Let yt be the log-of GDP. We are interested in identifying the dates of peaks and trough. The definition used here is a simplified version of the Bry and Boshan dating algorithm. Research has shown that when applied to historical data the algorithm identifies roughly the same dates of the NBER dating committee, see Harding and Pagan,
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A Comparison of the Real-Time Performance of Business Cycle Dating Methods
The Leap Blog: Dating the Indian business cycle
A new strategy for dating the business cycle turning points, both in the classical and the deviation sense, is presented. After reviewing the available solutions, and in particular the popular Bry and Boschan routine, the role of filtering operations in the preliminary identification of candidate turning points is discussed. Low-pass filters are employed to reduce the amplitude of those fluctuations with period less than the minimum cycle duration. Secondly, the alternation of phases and minimum duration ties are enforced by a dating algorithm based on a Markov chain. Final turning points are identified on the original series by a constrained search around the preliminary points. Dating the deviation cycle poses similar problems, but it requires band pass filters or cyclical models.
BRYBOSCHAN: RATS procedure to implement Bry-Boschan business cycle dating
This paper discusses formal quantitative algorithms that can be used to identify business cycle turning points. An intuitive, graphical derivation of these algorithms is presented along with a description of how they can be implemented making very minimal distributional assumptions. We also provide the intuition and detailed description of these algorithms for both simple parametric univariate inference as well as latent-variable multiple-indicator inference using a state-space Markov-switching approach. We illustrate the promise of this approach by reconstructing the inferences that would have been generated if parameters had to be estimated and inferences drawn based on data as they were originally released at each historical date. Waiting until one extra quarter of GDP growth is reported or one extra month of the monthly indicators released before making a call of a business cycle turning point helps reduce the risk of misclassification.
To identify freight industry expansions and recessions, our goal was to replicate as closely as possible common approaches used to identify the business cycle for the broader economy. There is no universally accepted definition of a recession. In practice, recessions can be approximated as two consecutive quarters of declining real output Gross Domestic Product. The challenge for us, then, was to create a metric that approximates real GDP, but for the freight industry.