concerning, 429.
Stereotyping invented by Ged, 555.
S , Sir James, Lord Advocate for Scotland, favourable to witchprosecutions, 135; his death, 382; Lt.-Gen. Sir James Steuart, his recollections of Duchess of Douglas at Paris, 507.
S , General, killed by Elliot of Stobbs, 523.
S of Kier, his trial for high-treason, 345.
S , John, ‘student in astrologico-physick,’ 85.
Storm, an extraordinary, in 1739, 603.
S , W.S., of Edinburgh, is robbed of a large sum, 333.
S , Earl of, killed in a drunken fray, 545.
Streets and Wynds of Edinburgh, in 18th century, 591.
S , Mackenzie of, killed at Inverroy, 16.
Summer of 1723, its sultriness, 480.
Sunday observance, 271, 342, 344, 397, 569.
S , James, in charge of the Physic Garden, 81; introduces culture of melons, 142.
Tain Tolbooth steeple falls, 277.
T , Master of, charged with a murder at Leith, 48.
Tascal-money, murder of Cameron for, 486.
Tavern-bill, example of one in Edinburgh, 183.
Taverns much frequented, 575.
Taverns open on Sunday, disturbance regarding, 271.
Taxes of Scotland and England equitably adjusted by Union, 328.
Tea, its disuse recommended in favour of beer, 613.
Tennis Court, theatricals in, 398.
Thanksgiving hypocritically ordered, 221.
Theatricals in Edinburgh (1715), 397, 518, 544, 550, 583, 598; at Glasgow, 550.
Thrashing-machine invented, 503.
Thunderstorm at Edinburgh (June 10, 1717), 424.
Tinklarian Doctor, a strange enthusiast, 358; visits the witch-boy of Calder, 449.
Tippermalloch’s Receipts, 53; medical practice and literature of the time, 53;
Tippermalloch’s pharmacopœia, 54; his dream about battles and ambassadors, 55.
Toasts, treasonable, drunk at Dumfries, 182.
Tobacco trade of Glasgow, 431, 516.
Tolbooth, Canongate, mutiny of recruits in, 601.
Tolbooth of Edinburgh stuffed with political prisoners, 11.
Toleration Act for Scottish Episcopalians, 367.
Torture employed after the Revolution, 39.
Travelling, formal permission required from government for persons of eminence, 51; slowness of, 222; means of, 406; coaches set up, 612; a difficult journey of Lord Lovat, 625.
Treasure lost at sea, dived for, 551.
T ’ Compendium of Latin Grammar, 582.
Trustees, Board of, established, 541.
Tyninghame Woods planted by Earl of Haddington, 417.
Union, changes in commerce produced by, 336; customs and excise of Scotland, 339.
Union, treaty of, 258.
University of Edinburgh, cleared of Episcopalian professors, 7; medical education introduced, 105.
Vice and immorality severely punished, 342.
V , Signora, an Italian rope-dancer, 625.
W , General, sent as commander-in-chief to disarm the Highlanders, 497;
pleads for exiled rebels, 523; his Highland roads, 526, 561; fête at Dalnaspidal, 561.
W , Helen, intercedes for her sister’s pardon, 602.
W , Patrick, his account of the expulsion of the bishops in 1689, 5; his account of the Seven Dear Years, 196; denounces the dancing assemblies, 482.
Walking-swords and other weapons worn by gentlemen, 49.
W , Captain John, long kept a prisoner for defending Holyroodhouse, 13; petition for release, 68.
W , Andrew, Glasgow shoemaker, 386.
——, a skipper, subscription in behalf of, 134.
Weapons worn by gentlemen, a fatal practice, 49.
Weights and measures, statutory, confided to various towns, 51.
Western Isles, Description of, by Martin, 278.
Whales in Firth of Forth, 77, 327; at Culross and Kilrenny, 458.
W ’ Primitive Christianity seized, 363.
W ’ open-air preaching, 606.
W III., crown settled on, 1; concern in massacre of Glencoe, 60; his sentiments on Catholic worship, 204; death of, 256.
W , Rev. J., of Musselburgh, his letter on ‘recent domestic events,’ 403.
W , Robert, a servant lad, stolen as a recruit, 44.
Windmill at Leith, building of, 290.
Winds, destructive, in Lothian, 471.
Wines, use of, and prices, 183, 270.
Witch-boy at Calder, 449.
——, Marion Lillie, at Spott, 275.
——, the last burnt in Scotland, 540.
Witchcraft jurisprudence, 135; laws against, repealed, 597.
Witches at Coldingham, 94; at Torryburn and Pittenweem, Fife, 298; at Inverness, 302.
Witches, five, burnt at Paisley, 172.
—— of Ross-shire treated leniently for the first time, 216; see also, 540.
Witches, various, proceedings against, 66, 94, 135, 193, 216, 275, 298, 302, 540.
W , Rev. Mr, his remarks on mercantile losses at Glasgow, 337, 487, 565; on plague of bugs at, 542; excursion into Galloway, 380; deplores religious changes at Glasgow, 432, 486, 515; sad account of general condition of the country, 491; condemns theatricals, 519, 544, 550; describes profligacy of manners, 521.
Wolf, last in Scotland, killed, 609.
Women of evil repute banished, 115.
Women’s ‘Girded Tails’ satirised, 448.
Wool forbidden to be exported, 238.
Woollen manufactures at Aberdeen, 156.
W M , Lady Mary, satirises Lady Murray of Stanhope, 479; introduces inoculation, 530.
Writers, malignant feelings displayed on opposing interests, case of; Leslie and Comrie, 278.
Writing, engine for, invented, 99.
York Buildings Company purchases forfeited estates, 443; leases Strontian mines, 475; its failure alluded to, 492; leases woods of Abernethy, 547.
Y , George, troubles from enforcing Sunday observance, 271.
Y , James, an ingenious mechanist and curiosity-monger, 99; House of Curiosities at Edinburgh, 100.
Edinburgh: Printed by W. and R. Chambers.
The state of the Leg-of-Mutton-School of verse[242] in Scotland at the end of the seventeenth century, may be pretty fairly inferred from this specimen.]
1. A very animated review of these affairs will be found in Mr Burton’s excellent History.
2. Collection of Papers, &c. London, Richard Janeway, 1689.
3. Account of the Pope’s Procession at Aberdene, &c., reprinted in Laing’s Fugitive Poetry of the Seventeenth Century.
4. Biographia. Presbyteriana, i. 221.
Old Tolbooth, Edinburgh.
5. Under this title, a pamphlet, detailing the outing and rabbling of the clergy, was published in London in 1690.
6. Stewart’s Sketches of the Highlanders, i. p. 99, note.
7. Wodrow’s Analecta, i. 338.
8. Life and Diary of Lieutenant-colonel Blackader of the Cameronian Regiment. By Andrew Crichton. Edin. 1824.
9. Privy Council Record, MS., Gen. Register House, Edinburgh.
10. Home of Crossrig’s Diary. Stevenson, Edinburgh, 1843.
11. Domestic Annals of Scotland, ii. 408, 432.
12. Acts of Scottish Parliament, ix. 12.
13. On the 12th February 1690, the Privy Council had under their notice the case of a man named Samuel Smith, who had been imprisoned in the Edinburgh Tolbooth for three years on a charge of theft, without trial, and ordained him to be set at large, there being ‘ no probation’ against him.
14. Privy Council Record.
15. Privy Council Record, under February 22, 1698.
16. Memoirs of Sir Ewen Cameron of Locheil [by Drummond of Balhadics], p. 243.
17. Memoirs of Sir Ewen Cameron of Locheil, p. 254.
18. C. K. Sharpe in note to Law’s Memorials.
19. Privy Council Record.
20. Justiciary Record.
21. Mrs Gibb seems to have been the person who managed the transmission or carrying between Edinburgh and Haddington.
22. Privy Council Record.
23. Privy Council Record.
24. Privy Council Record.
25. Privy Council Record.
26. Privy Council Record.
27. Privy Council Record.
28. Scots Acts, iii. 310.
29. Privy Council Record.
30. Contemporary broadsides.
31. Domestic Annals, ii. 384.
32. Privy Council Record.
33. Privy Council Record.
34. A picturesque glimpse of the Highland marauding of this period was obtained some years ago at second-hand from the memory of William Bane Macpherson, who died in 1777 at the age of a hundred. ‘He was wont to relate that, when a boy of twelve years of age, being engaged as buachaille [herd-boy] at the summering [i. e., summer grazing] of Biallid, near Dalwhinnie, he had an opportunity of being an eye-witness to a creagh and pursuit on a very large scale, which passed through Badenoch. At noon on a fine autumnal day in 1689, his attention was drawn to a herd of black-cattle, amounting to about six score, driven along by a dozen of wild Lochaber men, by the banks of Loch Erroch, in the direction of Dalunchart in the forest of Alder, now Ardverikie. Upon inquiry, he ascertained that these had been “lifted” in Aberdeenshire, distant more than a hundred miles, and that the reivers had proceeded thus far with their booty free from molestation and pursuit. Thus they held on their way among the wild hills of this mountainous district, far from the haunts of the semi-civilised inhabitants, and within a day’s journey of their home. Only a few hours had elapsed after the departure of these marauders, when a body of nearly fifty horsemen appeared, toiling amidst the rocks and marshes of this barbarous region, where not even a footpath helped to mark the intercourse of society, and following on the trail of the men and cattle which had preceded them. The troop was well mounted and armed, and led by a person of gentlemanlike appearance and courteous manners; while, attached to the party, was a number of horses carrying bags of meal and other provisions, intended not solely for their own support, but, as would seem from the sequel, as a ransom for the creagh. Signalling William Bane to approach, the leader minutely questioned him about the movements of the Lochaber men, their number, equipments, and the line of their route. Along the precipitous banks of Loch Erroch this large body of horsemen wended their way, accompanied by William Bane, who was anxious to see the result of the meeting. It bespoke spirit and resolution in those strangers to seek an encounter with the robbers in their native wilds, and on the borders of that country, where a signal of alarm would have raised a numerous body of hardy Lochaber men, ready to defend the creagh, and punish the pursuers. Towards nightfall, they drew near the encampment of the thieves at Dalunchart, and observed them busily engaged in roasting, before a large fire, one of the beeves, newly slaughtered.
‘A council of war was immediately held, and, on the suggestion of the leader, a flag of truce was forwarded to the Lochaber men, with an offer to each of a bag of meal and a pair of shoes, in ransom for the herd of cattle. This offer, being viewed as a proof of cowardice and fear, was contemptuously rejected, and a reply sent, to the effect that the cattle, driven so far and with so much trouble, would not be surrendered. Having gathered in the herd, both parties prepared for action. The overwhelming number of the pursuers soon mastered their opponents. Successive discharges of firearms brought the greater number of the Lochaber men to the
ground, and in a brief period only three remained unhurt, and escaped to tell the sad tale to their countrymen.’ Inverness Courier, August 17, 1847.
35. This post-boy appears to have been forty-four years old.
36. Lord Viscount Kingston was a cadet of the Winton family, and had delivered a Latin oration to Charles I., at his father’s house of Seton, in 1633.
37. In the parliament which sat down in September, robbing the post-packet was declared to be ‘robbery,’ to be punished with death and confiscation of movables. Scots Acts.
38. Privy Council Record.
39. Privy Council Record.
40. Privy Council Record. The privileges of Mr Hamilton were confirmed by the Estates in June 1693.
41. Privy Council Record.
42. Privy Council Record.
43. A portrait of the house, and some particulars of the family, are to be found in Robert Stuart’s Views and Notices of Glasgow in Former Times, 4to, 1847.
44. This must have been Lady Raeburn (Anne Scott of Ancrum).
45. Probably his sister Isobel’s husband, described in Burke as Captain Anderson.
46. Acts of General Assembly, 1690, p. 18.
47. See page 10.
48. Melville Correspondence, p. 150. The parliament, on the 18th July 1690, gave a warrant for subjecting one Muir or Ker to the torture, in order to expiscate the truth regarding the murder of an infant, of which he was vehemently suspected.
49. Mr Burton, in his History of Scotland from 1689 to 1748, gives the following account of this nobleman: ‘The Earl of Crawford, made chairman of the Estates and a privy councillor, was the only statesman of the day who adopted the peculiar demeanour and scriptural language of the Covenanters. It is to him that Burnet and others attribute the severities against the Episcopal clergymen, and the guidance of the force brought to bear in the parliament and Privy Council in favour of a Presbyterian establishment.’
50. Melville Correspondence. Privy Council Record.
51. Privy Council Record.
52. Privy Council Record.
53. Privy Council Record.
54. Privy Council Record.
55. Burt’s Letters, i. 128.
56. A phrase of the time, found in the Privy Council Record.
57. John Callander, master-smith, petitioned the Privy Council in June 1689, regarding smith-work which he had executed for Edinburgh and Stirling Castles, to the amount of eleven hundred pounds sterling, whereof, though long due, he had ‘ never yet received payment of a sixpence.’ On his earnest entreaty, three hundred pounds were ordered to be paid to account. On the ensuing 23d of August, he was ordained to be paid £6567, 17s. 2d., after a rigid taxing of his accounts, Scots money being of course meant. Connected with this little matter is an anecdote which has been told in various forms, regarding the estate of Craigforth, near Stirling. It is alleged that the master-smith, failing to obtain a solution of the debt from the Scottish Exchequer, applied to the English treasury, and was there so fortunate as to get payment of the apparent sum in English money. Having out of this unexpected wealth made a wadset on the estate of Craigforth, he ultimately fell into the possession of that property, which he handed down to his descendants.[58] John Callander was grandfather of a gentleman of the same name, who cultivated literature with assiduity, and was the editor of two ancient Scottish poems The Guberlunzie Man, and Christ’s Kirk on the Green. This gentleman, again, was grandfather to Mrs Thomas Sheridan and Lady Graham of Netherby.
58. Sir James Campbell’s Memoirs. A Week at the Bridge of Allan, by Charles Rogers, 1853, p. 334.
59. Justiciary Records.
60. Privy Council Record.
61. Privy Council Record.
62. Record of Convention of Burghs, MS. in Council Chamber, Edinburgh.
63. Anderson’s Prize Essay on the State of the Highlands in 1745, p. 95.
64. New Stat. Acc. of Scotland: Ross, p. 220.
65. Privy Council Record.
66. Dr John Brown: Locke and Sydenham, &c., 1858, p. 457.
67. The second edition of Tippermalloch was published in 1716, containing Dr Pitcairn’s method of curing the small-pox. It professes to be superior to the first edition, being ‘taken from an original copy which the author himself delivered to the truly noble and excellent lady, the late Marchioness of Athole, and which her Grace the present duchess, a lady no less eminent for her singular goodness and virtue than her high quality, was pleased to communicate to us and the public.’
68. Analecta Scotica, ii. 176.
69. Privy Council Record.
70. Crossrig’s Diary.
71. Kilravock Papers, Spald. Club, p. 388.
72. Privy Council Record.
73. Privy Council Record.
74. Life of Peden, Biogr. Presbyteriana, i. 112.
75. Privy Council Record.
76. Domestic Annals of Scotland, ii. 29.
77. Criminal Proceedings, a Collection of Justiciary Papers in Library of the Society of Antiquaries of Scotland.
78. Macdonald of Glencoe bore the subordinate surname of M‘Ian, as descended from a noted person named Ian or John.
79. Addressed to Sir Thomas Livingstone, commander-in-chief of the forces in Scotland.
80. See Papers Illustrative of the Political Condition of the Highlands from 1689 to 1696. Maitland Club. 1845.
81. Privy Council Record.
82. Privy Council Record.
83. This was the father of Mr Andrew Drummond, the founder of the celebrated banking-house in the Strand.
84. Privy Council Record.
85. From papers in possession of John Hall Maxwell, of Dargavel, Esq.
86. Privy Council Record. (See onward, under December 31, 1692, and July 13, 1697.)
87. Privy Council Record.
88. Fountainhall’s Decisions, i. 693.
89. Privy Council Record.
90. Fountainhall’s Decisions, i. 693.
91. Domestic Annals of Scotland, ii. 326.
92. Mem. of John Earl of Stair by an Impartial Hand, p. 7.
93. Murray’s Literary Hist. of Galloway, p. 155.
94. Privy Council Record.
95. Minutes of Merchant Company, MS. in possession of the Company.
96. Fountainhall’s Decisions, i. 518, 564.
97. Ibid., i. 525.
98. Ibid.
99. Privy Council Record.
100. Privy Council Record.
101. Privy Council Record.
102. Privy Council Record.
103. Privy Council Record.
104. Privy Council Record.
105. In July 1695, there was a further act ‘anent burying in Scots linen,’ ordaining that none should be used for sepulchral purposes above twenty shillings Scots per ell, and also commanding that the nearest elder or deacon of the parish, with one or two neighbours, should be called by the friends of deceased persons to see that the shroud was in all respects conform to the acts thereanent.
106. Wodrow Pamphlets, Adv. Lib., vol. 115.
107. Privy Council Record.
108. Acts of Scottish Parliament, ix. 429.
109. Privy Council Record.
110. Acts of Scottish Parliament, ix. 420.
111. See Domestic Annals of Scotland, ii. 398.
112. Privy Council Record.
113. Letter from a Gentleman in the Country to his Friend at Edinburgh, &c. Edin. 1696.
114. Privy Council Record.
115. Fountainhall’s Decisions, i. 590.
116. Privy Council Record.
117. Privy Council Record.
118. Privy Council Record.
119. Scottish Journal, ii. 200.
120. The troubles from the meeting-houses at Coldingham and two neighbouring parishes, led to their being entirely suppressed by the arm of the government in March 1700 [q. v.]
121. The above, and some other curious extracts from the parish register of Coldingham, are given in an interesting volume, entitled History of the Priory of Coldingham. By William King Hunter. Edinburgh, 1858.
122. Analecta, ii. 250. Wodrow tells us that Lady Dundee had been very violent against the Presbyterians, and ‘used to say she wished that, that day she heard a Presbyterian minister, the house might fall down and smother her, which it did.’
123. Analecta Scotica, i. 187. Wodrow’s Analecta, ii. 250.
124. William Livingstone survived his wife nearly forty years. In the Caledonian Mercury for February 6, 1733, is this paragraph: ‘We are assured private letters are in town, giving account, that on the 12th of last month, the Right Hon. the late Viscount Kilsyth died at Rome, in an advanced age, in perfect judgment, and a Christian and exemplary resignation.’
125. Privy Council Record.
126. A Summer’s Divertisement of Mathematical and Mechanical Curiosities, being an Account of the Things seen at the House of Curiosities, near Grange Park. Edinburgh: James Watson. 1695.
127. Nicolas’s spelling is here given literatim.
128. Privy Council Record.
129. From ‘ a double of the oath’ in the Kilravock Papers, Spald. Club publication, p. 387.
130. Fountainhall’s Decisions, i. 629.
131. Privy Council Record.
132. ‘James Peedie of Roughill and John Anderson of Dowhill were the first merchants who brought a loading of cherry-sack into this city.’ M‘Ure’s Hist. Glasg., p. 250.
133. Arnot’s Criminal Trials, p. 163.
134. Chalmers’s Life of Ruddiman, p. 30. Bower’s Hist. Univ. of Edinburgh, ii. 153.
135. Privy Council Record.
136. Privy Council Record.
137. These legends appear to have been intended to read as follows: ‘Three years thou shalt have to repent, and note it well. Wo be to thee, Scotland! Repent and take warning, for the doors of heaven are already barred against thee. I am sent for a warning to thee, to flee to God. Yet troubled shall this man be for twenty days and three. Repent, repent, Scotland, or else thou shalt’ .
138. On the 7th of January 1696, the Privy Council gave licence to George Mossman, stationer in Edinburgh, to ‘print and sell a book entitled A True Relation of an Apparition, Expressions, and Actings of a Spirit which infested the House of Andrew Mackie, in Ring-croft of Stocking, in the Parish of Rerrick, &c., ’ with exclusive right of doing so for a year.
139. Privy Council Record.
140. Caledonian Mercury, Nov. 20, 1732.
141. Privy Council Record.
142. From Information for his Majesty’s Advocate, &c., against James Edmonstoun of Newton.
143. Maclaurin’s Criminal Cases, p. 10.
144. Introductions, &c., to Waverley Novels, i. 255.
145. Acts of Scot. Par., ix. 452.
146. Hugh Miller’s Sketch-book of Popular Geology, pp. 13, 14.
147. Privy Council Record.
148. A few of the subscriptions are here subjoined: For £1000 each, the Faculty of Advocates, John Anderson of Dowhill, Provost of Glasgow, the Earl of Annandale; Alexander Brand, merchant in Edinburgh; James Balfour, merchant in Edinburgh; George Clerk, merchant in Edinburgh; Daniel Campbell, merchant in Glasgow; Sir Robert Dickson of Sorn-beg, Andrew Fletcher of Salton, the town of Glasgow, John Graham younger of Dougalston, the Earl of Haddington, Lord Yester, Sir David Home of Crossrig, Sir John Home of Blackader, Sir Alexander Hope of Kerse, William Hay of Drumelzier, Sir James Hall of Dunglass, Lockhart of Carnwath, William Livingstone of Kilsyth; George Lockhart, merchant in Glasgow; the Merchant House of Glasgow, the Marquis of Montrose, Sir John Maxwell of Pollock, Sir Patrick Murray of Auchtertyre, Francis Montgomery of Giffen, William Morison of Prestongrange, William Nisbet of Dirleton, Sir James Primrose of Carrington, the Countess of Rothes, the Countess of Roxburgh, Lord Ross, Lord Ruthven, William Robertson of Gladney, the Earl of Sutherland, the Earl of Southesk, Viscount Strathallan, Viscount Stair, Sir John Swinton, Sir Francis Scott of Thirlstain, Sir John Shaw of Greenock; Thomas Spence, writer in Edinburgh; John Spreul, alias Bass John, merchant in Glasgow; the Marquis of Tweeddale, Viscount Tarbat; Robert Watson, merchant in Edinburgh; George Warrender, merchant there; and William Wardrop, merchant in Glasgow: for £1200, the Merchant Company of Edinburgh: for £1300, James Pringle of Torwoodlee: for £1500, the Earl of Argyle, William Lord Jedburgh, and Patrick Thomson, treasurer of Glasgow: for £2000, Mr Robert Blackwood, merchant in Edinburgh; Sir Robert Chiesley, Lord Provost of Edinburgh, John Lord Glenorchy, Lord Basil Hamilton, the Earl of Hopetoun, the Earl of Leven; William Menzies, merchant in Edinburgh; the town of Perth, Sir William Scott of Harden: for £3000, Lord Belhaven, the Good Town of Edinburgh, the Duchess of Hamilton, the Duke of Queensberry, the Easter Sugarie of Glasgow, and Sir John Stuart of Grandtully.
149. Scots Acts, sub anno 1695.
150. [Sinclair’s] Statistical Account of Scotland, vi. 586.
151. In April 1703, John Dunbabbine, an Englishman, who in his own country had for several years followed the trade of pin-making ‘to the satisfaction of all those with whom he had any dealing,’ was now inclined to set up a work at Aberdeen, which he thought would be ‘ very much for the advantage of the kingdom [of Scotland] and all the inhabitants thereof.’ All he required previously was his work being endowed with the privileges and immunities of a manufactory; which the Privy Council readily granted.
152. Privy Council Record.
153. Mr James Foulis and Mr John Holland are probably identical with the persons of the same names who received some encouragement from the parliament in April 1693, for the setting up of a manufacture of Colchester Baises in Scotland. See Domestic Annals, under that date.
154. See a pamphlet by Mr Holland, published in 1715, under the title of The Ruine of the Bank of England and all Publick Credit inevitable.
155. Exchange was not dealt in by the Bank of England, any more than the Bank of Scotland, during many of its earlier years.
156. Account of the Bank of Scotland, published in 1728.
157. Acts of Scottish Parliament, ix. 465.
158. Culloden Papers, Introduction, p. xliv.
159. Privy Council Record.
160. Patrick Walker’s Life of Donald Cargill, Biog. Pres., ii. 24.
161. Patrick Walker.
162. Ibid.
163. Privy Council Record.
164. Privy Council Record.
165. We have no means of knowing if this concert was connected with the enterprise of Beck and his associates, noticed under January 10, 1694. The name of Beck does not occur in the list of performers on this occasion.
166. W. Tytler, Trans. Soc. of Antiq. of Scotland, i. 506.
167. Ramsay’s Scribblers Lashed.
168. Through her, as daughter of William first Duke of Queensberry, her descendant, the Earl of Wemyss, succeeded in 1810 to large estates in Peeblesshire and the earldom of March.
169. Privy Council Record.
170. Privy Council Record.
171. See under Feb. 2, 1693.
172. Privy Council Record.
173. Ibid.
174. Privy Council Record.
175. Privy Council Record.
176. Printed informations in the case. Justiciary Records.
177. Acts of Scot. Parliament.
178. Privy Council Record.
179. The authority for this is a very bad one the scurrilous book called Scots Presbyterian Eloquence Displayed; but on such a point, with support from other quarters, it may be admitted.
180. Calamy’s Account of his Own Life.
181. Watson’s Collection of Scots Poems, 1709.
182. Privy Council Record.
183. A tolerably full detail of Mr Hepburn’s persecutions is given in Struthers’s Hist. Scot. from the Union to 1748. 2 vols.
184. Privy Council Record.
185. Scots Acts, vol. iii.
186. See Domestic Annals, under date August 24, 1669.
187. Privy Council Record.
188. Privy Council Record.
189. Records of Parliament and Privy Council.
190. Acts of Scot. Parl., xi. 82.
191. Ibid.
192. Acts of Scot. Parl., xi. 111.
193. Privy Council Record.
194. Privy Council Record.
195. The above account of the prosecution of Aikenhead is derived from Howell’s State Trials, in which there has been printed a collection of documents on the case, collected by John Locke.
196. Preface to Two Sermons, &c., by Mr Lorimer.
197. Foun., Decisions.
198. Privy Council Record, under various dates.
199. Signed at Glasgow, December 31, 1696.
200. Domestic Annals, sub July 9, 1668, vol ii. p. 321.
201. Privy Council Record.
202. Justiciary Record.
203. New Stat. Acc. of Scotland, iv. Wigton, 226.
204. Criminal Proceedings, &c., MS., in possession of Ant. Soc. Scot.
205. New Stat. Acc. Scotland, ut supra.
206. Decisions, i. 522.
207. Privy Council Record.
208. A Voyage to St Kilda, &c., by M. Martin, Gent. 4th ed., 1753.
209. Macaulay’s History of St Kilda, 1766, p. 241.
210. Privy Council Record.
211. Ibid.
212. Privy Council Record.
213. Privy Council Record.
214. Letters from North of Scotland, ii. 134 (2d ed.).
215. Edin. Courant, May 1720.
216. Letters, &c., i. 135.
217. Arnot’s Crim. Trials, Anderson’s Hist. Fam. Fraser, Carstares’s State Papers.
218. Privy Council Record.
219. Privy Council Record.
220. Privy Council Record.
221. Fountainhall’s Decisions, ii. 5.
222. Privy Council Record.
223. Privy Council Record.
224. Acts of General Assembly.
225. Wodrow Pamphlets, Adv. Lib.
226. Under extremity of suffering during the dearth, in September 1699, one David Chapman, belonging to Crieff, broke into a lockfast place, and stole some cheese, a sugar-loaf, and about four shillings sterling of money. His sole motive for the crime, as he afterwards pleaded, was the desire of relieving his family from the pains of want. Apprehended that day, he confessed the crime, and restored the spoil; yet, being tried by the commissioner of justiciary for the Highlands, he was condemned to death.
On a petition, the Privy Council commuted the sentence to scourging through the town of Perth, and banishment to the plantations.[228]
227. Published in 1702.
228. Privy Council Record.
229. Coltness Collections.
230. Polit. Works of A. Fletcher, edit. 1749, p. 85.
231. Privy Council Record. Fountainhall’s Decisions.
232. Scots Acts, iii. 628.
233. [Leslie’s] Survey of the Province of Moray, p. 280.
234. The father of the present Earl of Stair, Sir John Dalrymple, was born in 1726, and might have heard these particulars from his grand-uncle, the second President Dalrymple, who died in 1737. Sir John’s Memoirs of Great Britain are here followed, therefore, as the best authority available.
235. Dalrymple’s Memoirs.
236. Memoirs of John Macky, Esq., 1733, p. 205.
237. Acts of S. Parl., x. 136. Wodrow’s History, i. 320.
238. Privy Council Record.
239. Ibid.
240. This gentleman, who became Earl of Hopetoun, first of the title, was married, on the 31st August 1699, to ‘the very vertuous Lady Henrietta Johnston,’ daughter of the Earl of Annandale. A congratulatory poem on the occasion contains the following passage:
May Hopetoun flourish still with Lady HenRietta, and have a stock of good childrén.[241]
241. Wodrow Pamphlets, Adv. Lib.
242. See Blackwood’s Magazine, ix. 345.
243. Privy Council Record.
244. Ibid.
245. Of this fact, the use of the word siller for money generally in Scotland is a notable memorial.
246. Account of Bank of Scotland, p. 6.
247. Letter of Earl of Argyle, Carstares Papers, 458.
248. James Donaldson seems to have been engaged in the poetic elegy trade; that is, the writing of deplorations in verse on great personages for sale in the
streets: see an example of his verse of this description under November 1695. He seems also to have been the author of Husbandry Anatomised, or an Enquiry into the Present Manner of Tilling and Manuring the Ground in Scotland, 12mo, 1697; and of A Picktooth for Swearers, or a Looking-glass for Atheists and Profane Persons, &c., small 4to, 1698. See Scottish Elegiac Verses, with Notes, 1847.
249. Privy Council Record.
250. Ibid.
251. Privy Council Record.
252. Privy Council Record.
253. Privy Council Record.
254. The Lord Rankeillor who assisted in giving things this favourable turn was paternal grandfather of Dr John Hope, well known towards the close of the last century as Professor of Botany in the Edinburgh University.
255. Quoted in Scots Magazine, Jan. 1810, ‘from a collection of pamphlets in the possession of Mr Blackwood.’
256. Privy Council Record.
257. The irascible temper of Fletcher is well known, and his slaughter of an associate in the Monmouth expedition is a historical fact. A strange story is told of him in Mrs Calderwood of Polton’s account of her journey in Holland (Coltness Collections). ‘Salton,’ she says, ‘could not endure the smoke of toback, and as he was in a night-scoot [in Holland] the skipper and he fell out about his forbidding him to smoke. Salton, finding he could not hinder him, went up and sat on the ridge of the boat, which bows like an arch. The skipper was so contentious that he followed him, and on whatever side Salton sat, he put his pipe in the check next him, and whiffed in his face. Salton went down several times and brought up stones in his pocket from the ballast, and slipped them into the skipper’s pocket that was next the water, and when he found he had loadened him as much as would sink him, he gives him a shove, so that over he hirsled. The boat went on, and Salton came down among the rest of the passengers, who probably were asleep, and fell asleep among the rest. In a little time, bump came the scoot against the side, on which they all damned the skipper; but, behold, when they called, there was no skipper; which would breed no great amazement in a Dutch company. ’
258. Privy Council Record.
259. Privy Council Record.
260. Privy Council Record.
261. Ibid.
262. Criminal Proceedings, MS. Ant. Soc.
