INTRODUCTION TO TIME-VARYING MODELING WITH MACROECONOMIC AND FINANCIAL DATA

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The dynamics of macroeconomic and financial series has evolved swiftly and asymmetrically since the end of the 1970s, and their statistical properties have also changed over time, suggesting complex relationships between economic and financial variables. The transformations can be explained by considerable changes in householder's behavior, market structures, and economic systems and by the alternation of exogenous shocks and financial crises that have affected the economic cycle, with significant evidence of time variation in the major economic variables. Hence, there is a need for new econometric protocols to take such changes into consideration. The introduction of ARMA (autoregressive moving average models) by Box and Jenkins (1970) led to the development of time-series econometrics, which had a major impact on the conceptual analysis of economic and financial data. This type of modeling offered a transition from a static setup to a new modeling process that reproduces the time-varying features of macroeconomic and financial series. However, the ARMA modeling system retains the constancy of the first and second moments, limits the phases of a cycle to symmetrical instances, and only reproduces the dynamics of stationary variables. It thus fails to adequately reproduce the nonstationary relationships between major economic and financial variables. Abrupt changes in economies and financial systems have given evidence of nonstationary series whose statistical properties are also time-varying, making it necessary to develop new econometric tools to capture the time variation of economic and financial series in the mean and in the variance, and to apprehend their dynamics in the short and long term. Among the most important and influential studies in the 1980s' econometrics literature were therefore those that dealt with the introduction of the ARCH (autoregressive conditional heteroskedasticity) model by Engle (1982) and the cointegration theory by Engle and Granger (1987). The ARCH model, which focuses on the time-varying features of volatility structure, was a major breakthrough, as it highlighted the importance of the second moment of time series, while the cointegration framework enabled the short- and long-term dynamics of nonstationary variables to be modeled.