The Statistical Analysis of the Sunspot and Lynx Cycles

The regularity and stability of the 'ten-year' lynx cycle in Canada, as revealed in the numbers trapped by the Hudson Bay Company (Elton & Nicholson, I942) naturally raised the question of it being in some way causally connected with the sunspot cycle. This question has been answered in the negative (Elton & Nicholson, I942; MacLulich, I937) and as appears from a careful examination of the figures, rightly so. However, in view of the extremely interesting nature of these two series it may be worth while to set out here the criteria by which such a question must be decided, particularly in view of the fact that the correct application of statistical theory to such a problem is not at all widely understood. In Fig. i, I have graphed Wolfer's sunspot numbers from I820 to I934 and the common logarithms of the numbers of lynx caught in the Mackenzie River district of the Northern Department of the Hudson Bay Company (or its equivalent modern area). The sunspot numbers were taken from Yule (I927) for the period I820-I924 and from the Monthly Weather Review for I925-34. The lynx numbers were taken from Elton & Nicholson (I942) and the Mackenzie River district values were chosen because they gave an uninterrupted sequence from I820 to I934, and because taking the values for a single district results in a greater regularity in the cycle. Because of the extremely large values at each peak the common logarithm was taken in order to stabilize the oscillations. The ordinary correlation coefficient between these two series,