We first present a Complex Singular Value Decomposition (CSVD) analysis of credit cyle and explore the lead-lag relation betweencredit cycle and business cycle, then propose a GeneralizedLinear Model (GLM) of credit rating transition probabilitiesunder the impact of business conditions.To detect the cyclic trend existence of credit condition in U.S.economy, all credit variables and business variables aretransformed to complex values and the transformed data matrix isapproximated by first order of CSVD analysis. We show that theeconomy, represented by both credit conditions and businessconditions, is changing recurrently but with different frequenciesfor different time periods. Credit variables making the greatestlinear contribution to first Principal Component can be identifiedas credit cycle indicators. The result of leading businessvariables to credit variables in an economy provides the basis topredict credit condition by business cycle indicators.The credit rating system is a publicly available measure of theriskiness of financial securities and a rating transition matrixquantifies the risk, by permitting calculation of the probabilityof downgrade or default. Credit migration is observed to beinfluenced both by business conditions and by an issuer's owncredit status. We assume the rating history for a particularinstitution is Markovian, and histories for differentinstitutions are assumed to be statistically independent, in bothcases the history of market conditions are known. With a simpleGLM, we investigate the significance of business conditions andtheir two major impacts - creditworthinessdeterioration/improvement and credit stability. We propose amodel of transition probability in discrete time and a model of instantaneous transition rates in continuous time, and fit themby maximum likelihood. Business conditions are shown to have asignificant effect: higher likelihood for credit qualityimprovement and stability under good business conditions whilehigher likelihood for credit quality deterioration and driftunder severe business conditions. The two business impacts aresignificant and business deterioration/improvement impact isgreater than its stability impact on credit rating transitions.Investment-grade rating transitions are more sensitive to longrate risk while speculative-grade rating transitions are moresensitive to short rate risk. Compared to a discrete model, thecontinuous transition model has much greater over-dispersion butis more practical.