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Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted for by the heavy-tailed distribution of interevent times, i.e., the time interval between two consecutive events. Yet, little is known about how correlations between consecutive interevent times systematically affect the decaying behavior of the autocorrelation function. Empirical distributions of the burst size, which is the number of events in a cluster of events occurring in a short time window, often show heavy tails, implying that arbitrarily many consecutive interevent times may be correlated with each other. In the present study, we propose a model for generating a time series with arbitrary functional forms of interevent time and burst size distributions. Then, we analytically derive the autocorrelation function for the model time series. In particular, by assuming that the interevent time and burst size are power-law distributed, we derive scaling relations between power-law exponents of the autocorrelation function decay, interevent time distribution, and burst size distribution. These analytical results are confirmed by numerical simulations. Our approach helps to rigorously and analytically understand the effects of correlations between arbitrarily many consecutive interevent times on the decaying behavior of the autocorrelation function.
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Skewed Opportunities: How the Distribution of Entrepreneurial Inputs and Outcomes Reconceptualizes a Research Domain
Over the last four decades, Academy of Management Review has devoted a great deal of attention to the scholarly debate about the theoretical nature of entrepreneurs, entrepreneurship, and entrepreneurial opportunities. Most recently, an entire Dialogue section of the journal was devoted to four articles that provided alternative ontological, epistemological, and philosophical views of “opportunity.” Inasmuch as the domain appreciates the effort to advance entrepreneurship theory, these arguments appear to constitute what past AMR editor-in-chief, Roy Suddaby, termed “fetishism,” where “theory becomes an exercise in writing and interpretation but is detached from the empirical world” (2014: 408). That reality was demonstrated in the Crawford, Aguinis, Lichtenstein, Davidsson, & McKelvey (2015) study, which discovered highly skewed power law distributions in all of the domain’s theoretically relevant input variables and all generalizable outcome measures. The significant number of outliers in these distributions provide necessary and sufficient cause for a paradigm shift in the domain. In response, this paper uses the empirical reality of power law distributed phenomena for 1) developing historical and empirical justification for the difficulties in building theory about opportunities and entrepreneurship, 2) identifying how the seemingly antithetical perspectives of discovery and creation theories can be synthesized, and 3) proposing a generalizable framework—of Endowments, Expectations, Engagement, and Environments—around which new entrepreneurship theory can be developed.
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- PAR ID:
- 10058144
- Date Published:
- Journal Name:
- Proceedings - Academy of Management
- ISSN:
- 0065-0668
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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