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RBA Glossary definition for business cycle

business cycle – The period between peaks or troughs of macroeconomic activity.

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Statistical Approaches

31 Dec 2004 RDP 2004-09
David Norman and Thomas Walker
RDP 2004-09: Co-Movement of Australian State Business Cycles 3. Statistical Approaches. ... where S. jt. represents the business cycle phase of state j at time t (1 represents expansion, 0 contraction).
https://www.rba.gov.au/publications/rdp/2004/2004-09/statistical-approaches.html

Previous Research and Data Issues

31 Dec 2004 RDP 2004-09
David Norman and Thomas Walker
RDP 2004-09: Co-Movement of Australian State Business Cycles 2. Previous Research and Data Issues. ... assessing business cycle synchronicity.
https://www.rba.gov.au/publications/rdp/2004/2004-09/previous-research-and-data-issues.html

An Unobserved Components Model

31 Dec 2004 RDP 2004-09
David Norman and Thomas Walker
RDP 2004-09: Co-Movement of Australian State Business Cycles 4. An Unobserved Components Model. ... This compromise is consistent with Burns and Mitchell's (1946) definition of business cycles as patterns observed across a range of economic data, and
https://www.rba.gov.au/publications/rdp/2004/2004-09/an-unobserved-components-model.html