Predicting business cycle regimes using discriminant analysis

Bowden, Dion Eldred (2000-12)

Thesis (MBA)--Stellenbosch University, 2000.

Thesis

ENGLISH ABSTRACT: The assumption underlying this study is that the regime of the economy imparts certain characteristics to the business cycle indicators and that by using a discriminant analysis it would be possible to gain information from the various indicators as to the state of activity in the economy. A discriminant analysis was developed on an Excel spreadsheet. The Schwartz Information Criterion, SIC, was calculated for the models. This value compares how closely the model follows the true data generating process. The discriminant analysis was performed using all the variables or indicators applicable to the model in question. Using a linear programming algorithm the variables were removed from the model in order to maximise the SIC value for the model. The result was a variable set that maximised the information about the regime of the economy available from the various economic indicators. The models' performance was evaluated for post sample performance in a test data set. Five models were developed. They were: • the coincident logistic model; • the one period ahead logistic CLI (composite leading indicator) model; • the one period ahead logistic component model; • the three period ahead logistic CLI model; and • the three period ahead logistic component model. All the models produced meaningful results in the estimation data set for the United States economy. In the test data set only the coincident logistic model was found to give a clear signal of the regime switch. All models applied to the US data showed activity around all the regime switches. Two of the models did not produce useful results when applied to South African economic data. For this reason the one and two period ahead logistic component models were not used. The remaining three models gave clear signals of regime switches for all regime switches in the estimation and the test data set. The best overall model as far as SIC value was the one period ahead logistic CLI model applied to the South African data. The highest SIC for a model applied to the United States data is the logistic coincident model. The models were also evaluated on the number of wrong classifications. The best model in this regard is the coincident logistic model and one period ahead logistic CLI model applied to the United States data. The most accurate model for the South African data was the one-month ahead logistic CLI model in the estimation data set and the logistic coincident model in the test data set. The models were more decisive in the South African data than in the United States data set having a much lower region of uncertainty. Taking into consideration the greater decisiveness in conjunction with accuracy the models performed better with the South African data. The discriminant analysis generates a probability of expansion, which is used in conjunction with a classification rule based on observed frequencies in the estimation data set. A plot of the probability of expansion calculated by the models versus the true data generating process reveals that the models provide meaningful information as to the regime of the economy. The models tend to lag the true data generating process but do show activity around the regime switches. The models when applied to the United States data show good correlation with the true data generating process over the estimation data set but not as good over the test data set. The models perform better when applied to South African data when evaluated graphically. The models when applied to the South African data give good clear signals over all regime switches in all data sets. Indications of regime switches in the estimation data set were clearer than in the test data set. The use of a discriminant analysis for regime classification has been proven to be effective. This method should be used in conjunction with other methods to evaluate business cycle regimes. Useful information is extracted as regards the state of the economy from the various economic indicators. For this reason discriminant analysis of business cycles can be used as an additional tool for the evaluation of business cycle regimes.

AFRIKAANSE OPSOMMING: Die onderliggende aanname van hierdie studie is dat die ekonomiese stelsel sekere eienskappe aan die sakesiklus verleen, en dat 'n diskriminant ontleding dit moontlik maak om inligting te verkry uit die verskeie aanwysers oor die stand van ekonomiese aktiwiteite. 'n Diskriminant ontleding is op 'n Excel-sigblad ontwerp. Die Schwartz Informasie Kriterium (SIK) is vir die modelle bereken. Hierdie waarde dui aan hoe getrou die model die ware datagenereringsproses volg. Die diskriminant ontleding is gedoen deur gebruik te maak van al die veranderlikes of aanwysers wat van toepassing is op die betrokke model. Die veranderlikes is uit die model verwyder deur die gebruik van 'n lineêre programmerings algoritme, ten einde die SIK-waarde van die model te maksimaliseer. Die resultaat was 'n stel veranderlikes wat inligting via die verskeie ekonomiese aanwysers oor die beskikbare ekonomiese stelsel maksimaliseer het. Die model is vir buite-steekproef prestasie in 'n toetsdatastel evalueer. Die volgende vyf modelle is ontwikkel: • samevallende logistiese model • een periode vooruit logistiese saamgestelde leidende aanwysers (SLA)- model • een periode vooruit logistiese komponentmodel • drie periode vooruit logistiese SLA-model • drie periode vooruit logistiese komponentmodel. Al die modelle het betekenisvolle resultate in die steekproefdata vir die ekonomie van die VSA gelewer. In die toetsdatastel het slegs die samevallende logistiese model 'n duidelike aanduiding van regime-verandering gegee. Alle modelle wat op die VSA data toegepas is, het aktiwiteite rondom al die regime-veranderings aangetoon. Twee van die modelle wat op Suid-Afrikaanse data toegepas is, het nie bruikbare resultate opgelewer nie, en om hierdie rede is die een en twee periodes vooruit logistiese komponentmodelle nie gebruik nie. Die oorblywende drie modelle het duidelike aanduidings van regime-veranderings vir alle regime-veranderings aangetoon in die steekproefdata en die toetsdatastel. Die beste oorkoepelende model in terme van SIK-waarde was die een periode vooruit logistiese SLA-model wat op Suid-Afrikaanse data toegepas is. Die grootste SIK-waarde vir 'n model wat op VSA-data toegepas is, is vir die samevallende logistiese model. Modelle is ook evalueer in terme van die foutiewe klassifikasies. Die beste model in hierdie verband is die samevallende logistiese model en die een periode vooruit logistiese SLA-model wat op VSA-data toegepas is. Die mees akkurate model vir Suid-Afrikaanse data was die een maand vooruit logistiese SLA-model in die steekproef datastel en die samevallende logistiese model in die toetsdatastel. Die modelle was meer beslissend in die Suid-Afrikaanse data as in die VSA-datastel, omdat die Suid-Afrikaanse data 'n baie kleiner onsekerheidsgebied openbaar het. Gegewe die groter beslistheid tesame met akkuraatheid, het die modelle beter presteer met Suid-Afrikaanse data. Die diskriminant ontleding skep 'n opswaaiwaarskynlikheid, wat saam met 'n klassifikasiereël, gebaseer op die waargenome frekwensies in die steekproefdata, gebruik word. 'n Stip van die opswaaiwaarskynlikhede, bereken volgens die modelle versus die ware datagenereringsproses, dui daarop dat die modelle betekenisvolle inligting oor die ekonomiese stelsel bied. Die modelle neig om die ware datagenereringsproses te volg, maar toon tog beweging rondom regime-veranderings. Die modelle het goeie korrelasie met die ware datagenereringsproses oor die steekproefdatastel getoon op die VSA-data, maar nie juis goeie korrelasie oor die toetsdatastel nie. Die modelle presteer beter wanneer dit op Suid-Afrikaanse data toegepas word, en gee goeie, duidelike tekens oor alle regime-veranderings in alle datastelle. Aanduidings van regime-veranderings in die steekproefdatastel was duideliker as in die toetsdatastel. 'n Diskriminant ontleding vir stelselklassifikasie het effektief geblyk te wees. Hierdie metode behoort saam met ander metodes gebruik te word om sakesiklusstelsels te evalueer. Nuttige inligting word uit die verskillende ekonomiese aanwysers verkry oor die stand van die ekonomie. Juis om hierdie rede kan 'n diskriminant ontleding van sakesiklusse as bykomende instrument gebruik word om sakesiklusse te evalueer.

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