Regularities in Sequences of Observations

ABSTRACT

The objective of this paper is to propose an adjustment to the three methods of calculating the probability that regularities in a sample data represent a systemic influence in the population data. The method proposed is called data profiling. It consists of calculating vertical and horizontal correlation coefficients in a sample data. The two correlation coefficients indicate the internal dynamic or inter dependency among observation points, and thus add new information. This information is incorporated in the already established methods and the consequence of this integration is that one can conclude with certainty that the probability calculated is indeed a valid indication of systemic influence in the population data.

The objective of this paper is to propose an adjustment to the three methods of calculating the probability that regularities in a sample data represent a systemic influence in the population data. The method proposed is called data profiling. It consists of calculating vertical and horizontal correlation coefficients in a sample data. The two correlation coefficients indicate the internal dynamic or inter dependency among observation points, and thus add new information. This information is incorporated in the already established methods and the consequence of this integration is that one can conclude with certainty that the probability calculated is indeed a valid indication of systemic influence in the population data.

Cite this paper

M. Khoshyaran, "Regularities in Sequences of Observations,"*Open Journal of Statistics*, Vol. 2 No. 4, 2012, pp. 408-414. doi: 10.4236/ojs.2012.24049.

M. Khoshyaran, "Regularities in Sequences of Observations,"

References

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[2] H. W. Clough, “A Statistical Comparison of Meteorological Data with Data of Random Occurrence,” Journal of Monthly Weather Review, Vol. 49, No. 3, 1921, pp. 124-132. doi:10.1175/1520-0493(1921)49<124:ASCOMD>2.0.CO;2

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[4] E. W. Wooland, “On the Mean Variability in Random Series,” Journal of Monthly Weather Review, Vol. 53, No. 3, 1925, pp. 107-111. doi:10.1175/1520-0493(1925)53<107:OTMVIR>2.0.CO;2

[5] H. Working, “A Random Difference Series for Use in the Analysis of Time Series,” Journal of American Statistical Association Quarterly Publication, Vol. 24, 1934, pp. 11- 24. doi:10.1080/01621459.1934.10502683

[6] W. O. Kermack and A. G. McKendrick, “A Measure of Dispersion for Ordered Series,” Journal of the Proceedings of the Royal Society Edinburgh, Vol. 57, 1937, pp. 228-240.

[7] D. Alter, “A Group or Correlation Periodogram with Application to the Rainfall of the British Iles,” Journal of Monthly Weather Review, Vol. 55, No. 210, 1927, pp. 263-266. doi:10.1175/1520-0493(1927)55<263:AGOCPW>2.0.CO;2

[8] C. Chree, “Periodicities Solar and Meteorological,” Journal of the Royal Meteorological Society, Vol. 85, 1924, pp. 87-97.

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[10] E. L. Dodd, “The Probability Law for the Intensity of a Trail Period with Data Subject to the Gaussian Law,” Bulletin of the American Mathematical Association Society, Vol. 33, 1927, pp. 681-684. doi:10.1090/S0002-9904-1927-04451-2

[11] S. Kuznets, “Random Events and Cyclical Oscillations,” Journal of the American Statistical Association, Vol. 24, 1929, pp. 258-275. doi:10.1080/01621459.1929.10503048

[12] R. W. Powell, “Successive Integration as a Method of Finding Long Period Cycles,” Annals of the Mathematical Statistics, Vol. 1, No. 2, 1930, pp. 123-136. doi:10.1214/aoms/1177733127

[13] K. Stumpff, “Grunlagen und Methoden der Periodenforschung,” Springer, Berlin, 1925.

[14] G. T. Walker, “On Periodicity—Criteria for Reality,” Memorandum of the Royal meteorological Society, Vol. 3, No. 25, 1930, pp. 97-101.

[15] C. F. McEwen and E. L. Michel, “The Functional Relation of One Variable to Each of a Number of Correlated Variables Determined by a Method of Successive Approximations to Group Averages,” Proceedings of the American Academy of Arts and Sciences, Vol. 55, No. 8, 1919, pp. 89-133.

[16] C. F. McEwen, “The Minimum Temperature, a Function of the Dew Point and Humidity, at 5 p.m. of the Preceding Day; Method of Determining This Function by Successive Approximations to Group Averages,” Monthly Weather Review Supplement, No. 16, 1920, pp. 64-69.

[17] C. F. McEwen, “The Reality of Regularities Indicated in Sequences of Observations,” Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, San Francisco, 13-18 August 1945, pp. 229-238.

[18] R. A. Fisher, “Statistical Methods for Research Workers,” 4th Edition, Biological Monographs and Manuals, London, 1932.

[19] G. U. Yule and M. G. Kendall, “An Introduction to the Theory of Statistics” 11th Edition, Charles Griffin and Company Ltd., London, 1937.

[20] R. A. Fisher and F. Yates, “Statistical Tables for Biological, Agricultural, and Medical Research,” Oliver and Boyd, London, 1938.

[1] L. Besson, “On the Comparison of Methodological Data with Results of Chance,” Journal of Monthly Weather Review, Vol. 48, 1920, pp. 89-94.

[2] H. W. Clough, “A Statistical Comparison of Meteorological Data with Data of Random Occurrence,” Journal of Monthly Weather Review, Vol. 49, No. 3, 1921, pp. 124-132. doi:10.1175/1520-0493(1921)49<124:ASCOMD>2.0.CO;2

[3] W. L. Crum, “A Measure of Dispersion for Ordered Series,” Journal of American Statistical Association Quarterly Publication, Vol. 17, 1921, pp. 969-975.

[4] E. W. Wooland, “On the Mean Variability in Random Series,” Journal of Monthly Weather Review, Vol. 53, No. 3, 1925, pp. 107-111. doi:10.1175/1520-0493(1925)53<107:OTMVIR>2.0.CO;2

[5] H. Working, “A Random Difference Series for Use in the Analysis of Time Series,” Journal of American Statistical Association Quarterly Publication, Vol. 24, 1934, pp. 11- 24. doi:10.1080/01621459.1934.10502683

[6] W. O. Kermack and A. G. McKendrick, “A Measure of Dispersion for Ordered Series,” Journal of the Proceedings of the Royal Society Edinburgh, Vol. 57, 1937, pp. 228-240.

[7] D. Alter, “A Group or Correlation Periodogram with Application to the Rainfall of the British Iles,” Journal of Monthly Weather Review, Vol. 55, No. 210, 1927, pp. 263-266. doi:10.1175/1520-0493(1927)55<263:AGOCPW>2.0.CO;2

[8] C. Chree, “Periodicities Solar and Meteorological,” Journal of the Royal Meteorological Society, Vol. 85, 1924, pp. 87-97.

[9] J. B. Cox, “Periodic Fluctuations of Rainfall in Hawaii” Proceedings of the American Society of Civil Engineers, Vol. 87, 1924, pp. 461-491.

[10] E. L. Dodd, “The Probability Law for the Intensity of a Trail Period with Data Subject to the Gaussian Law,” Bulletin of the American Mathematical Association Society, Vol. 33, 1927, pp. 681-684. doi:10.1090/S0002-9904-1927-04451-2

[11] S. Kuznets, “Random Events and Cyclical Oscillations,” Journal of the American Statistical Association, Vol. 24, 1929, pp. 258-275. doi:10.1080/01621459.1929.10503048

[12] R. W. Powell, “Successive Integration as a Method of Finding Long Period Cycles,” Annals of the Mathematical Statistics, Vol. 1, No. 2, 1930, pp. 123-136. doi:10.1214/aoms/1177733127

[13] K. Stumpff, “Grunlagen und Methoden der Periodenforschung,” Springer, Berlin, 1925.

[14] G. T. Walker, “On Periodicity—Criteria for Reality,” Memorandum of the Royal meteorological Society, Vol. 3, No. 25, 1930, pp. 97-101.

[15] C. F. McEwen and E. L. Michel, “The Functional Relation of One Variable to Each of a Number of Correlated Variables Determined by a Method of Successive Approximations to Group Averages,” Proceedings of the American Academy of Arts and Sciences, Vol. 55, No. 8, 1919, pp. 89-133.

[16] C. F. McEwen, “The Minimum Temperature, a Function of the Dew Point and Humidity, at 5 p.m. of the Preceding Day; Method of Determining This Function by Successive Approximations to Group Averages,” Monthly Weather Review Supplement, No. 16, 1920, pp. 64-69.

[17] C. F. McEwen, “The Reality of Regularities Indicated in Sequences of Observations,” Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, San Francisco, 13-18 August 1945, pp. 229-238.

[18] R. A. Fisher, “Statistical Methods for Research Workers,” 4th Edition, Biological Monographs and Manuals, London, 1932.

[19] G. U. Yule and M. G. Kendall, “An Introduction to the Theory of Statistics” 11th Edition, Charles Griffin and Company Ltd., London, 1937.

[20] R. A. Fisher and F. Yates, “Statistical Tables for Biological, Agricultural, and Medical Research,” Oliver and Boyd, London, 1938.