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The second phase involves actually collecting the gold prices and generating the indicator series on worksheets for analysis. After obtaining a set of gold prices, a computer program was written to generate the indicator series (single exponentially smoothed gold prices) and arrange them alongside the raw gold prices for analysis. The results are shown in Table A. For each year there are seven columns of information. The first column gives the year and the week number. The second column gives the closing price of gold for that week. The third column gives the fast smoothed gold price derived from column 2. The fourth column gives the slow smoothed gold price also derived from column 2. Column 5 is the difference obtained by subtracting column 4 from column 3. Column 6 is the fast smoothed series of the data collected in column 5. Column 7 is the one-week momentum (decimal fraction or ratio of the current period's value divided by the previous period's value) of column 6. Column 8 contains the ratio of column 5 divided by column 4, providing a measure of volatility. Columns 7 and 8 are the series to be tested. This table can either be created by the computer and printed out for visual study, or developed in the computer and held in memory for computerized analysis.

Decision rules

The third phase involves developing a set of decision rules for the indicator series to be tested for their effectiveness in identifying patterns in the gold price series. The decision rules are displayed in Figure 1. Testing and evaluation

In the fourth phase, the indicator and gold series are screened through the decision rules. There are several ways in which testing of the rules can be implemented. The rules can be tested incrementally over several time periods (say ten year intervals or business cycles). They can be tested first over Friday quotations and then retested against quotations for other days of the week. Procedural refinements of this type can be used to reduce the possibility of overfitting the model so that it will not be whipsawed by noise in real-time applications.

The results of the fourth phase are shown in Tables B and C. Table B details the essential characteristics of each trade. Column 1 enumerates each trade chronologically. Column 2 indicates the entry and exit date for each trade. The first item (104, 1861) is January 4, 1861. Column 3 indicates the three kinds of transactions included in the study. Out-of-market transactions were periods where liquid funds were invested in high-quality commercial paper. Column 4 indicates the duration of each transaction in weeks. Column 5 indicates the price of gold on the entry and exit date of each transaction. Performance of other transactions is recorded in columns 6 and 7. The profit or loss of a transaction in the gold market is given as the market return, while the yield of commercial paper over the same period is indicated as COM PAP. Finally, columns 8 and 9 indicate date, number of weeks from entry and magnitude of the maximum temporary loss which one would have had to endure for each transaction.

Table C is a trading performance summary of Table B. The rules developed for gold bullion for the period from 1861 through 1985 resulted in a total of 55 transactions over the 125 years. One-half (27) of the trades were out-of-market trades valued by investing in high grade commercial paper as an alternative to gold. The other 28 transactions consisted of 18 long and 10 short trades in gold. Out-of-market periods predominate because of the long periods with little change in the price of gold from 1879 through 1933 and from 1935 through 1967. As a result, the out-of-market periods account for 86 percent of the 125-year period studied. Investing in commercial paper over these out-of-market time periods results in an average interest income of 4.4 percent per year.