Grain Prices in Pisa 1548-1818

Cycles in prices and supply of commodities

Grain Prices in Pisa 1548-1818

Postby RayTomes » 03 Aug 2010, 03:10

On the International Institute of Social History site there is a large list of collections of time series of commodity prices at http://www.iisg.nl/hpw/data.php. One of these collections is from Pisa:

Grain prices and prices of olive oil in Pisa, 1548-1818 (monthly averages)
- Author: Paolo Malanima
http://www.iisg.nl/hpw/grainprices.xls

Such long series are valuable for studying cycles and determining periods accurately. From the various grains included I made an index of the 8 grains that had data recorded throughout the time period 1553-1818. The index was calculated as the average of the logs of the prices.

grain8index.png
Index of 8 grain prices in Pisa 1553-1818
grain8index.png (41.5 KiB) Viewed 8345 times


A spectrum of this series was determined.

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Spectrum of Index of 8 grain prices in Pisa 1553-1818
grain8index-spectrum.png (58.24 KiB) Viewed 8345 times


One of the interesting things about this analysis is to see how accurately CATS was able to determine the seasonal cycles. We can expect the seasonal pattern to consist of cycles of periods 12/n months where n=1,2,3,4,5 because with monthly data, only cycles of longer than 2 months can be determined. That means 12, 6, 4, 3, 2.4 months respectively. The cycles actually found have periods very close to that. Assuming that the "real cycles" are exact fractions of the year, then these 5 figures give some idea of how accurately cycles periods can be found. The critical measure is how many cycles there are in the full data period. For an annual cycle there are 265 cycles in the 265 year data period, and for the other seasonal cycles there are multiples of this. CATS determines the best fit cycle to an accuracy of 0.01 cycles. In practice this is more than sufficient.

grain8seasonalcycles.png
Grain seasonal cycles
grain8seasonalcycles.png (4.41 KiB) Viewed 8345 times


It can be seen that the seasonal cycles can be determined to an average accuracy of 0.050 cycles. My experience with looking at such known length cycles is that the typical accuracy is 0.030 to 0.100 cycles. This can be applied in unknown situations to estimate cycle period accuracy by the formula:
period uncertainty = period * 0.050 / (no. of cycles)

Of course the non-seasonal cycles are probably more interesting and deserve looking at some time. And now we know how accurate they are likely to be.
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Re: Grain Prices in Pisa 1548-1818

Postby RayTomes » 01 Sep 2012, 12:14

Of course 634 months cycle is rather strong, which is about 53 years, or the Kondratieff cycle in prices.
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