The evolution of the PPI of copper ores

Since 2008, we have been reporting that the evolution of various components of CPI and PPI in the United States is not a random process but rather a predetermined one with long-term sustainable trends [1, 2]. Using these trends, one can predict consumer and producer price indices for various goods, services and commodities.  For example, in [3, 4], we presented the evolution many goods and services with varying weight in the CPI. But there are more goods, services, and commodities of interest for producers, consumers, and investors. Here we revisit the index for copper ores. This is an example showing that some commodity prices are not well predictable.

 

Figure 1 displays the difference between PPI and the index for copper ores since 1988. This difference has a remarkable history: no big change between 1988 and 2003, and then a sudden surge in the copper index started. The peak was reached in the middle of 2006. It survived before the second quarter of 2008. Then the copper index dropped by almost 300 units back to the PPI level. In 2010, the index increased above 500.  One may consider these changes as associated with the rise-fall cycles in oil price. We have to admit that there is no sustainable trend in the copper index and the future of the copper ores index. Currently, the difference is right in the middle between the previous peak and trough. It may go any direction in 2013. I would refrain from buying/selling any paper related to this commodity before the next clear sign of the future evolution. My best guess is the surge in price in the first half of 2013 and a steep fall in the fourth quarter of 2013.   

Figure 1. Evolution of the price index of copper ores relative to the PPI.

In a year, the rate of unemployment may fall below 6%

A month ago, we discussed the rate of unemployment in the US and published our forecast for 2013. Two months ago, we predicted an extended unemployment fall period down to the level of 6.2% in the third quarter of 2013. This prediction was made after we accurately forecasted (on March 1, 2012) the rate of unemployment in the US to fall down to 7.8% by the end of 2012. First time in 2012, the BLS announced 7.8% in September and the rate for November is 7.7%.  One may expect a lower figure in December 2012. Here we update our model and estimate that the rate of unemployment in the fourth quarter of 2013 may fall below 6%.

In 2006, we developed three individual empirical relationships between the rate of unemployment, u(t), price inflation, p(t), and the change rate of labour force, LF(t), in the United States. We also revealed a general relationship balancing all three variables. Since measurement (including definition) errors in all three variables are independent it may so happen that they cancel each other (destructive interference) and the general relationship might have better statistical properties than the individual ones. For the USA, the best fit model for annual estimates was a follows:

u(t) = p(t-2.5) + 2.5dLF(t-5)/dtLF(t-5) + 0.0585 (1)

where inflation (CPI) leads unemployment by 2.5 years (30 months) and the change in labor force leads by 5 years (60 months). We have already posted on the performance of this model several times.

For the model in this post, we use monthly estimates of the headline CPI, u, and labor force, all reported by the US Bureau of Labor Statistics. The time lags are the same as in (1) but coefficients are different since we use month to month-a-year-ago rates of growth. We have also allowed for changing inflation coefficient. The best fit models for the period after 1978 are as follows:

u(t) = 0.63p(t-2.5) + 2.0dLF(t-5)/dtLF(t-5) + 0.07; between 1978 and 2003

u(t) = 0.90p(t-2.5) + 4.0dLF(t-5)/dtLF(t-5) + 0.30; after 2003

There is a structural break in 2003 which is needed to fit the predictions and observations in Figure 1. Due to strong fluctuations in monthly estimates of labor force and CPI we smoothed the predicted curve with MA(24).

The structural break in 2003 may be associated with the change of sensitivity of the rate of unemployment to the change of inflation and labor force. Alternatively, definitions of all three (or two) variables were revised around 2003, which is the year when new population controls were introduced by the BLS. The Census Bureau also reports major revisions to the Current Population Survey, where the estimates of labor force and unemployment are taken from. Therefore, the reason behind the change in coefficients night be of artificial character - the change in measuring units.

On March 1, 2012 the monthly model predicted a drop from 8.3% in February to 7.8% by the end of 2012. Figure 1 depicts the original prediction (upper panel) and the observed fall in the rate of unemployment (lower panel). Figure 2 shows that the observed and predicted time series are well correlated (R²=0.82). This is a good statistical support to the model.

Figure 3 depicts the predicted rate of unemployment for the next 12 months. The model shows that the rate will fall to 5.8% by November 2013 and even lower in the fourth quarter of 2013. For 107 observations since 2003, the modelling error is 0.4% with the precision of unemployment rate measurement of 0.2% (Census Bureau estimates in Technical Paper 66). Hence, one may expect 5.8% [±0.4%].

Figure 1. Observed and predicted rate of unemployment in the USA as obtained in April and November 2012.

 

Figure 2.  Observed vs. predicted rate of unemployment between 1967 and 2012. The coefficient of determination   Rsq=0.82.

 

Figures 3. The predicted rate of unemployment. We expect the rate to fall down to 5.8% in November 2013.

International Data Centre: Reviewed Event Bulletin vs. Waveform Cross Correlation Bulletin

We have published a preprint on arxiv.org. A PDF copy is available:

International Data Centre: Reviewed Event Bulletin vs. Waveform Cross Correlation Bulletin

 

Abstract: Our objective is to assess the performance of waveform cross-correlation technique, as applied to automatic and interactive processing of the aftershock sequence of the 2012 Sumatera earthquake relative to the Reviewed Event Bulletin (REB) issued by the International Data Centre. The REB includes 1200 aftershocks between April 11 and May 25 with body wave magnitudes from 3.05 to 6.19. To automatically recover the sequence, we selected sixteen aftershocks with mb between 4.5 and 5.0. These events evenly but sparsely cover the area of the most intensive aftershock activity as recorded during the first two days after the main shock. In our study, waveform templates from only seven IMS array stations with the largest SNRs estimated for the signals from the main shock were used to calculate cross-correlation coefficients over the entire period of 44 days. Approximately 1000000 detections obtained using cross-correlation were then used to build events according to the IDC definition. After conflict resolution between events with similar arrivals built by more than one master all qualified event hypotheses populated the automatic cross-correlation Standard Event List (aXSEL). The total number of distinct hypotheses was 2763. To evaluate the quality of new events in the aXSEL, we randomly selected a small portion of XSEL events and analysts reviewed them according to standard IDC rules and guidelines. After the interactive review of a small portion of the final product of cross correlation was obtained which we call the interactive XSEL. We have constructed relevant frequency and probability density distributions for all detections, all associated detection and for those which were associated with the aXSEL and final XSEL events. These distributions are also station and master dependent

S&P 500 in December 2012

In March 2012, we first published a graph which showed that the S&P 500 index would have a local fall in May 2012 to the level 1300.  In a few sessions, we bought S&P 500 index in May/June 2012 at the level 1287 to 1322.  The initial idea was to sell by the end of 2013 at 1525 and get a 12% to 14% return. In September, the S&P was at 1450, which was far above the expected level, and we decided to sell and wait a negative correction to 1350 to 1375 to re-enter the index. Selling at ~1360, we obtained an approximately 10% return in September.  In October, the S&P 500 fell to 1350 as had been predicted in September and we re-entered in two sessions at 1348 and 1355. By the end of November the S&P 500 regained 4.5% (1416). Now we expect the index to rise to 1430 to 1450 in December 2012. This will be the best time to sell before the next negative correction in the beginning of 2013. We will buy the S&P 500 at 1400 in 2013 and obtain another 10% return selling at 1550 in October 2013.

Below we present the evolution of the S&P 500 and the step-by-step assumptions illustrating the decisions we have made since March 2012.

Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007.  There are two deep troughs in 2002 and 2009 which are marked by red and green lines.  For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious – in the long run the stock market depends on the overall economic growth.

Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line).  When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360).  The black curve returned to the blue one in August/September 2011. From December 2011, we observed a middle-size deviation of about 100 units.

Figure 1. The evolution of the S&P 500 market index between 1980 and 2012.

In April 2012, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. Figure 2 shows the predicted behavior in April and May 2012, with the predicted segment shown by red line. We expected that the path observed in the previous rally would be repeated with the bottom points coinciding.  When this prediction realized, we invested at the average price 1320. In May 2012,the expected exit level was 1500 in October 2013.

Figure 2. The original S&P 500 curve (black line) and that shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in March to 1300 in May.

Figure 3 shows the evolution of the S&P 500 monthly closing price between May and August 2012. The S&P 500 closing level for August was 1430 and reached 1469 in the middle of September. This level provided a ten percent return over approximately 4 months. One can see that the observed level was far above the expected level (blue line). The return and the deviation from the expected level both made us think that this was the best time to exit. We sold the index on September 21 (1460) anticipating strong turbulence (economic, financial, and political) and an overall fall to 1375 at a few month horizon.   

Figure 3. Same as in Figure 2 with an extension between May and August.

Figure 4 shows the evolution of the S&P 500 monthly closing price in September-November 2012. The October’s closing level was 1411. On October 26 , we put the November’s level down to 1375. One can see that the red line intersects the blue curve. The previous history of the black and red lines intersection with the blue one made us think that the time to enter the market (S&P 500 index) was approaching. We expected to buy at 1350 to 1375.  

Figure 4. Same as in Figure 2 with an extension between September and November 2012.  

Finally, Figure 5 depicts the current (December 3) state of the S&P 500.  The index had a local minimum of 1347 in the middle of November and recovered to 1416 on November 30. This is 25 points less than the expected level of 1440 in December 2012. The red line intersects the blue one in January 2013 and then a negative correction to 1400 (or less) is expected again. We will not wait before this fall and are going to sell at the earliest opportunity between 1430 and 1450 accruing another 5% to 6% since October. We still have in view to buy the S&P 500 at 1400 in 2013 and obtain another 10% return selling at 1550 in October 2013, as the blue line implies.

Figure 5. Same as in Figure 4 with an extension into December 2012.