Oscillatory Movements in English Agriculture

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Abstract
This article contains analyses of time series of data pertaining to the yield, acreage and price of wheat, barley, oats, potatoes, and the numbers of pigs, cows, sheep, and horses from about 1871 to 1937. Trends were removed from the data by use of 9-yr. moving averages. Correlograms were used to determine the periods of each series. Correlograms are obtained by plotting the correlations coeff. [image] against the value k. These plots suggest real periods for these time series. Comparison is made of the Fourier analysis and the autoregression system. The autoregression system depends upon a difference equation of the form, ut +2 + aut +1 + but + [image]t = 0, where e is a random variable, and a and b are constants found by the method of least squares. A 2d autoregression equation is used in which a and b are quadratic function of t, the time. There is very little difference between these 2 equations. Interactions are calculated by-use of log correlations. The results of this inquiry may be summarized as: "1. The short-term movements in English agricultural time series can be explained as damped oscillations continually regenerated by external impulses. 2. The various series are inter-correlated, and some at least are probably inter-related. 3. No systematic effects were detected in the yields per acre of potatoes, and it is very doubtful whether significance can be attached to a small four-year period in cereal yields. 4. There are systemic effects in the cereal prices and in acreages and livestock numbers. 5. Different products have, in general, different mean periods. 6. Although, from the interactions of the series and the general complexity of the agricultural situation it is difficult to isolate elements of individual series for separate study, it appears that most of the series can be represented by a simple autoregressive scheme with a disturbance function which may be random and a superposed element which may or may not be random.".

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