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45 Effects of a Few Volatile Years All seasonal calculations can be distorted by a few very volatile years that show large percentage price changes, especially during a time when there is not normally a strong seasonal bias. For example, if heating oil prices were stable for four years, or tended slightly lower, then jump 100°o in one unusual period, the result of an OPEC announcement coupled with low inventories, the average will show a seasonal increase of 20° o. In fact, that is what hsppens in many markets in which one or two unrelated events cause a price change that can be interpreted as seasonal. In a computerized environment, the use of the median (discussed above) or more data can prevent mistakes: however, common sense will also show that a single odd year will erroneously distort the average. Yearly Averages The most basic way of measuring or describing seasonality is by the monthly variation From the yearly average or crop average (for agricultural products), usually calculated as a ratio or percentage. The results of this technique using the 1975 com prices can be seen in Table 7-2. During this one year, the highest prices occur in January and August and the lowest at the end of the year after harvest, confirming what we might expect of the com season, with the exception of the January high. The average price for 1975 was 2.92, and the extent of variation throughout the year ranges, coincidentally, 13.7°o above and below the average. By sppljing this method to the 20 years of data for com shown in Table 7-3, the percentage variation can be shown in the corresponding Table 7-4. For those who prefer using negative percentages to show when values are below the average, simply subtract 100 from each number. The long-term seasonality, called the seasonal adjustment factor, is the monthly average of the percentages shown in Table 7-4 and sppears at the bottom of Table 7-4 and in Figure 7-1. These values must be divided by 100 before they can be correctly used as percentages, in both cases, the analjsis has been separated into the two periods. 1956-1970 and 1971-1975, to indicate the changing volatility and slight change in pattern. The shaded area in Figure 7-1 represents the range in the percentage variation for the 1956-1970 period, and the broken lines show the corresponding 1971-1975 results. Figure 7-1 shows that the fraditional seasonality can also have sha fluctuations, reduced to intervals of short duration. The more recent period reflects the fraditional seasonal highs and lows, but shows that there is a considerable wide range of other possibilities. All methods of determining seasonality will be influenced by those years in which unusual, overwhelming factors caused prices to move counter to normal s pattems. A later section will discuss the advantages of distinguishing seasonal and nonseasonal years. TABLE 7-2 Percentage Monthl/ Com Prices to the Average | | | | | | | | Price" | 2.70 | 3.07 | 2.86 | 2.67 | 2.68 | 2.66 | | Percent | 100.0 | 113.7 | 105.9 | 98.9 | 99.2 | 98.5 | | | | | | | | | | Price | | | 2.95 | 2.76 | 2.62 | 2.33 | | Percent | | 1007 | 109.2 | 102.2 | 97.0 | 86.3 | |
•MIdmonih US. farm pricc.i 97S.
Jur, Jul Aug sgp i 60 .03 (972 rlne- . ..h from 1 12 ears In the analysis for iri<.>"nll ˆjf < - n This formula may be spplied to weekly or quarterly average prices by changing the 12 to 52 or 4, respectively. The use of an annual average price can bias a clear seasonal pattem because of its inability to account for a long-term trend in the price of the commodity. If the rate of inflation in the United States is 6°o, there will be a tendency for each month to be l/2>o higher, resulting in a trend toward higher prices at the end of the year. Longer trends, such as the steadjrise in grain prices from 19721975, followed by a longer decline in the 1980s, will obscure or even distort the seasonality unless the frend is removed.
TABLE 7-4 Corn Price as Percentage Average (Annual) Veor | | | | | | | | | | | | | | 1956 | 1.30 | 87.6 | 89.2 | 91.5 | 1015 | 108.5 | 110.8 | 1115 | 1123 | III.S | 86 1 | 93.8 | 94 6 | 1957 | 1.25 | 97.6 | 92.6 | 94.4 | 94.4 | 96.0 | 96.0 | 96.8 | | | | 75 4 | 80.8 | 1958 | I.IO | 88.2 | | 94.5 | 107.3 | 109 1 | lll£ | II 1.8 | 112.7 | 88.5 | 92.7 | 85.4 | 94.5 | 1959 | 1.09 | | 97.2 | 99 1 | 107 3 | 108 2 | 109.2 | 107.3 | 107 3 | 100.0 | 88.1 | | 90.1 | I960 | 1.03 | 100.0 | 101.0 | 101.0 | 105.8 | 107 8 | 107.8 | 107.8 | 105.8 | 103 9 | 94.2 | | 89.3 | 1961 | | 98.0 | 102.0 | 103.0 | 97.0 | 103.0 | I03.O | 104.9 | 103.0 | 1010 | 99 0 | 90 1 | 93.1 | 1962 | | 95.9 | 96.9 | 97.9 | 100.0 | 105.1 | 105.1 | 104 1 | 103 1 | 102 0 | 95 9 | 92.8 | 102.0 | 1963 | l.ll | 92.8 | | 95.5 | 98.2 | 1010 | 107.2 | 109.0 | 1090 | 110.8 | | 91.9 | | 1964 | 1.13 | 99.1 | | 100.0 | 101.8 | 104.4 | 103.5 | 1009 | 100.9 | 103.5 | 92,9 | 92X1 | 1009 | 1965 | i.ie | 98.3 | 99.1 | 100.8 | 103.4 | 105 9 | 106.8 | 1051 | 101 7 | 1000 | 93 2 | | 95.8 | 1966 | 1.25 | 95.2 | 96.0 | | 95.2 | 96.8 | 96.0 | 101.6 | 107.2 | 108.0 | 1032 | 1008 | 103.2 | 1967 | 1.17 | 109.4 | 107 7 | 109.4 | 1077 | 106.8 | 1077 | 103.4 | 94.9 | | 88.9 | 82.9 | 88.0 | 1968 | 1.04 | 100.0 | 101.9 | 1019 | 1019 | 104 8 | 102.9 | 1000 | 95 2 | | 92,3 | 1000 | 1010 | 1969 | 1.12 | 96.4 | 97.3 | 97.3 | 1000 | 106.2 | 105.3 | 96.4 | 105 3 | 102 7 | 1000 | 95.5 | 97 3 | 1970 | | 90 3 | 91.9 | 91 1 | 92.7 | 95.2 | 97.6 | 1000 | 102.4 | 1113 | 108.1 | 1040 | 112 1 | 1956-1970 | Av£ | 96.3 | 96.9 | 98.1 | 100.9 | 103.9 | 1047 | 104.0 | 103.9 | 101.5 | 94.3 | | | 1971 | 1.27 | II 1.8 | 112.6 | 112.6 | II 1.0 | 108.7 | 112* | 107.1 | 93 7 | 87.4 | | | 85.0 | 1972 | 1.17 | 93.2 | | 94.0 | | 98.3 | 96.6 | | 98.3 | 1043 | 1017 | 1026 | 1214 | 1973 | | 74 7 | 72.6 | 73 6 | 76.3 | 62.4 | 107.0 | 1091 | 144.1 | 1156 | 1167 | 1172 | 1285 | 1974 | 2,92 | | 94.5 | 91.8 | 82.5 | 83.9 | 88.0 | | 1154 | 113.0 | 118-1 | 1137 | 112,0 | 1975 | 2.70 | | 105.9 | 98.9 | 99.2 | 98.5 | 99 2 | 1007 | 109.2 | 102,2 | 97 0 | 86.3 | 87.8 | 1971-1975 | | 96.4 | 95.8 | 94.2 | 93 1 | 90.1 | 100 7 | 102.8 | 1121 | 104.5 | 1024 | 99 2 | 106.9 |
Removing tlie Trend Jake Bernstein, most well known for his seasonal studies,2 uses the method of first differences to remove the trend from prices before calculating the seasonal adjustment factor. He offers the following steps for determinine the cadi price seasonality: 1. Arrange the data used in a table with each row as one year. Columns can be daily, weekly, or monthly, although most analj-ses will use monthly. Average prices are preferred for each period (see Table 7-1). 2. Compute a second table of month-to-month differences by subfracting month 1 from month 2, month 2 from month 3, and so on. This new table contains detrended values. 3. Calculate the sum of the price differences in each column (month) in the new table. Find the average for thai column by dividing the number of years of data (columns may have different numbers of enfries). This is the average price change for that month. 4. From the table, count the times during each month (column) that prices were up. down, or unchanged. This will give the frequency (expressed as a percent) of movement in each direction. Bernstein adds the average monthly changes together, expresses the frequency of upward price changes, and presents the results of com in Figure 7-2. - :6B«l»in.5.eO««l:.„ceft.-mFutureETraW(J..hii4uley&SonE NewY.dc 1S9« FIGURE 7-1 Changes in volatility and variations in seasonal pattems for corn.
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