Estimating the probability of forecasted events


  • Alexander Madera National Research University Higher School of Economics





Events, Eigenvector, Eigenvalue, Forecast, Probability.


The article elaborates a method for estimating the probabilities of occurrence of prognosticated events in future. On the basis of the data from the previous periods about prognosticating the relevant events, as well as the data about the trends observed at present, two matrices are formed, the product of which is the matrix for the prognosis errors committed by the individual or the expert. The article shows that the vector for probabilities of the prognosticated events is the eigenvector of the prognosis error matrix, which corresponds to its single eigenvalue. Application of the elaborated method is shown on the definite example for forecasting demand of new products.


[1] Armstrong JS, ed. (2001) Principles of Forecasting: A Handbook for Researchers and Practitioners, Kluwer.

[2] Bellman R (1960) Introduction to Matrix Analysis, McGraw-Hill Book Company Inc.

[3] Boer P.T, Ecuyer P, Rubino G, Tuffin B. Estimating the probability of a rare event over a finnite time horizon (2007). Proceedings of the 2007 Winter Simulation Conference 403-411.

[4] Clauset A, Woodard R (2013) Estimating the histirical and future probabilities of the large terrorist events. The Annals of Applied Statistics 7, 1838-1865.

[5] Clemen R (1989) Combining Forecast. International Journal of Forecasting 5, 559-583.

[6] Green WH (2012) Econometric Analysis. Pearson, Boston.

[7] Haan L, Sinha AK (1999) Estimating the probability of a rare event. The Annals of Statistics 27, 732-759.

[8] Hanke JE, Reitsch AG, Wichern DW (2001) Business Forecasting. Prentice Hall Inc., N.J.

[9] Horn RA, Johnson CR (2013) Matrix Analysis. Cambridge University Press, N.Y.

[10] Kahneman D, Slovic P, Tversky A (2001) Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge.

[11] Madera AG (2014 a) Risks and Chances: Uncertainty, Forecasting and Evaluation. Krasand, Moscow.

[12] Madera AG (2014 b) Interval stochastic uncertainty of estimates in multiple criteria decision making problems. Artificial Intelligence and Decision Making 3, 105-115.

[13] Madera AG (2015) Interval Uncertainty of estimates and judgments of subject in decision making in multi-criteria problems. International Journal of the Analytic Hierarchy Process 7, 337-348.

[14] Makridakis S. (1986) the art and science of forecasting. International Journal of Forecasting 2, 15-39.

[15] Mantegna RN, Stanley HE (2000) an Introduction to Econophysics. Correlations and Complexity in Finance. Cambridge University Press, Cambridge.

[16] McNees SK (1990) the role of judgment in macroeconomic forecasting accuracy. International Journal of Forecasting 6, 287-299.

[17] Mirkin J ed (2014) International Practice of Forecasting World Prices in the Financial Markets (Raw Materials, Stocks, Exchange Rates). Magistr, Moscow.

[18] Mohler G (2013) Discussion of “Estimating the historical and future probabilities of the large terrorist events†by Aaron Clauset and Ryan Woodard. The Annals of Applied Statistics 7, 1866–1870.

[19] Riley P (2012) on the probability of occurrence of extreme space weather events. Space Weather 10, 12 p.

[20] Rossi E (2010) Univariate GARCH models: A Survey. Quantile 8, 1-67.

View Full Article: