1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

answering that question is extremely restricted. In the sources citedabove there is in essence only one example of a forecast, see Fig. 5borrowed from Box, Jenkins & Bacon (1967). The continuous brokenline shows the logarithms of the monthly receipts from the sale ofplane tickets during 1949 – 1960. The dotted line is the result of aforecast made from data up to July 1957. The straight lines above andbelow the graph show the result of an experiment consisting insmoothing the yearly extrema by a straight line and forecasting by theeye the future results.This is shown by continuing those two straight lines through August1957 – 1960. The forecast almost coincided with that provided by thethree authors. The extrema corresponded to July or August or to one ofthe winter months (maxima and minima respectively) of each year. Itis impossible to repeat that experiment for other months because thedata on the graph are unreadable and no table of the forecast results isprovided.It is strange that Box & Jenkins (1970) did not show the describedexperiment on their Fig. 9.2 (p. 308). Here, their forecast is essentiallybetter than that made by eye, and it is closer to the actual data.However, the model, its parameters and the interval of prediction, allare the same, so how can we explain the improvement? In general, thecontributions of that school do not pass an attentive analysis.Borrowing an expression from the Russian author Bulgakov, theirstatistics can be called a statistics of a light-weighted type since it ispresented as universally applicable and not demanding statisticalchecks, and it is intended to be generally popular but it does not ensurea reliable result.The general conclusion from all the above is that we should notespecially rely on statistical methods of forecasting. For applying, andrelying on them we should first of all establish whether the studiedphenomenon can be described by a model of stochastic process.Notes1. Moran (see § 3.4) possibly was an exception. O. S.2. The separation of the random from divine design was De Moivre’s main goal,see his Dedication to Newton of the first edition of his Doctrine of Chances reprintedin its third edition. O. S.3. The formal introduction of least squares was due to Legendre. The author’sexample of an artificial object in space certainly had nothing in common with thosetimes. O. S.4. In the sequel, the author applied the three curves of that figure. Their equationsare of the form c 0 + c 1 t 2 + c 2 t 4 . All the other Figures are sufficiently described in themain text. O. S.5. Those magnitudes are frequencies rather than periods. O. S.6. Following a nasty tradition, Venn did not provide an exact reference, and Fisherfollowed suit. Abraham Tucker (1705 – 1774) is remembered for his contribution(1768 – 1778). O. S.7. On the history of the notion of function see Youshkevich (1977). O. S.8. Not clear enough. O. S.9. The author apparently had in mind Karl Pearson’s generally knownshortcomings. Student (Gosset) was also serious, but Kendall did not at all belong tothe Pearson school. O. S.Bibliography83