Greetings from France! I thought it would be interesting to look at the relation between the price of gold in euros vs the euro itself. I have attached a graph of this from Stockcharts. Starting in Jan 2009 until April 2009 the two go in opposite directions. Then from April 2009 up to Jan 2010 they more or less run parallel. After Jan 2010, they diverge dramatically, showing that during that period they were inversely correlated. So at this point, it is the euro and not the dollar that is a foil to gold.
This may seem a little out of the mainstream, but not really. On visiting the website of Fabius Maximus, who writes about geopolitics, including economics and is one of the more interesting websites around(http://tinyurl.com/yanpvxv), I came across an article on "polywell" fusion. This is "hot" fusion--not the "cold" fusion of Pons and Fleischer--and has already gone through several prototype trials and shown that it is a feasible, low-cost approach to nuclear fusion that could be commercialized within possibly as little as five years. It is an alternative to the tokamut reactor design which, though it has been proven to work, is extremely expensive and would take a minimum of 30 years to implement. As you know already, nuclear fusion is _clean_ energy that leaves behind no radiactive or toxic waste. The company engaged in this research and development is called EMC^2. In the following paper, which is a PDF file that you must download to read, they show that this reactor design represents the end of fossil fuels and could represent free energy for all of humanity for the indefinite future if they use deuterium and tritium for the fuel. It is a small reactor and the company needs to raise $200M to bring it to the threshold of commercialization. A piddling sum, but our all-wise government has cut funding of speculative projects such as this that have long-term potential. Instead the govenment feels that their scarce monetary reserves should be thrown at TBTS banks, to the tune of trillions of dollars. This paper is a fascinating read and I think you will agree that this is the direction we should be taking. Perhaps the Chinese-or who knows, maybe even the Indonesians- have already gotten started on this as we here in the US watch our middle class go down. Sorry for the diatribe, but I'm revolted by our corruption and short-sightedness.
Not that it adds much to Bill's WIR, which I look forward to reading each week, sometimes I like to graph some of the information provided in the WIR. Great WIR by the way--always an education to read.
In this case, I was curious about which sectors were performing better or worse since the January top around 8 Jan to 10 Jan, so I ran a Stockcharts performance graph (this is easily read from the two-week column of the sector ETF summary in the WIR). I realized all the squiggly lines in the Stockcharts default performance chart were not doing much for me so I switched to a bar chart. Consumer and Healthcare were the least effected by the downturn, Telcom, Tech, Energy, and Financial the worst. So if we do have a crash, I'm guessing these would fall the hardest.
By the way, if you look at Stockcharts performance charts, they offer quite a well rounded selection, including such things as biotechs and solars. I don't find their market carpets very helpful, but I would love to see market carpets for the various ETFs in the WIR, whether they be foreign or domestic. I don't see that Stockcharts offers self-selected market carpets, however.
Welcome back to all those who made it to the Bahamas--I'm green with envy!
I posted this this morning, but since it was one of the last two comments on yesterdays thread, I decided to post it today for the benefit of anyone who is interested. Thank you in advance for any comments you may have.
Mackinaw, very good analysis! You must have a quantitative background. However, as opposed to steps 2 and 3 that you mention in your comment, the two frequencies are found at the same time. An obvious weakness of this is that the shorter period curve must complete several cycles in the time that the longer frequency curve completes just one or two cycles. Thus the regularity of the peaks and valleys in my graphs. It seems unrealistic that there would not be some contraction or expansion of the period and amplitude of any given frequency over time. How to incorporate this in the algorithm I use could be a headache.
Thus, I'm inclined to follow your idea of doing a one frequency fit to get the long cycle and do the short cycle frequency fit only for more recent data. That way, the short frequency cycle would have a more up-to-date frequency and period. This would also permit me to add even shorter cycles, effectively producing an n-frequency fit, possibly giving rise to a good trading indicator.
Regarding residuals, the assumption has been that since these are best-fit curves, they accurately find the dominant two cycles in the smoothed data. Any residuals are thus considered to be noise for this analysis.(I hope this also answers Jack Black above.) I agree with you in general about curve fitting being dangerous business, which is why I emphasize in my posts that these results are suggestive only. I also say that one should not project forward more than one or even one-half of the shorter period using this approach (though my graphs show much longer projections, just to emphasize that having an underlying equation allows for prediction of the future.)
I view this as another tool for technical analysis. Many chart patterns such as triangles and head and shoulders can be easily "explained" by adding cycles of different periods and phases. Hence, why not try to uncover these cycles? Rather than waiting to see if a triangle is going to have an upside or a downside breakout, you can make a very good guess ahead of time using extracted cycles. It will be interesting to assess the accuracy of my results for $GOLD, $SPX, and $USD in three to six months.
One of my motivations in doing this work is that technical indicators tend to either lag the data or are at best concurrent with the data. If this curve fitting, which seems to give a hint as to future direction, is consonant with, for example, the MACD and the ADX indicators as they develop after the the last data point used for the fit, that would be a strong argument in its favor.
Mackinaw, very good analysis! You must have a quantitative background. However, as opposed to steps 2 and 3 that you mention in your comment, the two frequencies are found at the same time. An obvious weakness of this is that the shorter period curve must complete several cycles in the time that the longer frequency curve completes just one or two cycles. Thus the regularity of the peaks and valleys in my graphs. It seems unrealistic that there would not be some contraction or expansion of the period and amplitude of any given frequency over time. How to incorporate this in the algorithm I use could be a headache.
Thus, I'm inclined to follow your idea of doing a one frequency fit to get the long cycle and do the short cycle frequency fit only for more recent data. That way, the short frequency cycle would have a more up-to-date frequency and period. This would also permit me to add even shorter cycles, effectively producing an n-frequency fit, possibly giving rise to a good trading indicator.
Regarding residuals, the assumption has been that since these are best-fit curves, they accurately find the dominant two cycles in the smoothed data. Any residuals are thus considered to be noise for this analysis.(I hope this also answers Jack Black above.) I agree with you in general about curve fitting being dangerous business, which is why I emphasize in my posts that these results are suggestive only. I also say that one should not project forward more than one or even one-half of the shorter period using this approach (though my graphs show much longer projections, just to emphasize that having an underlying equation allows for prediction of the future.)
I view this as another tool for technical analysis. Many chart patterns such as triangles and head and shoulders can be easily "explained" by adding cycles of different periods and phases. Hence, why not try to uncover these cycles? Rather than waiting to see if a triangle is going to have an upside or a downside breakout, you can make a very good guess ahead of time using extracted cycles. It will be interesting to assess the accuracy of my results for $GOLD, $SPX, and $USD in three to six months.
One of my motivations in doing this work is that technical indicators tend to either lag the data or are at best concurrent with the data. If this curve fitting, which seems to give a hint as to future direction, is consonant with, for example, the MACD and the ADX indicators as they develop after the the last data point used for the fit, that would be a strong argument in its favor.
I have uploaded a "study" of $USD, similar to what I have previously uploaded for $GOLD and $SPX. (Incidently, those two both seem to be accurate at this point, correctly predicting the turn, though it may be too early to evaluate the results or the methodology.) This amounts to doing a two frequency sine-cosine curve fit to the 10 week centered MA for $USD. The price series from Oct 1, 2006 to Oct 1, 2009. I have included a separate graph of the two sinusoidal frequencies as well as a graph of the full curve fit with the long term trend and the two frequency graphs represented in a single mathematical curve which can be used to predict future behavior of the index. I should caution that there are good arguments against this type of curve fitting. This curve fit represents the "best fit" in terms of frequencies, amplitude, and phase. A possible weakness is the fact that I used a least squares *linear* regression for the long term trend. This is standard practice but, in this case, it tends to lower future estimates perhaps more than necessary. (Notice that the bottom of the current downtrend is at 72. I'm inclined to think it is around 74.5 base on extending a trend line on an OHLC graph from the previous low at 72.) If it turns out that we are in a bull phase for the $USD, it would be perhaps better to use a quadratic regression for the long term trend.
The tick marks on the t-axis are in units of three months on the "USD Oct06 to Oct09" graph. Oct 1, 2009 represents t=12 and Jan 1, 2010 represents t=13.
I am also including a Stockcharts version of the original data curve at
Gold bugs are an interesting crowd. They tend to be driven (almost exclusively) by fundamental data points and emotionally laden personal opinions. With gold in a secular bull market since late-September 1999, we at Fibozachi believe that the shiny, yellow metal will see much, much higher prices years down the road. Our long-term personal belief out of the way, the synthetic-cash asset of gold remains the only commodity (if not the only non-cash asset) to have escaped the guillotine over the past two years/ one decade.
Our intermediate-term personal belief, which is far from the hard right edge (the next bar on a chart, coined by Alan Farley), is that the spot PoG (price of gold) will be heavily depressed by the next all-encompassing round of deflationary pressures. We think that a monstrous DX/ $USD rally combined with an “all-the-same-markets” deleveraging of assets across the board will depress gold back toward prior inflection points between 760 and 660 over the next 21 months … before precious metals (as a collective group, denominated in all G-8 currencies) resume their long-standing date with destiny in Q3 of 2011, during the next leg of the fiat currency death spiral. Again, this is merely off-peak anal-ysis, which, at the end of the day, is nothing more than semi-educated personal speculation.
Such personal opinion and off-the-cuff anal-ysis during off-peak hours has absolutely nothing to do with either the Identification, Isolation, Timing, Execution and Management of actual trading signals during peak-hours or the Probabilistic Nature of Trading. Fundamental data points and fevered speculation (albeit warranted) about blatant central bank manipulation versus technical indicators and actual trading signals; we’ll leave the emotionally laden adjectives to others, recommend that any trader read/ re-read Mark Douglas’ seminal work, “Trading in the Zone”, and continue to focus on things that will actually make us money (technicals and price action).
I posted a chart like this one before, but it occurred to me to use envelopes whose lengths are derived from my best fit sine-cosine wave analysis. Based on the periods of the two frequency curve fit for gold I posted previously (posted again here for easy reference) I took one half of each period and built the Hurst envelopes around those (using centered MA's). The results are more satisfactory than before.
I used period lengths of one-half the indicated sine-cosine wave periods because that allows those cycles to show through clearly. In general, cycles whose periods are twice as long as the MA will have their amplitudes reduced by half by the MA. Cycles that are less than twice as long become progressively harder to see and can even be inversed by the MA (MA decreasing while prices are increasing, for example). I have also included a chart where the prices are almost transparant so that the centered MA cross-overs display some of their cyclic behavior:
I have also used the slope of the MACD in these charts. Note that it gives earlier signals than the MACD crossover themselves! I got this idea from the following, accessible to members of Stockcharts:
I have also attached a graph in pdf format showing the 10 week average represented as little circles and the two frequency trigonometric curve fit as a red curve. Since the curve fit is the graph of an equation, it can be used to predict the future of $SPX. The little circles represent 13 equally spaced data points of the 10 week MA from Oct 1, 2006 to Oct 1, 2009. Thus the interval between data points is 3 months. Oct 1, 2009 is represented by the last little circle. Note that the spread of the data points above and below the centered moving average is about 50 to 100 points on the Stockcharts graph, so this trigonometric curve may very well miss the top or bottom by that amount.
In general, with this method, you should only use it to predict as far as one half of the shorter period. Half of the shorter period is about 1.8 months or about 11 weeks.
This is only meant to be suggestive and there are a lot of possible objections to this approach. Comments and criticisms are welcome. DYODD.
I posted a graph of the 10 week *centered* moving average for $GOLD in the beginning of November. At the time I was unable to plot a graph of this 10 week MA with the mathematically defined curve that I had come up with. What I have done in the attached graph is to plot selected points of the 10 week centered moving average with the sine-cosine curve fit shown as a continuous curve. The curve was based on the period from Oct 2006 to Oct 2009. This represents 36 months. Since I had 13 equally spaced data points, the first data point, numbered 0 in the graph shown represents 1 Oct 06, and the last data point, numbered 12 represents 01 Oct 09. Thus the Oct 09 value for $GOLD is $1025. Extrapolating forward, since each tick mark on the x-axis represents 3 months, the sine-cosine curve is indicating a high for the 10 week moving average of around $1200 end of December beginning January. Since there appears from the graph of the 10 week average that prices vary between $50 above and below the 10 week MA, that means we might be looking at a high of either $1250 at that time or of $1200 about right now. But then markets always overshoot at extremes
Whether this will play out is anybody's guess. However, this is yet another tool in the tool box that is suggestive of where things could go. I have not backtested this curve fit at this point, but in making predictions using this approach, it is best not to advance further than one half period for the shorter frequency. The short frequency curve has a period of 3.5 months which equals about 15 weeks. Thus, you could go as far as say 7 weeks from Oct 1 which would put you at tick mark 13.5 or mid November. DYODD
Comments always appreciated. I hope this is useful for you. I will be doing a similar analysis for the S&P 500.
fjd10595, you talk about cutting teachers' salaries. Do you really think teachers are overpaid? I can see demanding improved performance and educational standards for teachers, but cutting their pay is not a good long term solution. It is already hard to attract intelligent, competent people to teaching who are passionate about their subject--this is true especially in the hard sciences and math. Lower salaries just exclude the best candidates for teaching and reinforce the mediocrity we currently have in our educational system. The pay structure in this country reflects the values of this country--high pay for athletes and pure money makers à la Goldman, JPM; low pay for dedicated public servants such as teachers, police, fireman, all three of which risk their very lives each day. The crisis we are in now reflects not only the corruption of the best (Ausrottung der Beste, as in the collapse of the Roman empire) but also the ignorance of the plebian class, if I may stretch the Rome thing a little. Education of youth is a form of infrastructure and we should promote it by hiring the best money can buy (I am not optimistic on that score). Not all public sector employees are equal.
Thanks for your comments and your work, Quasi! I would like to explore the Paint Net option as it seems to be a good way to go. I also appreciate your idea of using Excel with the downloaded data. Pardon me for my mistake in saying when the data begins. The t=12 chart should start 1 Nov 06 (not 07 as I mistakenly said) and should end 29 Oct 09. Notice that the Stockchart data was made to start in Jan 07. That means that in overlaying the t=12 chart over the actual price data, you would have anchor the left end of the chart really on 1 Nov 06 (equivalent to anchoring t=1 at 1 Jan 07) and stretch the other end until it coincides with 29 Oct 09. That should cause things to line up very well with the *centered* 10 week MA. Notice that the curve fitting did distort the two humps in March and mid-June of 2008, making the first hump lower than the second. In fact the first hump doesn't really show as a hump but rather as a simple rise.
Likewise, the 20 week chart would need to be stretched so that the first highest bump would occur slightly after 1 Nov 09. By the way, I also noticed that I did not include the quadratic trend in my equation on my last post:
y = -1.6*t^2+48*t+636+38.89*cos(.9517*t)-45.82*sin(.9517*t)+(-19.87*cos(2.259*t)+.5502*sin(2.259*t))
It is possible that the two curve fits would require some vertical stretching as well so that the scales line up.
With this first effort of generating a two frequency curve fit, I was mostly interested in just applying the algorithm and trying to get a general idea of how the results would pan out. If you would like to use Paint Net to adjust the overlays, that would be great to see. I'm going to try to arrive at a similar result using a spreadsheet. I don't have Excel for the Mac at this point, so I'm going to check out the Appleworks program I have, or I may find a way to do the same thing in Maple. What would really be nice is to overlay the curve fits on a standard Open High Low Close chart of $GOLD.
Meanwhile, the spreadsheet I developed does allow you to simply change the data set for any other price series and get an instantaneous set of parameters for generating a two frequency sine-cosine best curve fit.
One further consideration is how to make the curve fit more accurate for prediction. I'm inclined to think that for any single trig curve generated, it would be best just to predict a half-period ahead of the current date. One could do a single frequency curve fit on the longer term data and then zero in on the more recent data to do another single frequency curve fit of shorter period, which might be better than having the shorter frequency curve be fit all the way back to Nov 06. It would actually suffice to fit one complete period only for each curve. These could be easily updated as the period, amplitude, or phase changes with the data.
(Pardon me I hit the save button by mistake.) Then I subtracted from the 10 week centered MA a quadratic regression curve to "detrend" the data. I was not surprised to see that the trend curve was very slightly concave down. I then computed the sine-cosine regression and obtained using a spreadsheet and a mathematical program (Maple) the following curves. The t=12 curve runs from Oct 07 to the current date. The t=20 curve extends the curve beyond the current date. Each t-value represents three months. The equation for the curve fit is
Unfortunately, at this point, I am unable to overlay the mathematically obtained curves over the Stockcharts 10 week MA. I hope someone can suggest to me a method for doing that.
Note that the mathematical curve gives a very good fit to the data, but it is not perfect. There are undoubtedly smaller cycles that can be obtained that will give an even better fit. Note also that this algorithm predicts the future 10 week average, not the data itself which jumps above and below the 10 week MA.
Note also that in making predictions, one is generally safer using near-term predictions on the order of a half period and no more that a full cycle for the higher frequency component.
Comments and criticisms are always appreciated. You may have to view the attached PDF files using a program such as Preview if you have a Mac. Something similar for the PC.
As I mentioned previously, I was going to do a least squares sine-cosine curve fit to $GOLD. I did a two frequency fit. The algorithm I use finds the best frequency fit as well as the best amplitude and phase fit. First, I took a 10 week moving average from Nov 07 to the present. That can be seen on the following chart:
I just watched the Frank Holmes interview on Yahoo. He's saying that gold will go to $2000 or $2300. I read a book on gold by him and another writer whom I've forgotten, and found that he had very good things to say, particularily wrt how mining companies leverage the gold price and how it's also important to look at the currency of the country of origin for a miner. What I don't understand is why it is only now, now that gold is over $1000 that we hear from him. Is it because he would not have been offered an interview by Yahoo in March or last December? Or is it because now that gold is so high, he thinks that he will have more of an audience for what he has been thinking all along? It seems like we only hear what a great investment gold or anything else is only after a prolonged rise in the price. Does anyone know who might have said the S&P was a great bargain at 666 in March and would rise in six months to practically 1100? (I'm sure Bill said something about the market being very oversold in March, but perhaps I wasn't paying enough attention myself.) I just find it frustrating to hear about these great investments *after* a prolonged rise in price.
What saddened me was the terrible human cost shown by those pictures. Yes the pollution is terrible, but that can be remedied. The damage to all those innocent people is forever. Thankfully, there are those poor folks who are adopting those unwanted defective children--heroism in the midst of misery.
What saddened me was the terrible human cost shown by those pictures. Yes the pollution is terrible, but that can be remedied. The damage to all those innocent people is forever. Thankfully, there are those poor folks who are adopting those unwanted defective children--heroism in the midst of misery.
Thanks for posting this, baz22. I found it one of the most well-reasoned and informative things I've read recently. It's also nice to have a more long-term perspective as well as a perspective on global factors that factor into the price of gold.
Quasi, I looked at your revised chart and agree that using PPO vs MACD and using a log chart makes a lot more sense. Thank you for your input. With regard to the MACD being a coincident indicator to the moving averages used to construct the envelopes, I see your point. However, the RSI is also a coincident indicator, and yet if you look at the RSI on the chart, it is giving signals that do not coincide with the inner cycle hitting the bottom or top of the large envelope the way the MACD or the PPO do. Therefore, I'm not sure I see a reason not to use the PPO as a way to extend the envelope to the point in time when they both show a crossover.
Ultimately, as I've mentioned before, I will make best fit sine wave approximations to the two centered moving averages and attempt to project forward one period using the equation for the composite wave, just to see how that works. Actually, the method I will use gives a best fit for the periods of the cycles as well. When I get that done, I will certainly upload it here. Meanwhile, I'm going to do a Hurst wave fit to the S&P 500.
"Nuking the ocean to save America" Absolutely classic--I can't stop smiling. I guess our nuclear arsenal was needed afterall!
Greetings from France! I thought it would be interesting to look at the relation between the price of gold in euros vs the euro itself. I have attached a graph of this from Stockcharts. Starting in Jan 2009 until April 2009 the two go in opposite directions. Then from April 2009 up to Jan 2010 they more or less run parallel. After Jan 2010, they diverge dramatically, showing that during that period they were inversely correlated. So at this point, it is the euro and not the dollar that is a foil to gold.
http://tinyurl.com/2us9fry
This may seem a little out of the mainstream, but not really. On visiting the website of Fabius Maximus, who writes about geopolitics, including economics and is one of the more interesting websites around(http://tinyurl.com/yanpvxv), I came across an article on "polywell" fusion. This is "hot" fusion--not the "cold" fusion of Pons and Fleischer--and has already gone through several prototype trials and shown that it is a feasible, low-cost approach to nuclear fusion that could be commercialized within possibly as little as five years. It is an alternative to the tokamut reactor design which, though it has been proven to work, is extremely expensive and would take a minimum of 30 years to implement. As you know already, nuclear fusion is _clean_ energy that leaves behind no radiactive or toxic waste. The company engaged in this research and development is called EMC^2. In the following paper, which is a PDF file that you must download to read, they show that this reactor design represents the end of fossil fuels and could represent free energy for all of humanity for the indefinite future if they use deuterium and tritium for the fuel. It is a small reactor and the company needs to raise $200M to bring it to the threshold of commercialization. A piddling sum, but our all-wise government has cut funding of speculative projects such as this that have long-term potential. Instead the govenment feels that their scarce monetary reserves should be thrown at TBTS banks, to the tune of trillions of dollars. This paper is a fascinating read and I think you will agree that this is the direction we should be taking. Perhaps the Chinese-or who knows, maybe even the Indonesians- have already gotten started on this as we here in the US watch our middle class go down. Sorry for the diatribe, but I'm revolted by our corruption and short-sightedness.
The download can be found at http://tinyurl.com/yzrtwo6.
Not that it adds much to Bill's WIR, which I look forward to reading each week, sometimes I like to graph some of the information provided in the WIR. Great WIR by the way--always an education to read.
In this case, I was curious about which sectors were performing better or worse since the January top around 8 Jan to 10 Jan, so I ran a Stockcharts performance graph (this is easily read from the two-week column of the sector ETF summary in the WIR). I realized all the squiggly lines in the Stockcharts default performance chart were not doing much for me so I switched to a bar chart. Consumer and Healthcare were the least effected by the downturn, Telcom, Tech, Energy, and Financial the worst. So if we do have a crash, I'm guessing these would fall the hardest.
By the way, if you look at Stockcharts performance charts, they offer quite a well rounded selection, including such things as biotechs and solars. I don't find their market carpets very helpful, but I would love to see market carpets for the various ETFs in the WIR, whether they be foreign or domestic. I don't see that Stockcharts offers self-selected market carpets, however.
Welcome back to all those who made it to the Bahamas--I'm green with envy!
I posted this this morning, but since it was one of the last two comments on yesterdays thread, I decided to post it today for the benefit of anyone who is interested. Thank you in advance for any comments you may have.
Mackinaw, very good analysis! You must have a quantitative background. However, as opposed to steps 2 and 3 that you mention in your comment, the two frequencies are found at the same time. An obvious weakness of this is that the shorter period curve must complete several cycles in the time that the longer frequency curve completes just one or two cycles. Thus the regularity of the peaks and valleys in my graphs. It seems unrealistic that there would not be some contraction or expansion of the period and amplitude of any given frequency over time. How to incorporate this in the algorithm I use could be a headache.
Thus, I'm inclined to follow your idea of doing a one frequency fit to get the long cycle and do the short cycle frequency fit only for more recent data. That way, the short frequency cycle would have a more up-to-date frequency and period. This would also permit me to add even shorter cycles, effectively producing an n-frequency fit, possibly giving rise to a good trading indicator.
Regarding residuals, the assumption has been that since these are best-fit curves, they accurately find the dominant two cycles in the smoothed data. Any residuals are thus considered to be noise for this analysis.(I hope this also answers Jack Black above.) I agree with you in general about curve fitting being dangerous business, which is why I emphasize in my posts that these results are suggestive only. I also say that one should not project forward more than one or even one-half of the shorter period using this approach (though my graphs show much longer projections, just to emphasize that having an underlying equation allows for prediction of the future.)
I view this as another tool for technical analysis. Many chart patterns such as triangles and head and shoulders can be easily "explained" by adding cycles of different periods and phases. Hence, why not try to uncover these cycles? Rather than waiting to see if a triangle is going to have an upside or a downside breakout, you can make a very good guess ahead of time using extracted cycles. It will be interesting to assess the accuracy of my results for $GOLD, $SPX, and $USD in three to six months.
One of my motivations in doing this work is that technical indicators tend to either lag the data or are at best concurrent with the data. If this curve fitting, which seems to give a hint as to future direction, is consonant with, for example, the MACD and the ADX indicators as they develop after the the last data point used for the fit, that would be a strong argument in its favor.
Hear! Hear! to muniman and cwinsor.
Mackinaw, very good analysis! You must have a quantitative background. However, as opposed to steps 2 and 3 that you mention in your comment, the two frequencies are found at the same time. An obvious weakness of this is that the shorter period curve must complete several cycles in the time that the longer frequency curve completes just one or two cycles. Thus the regularity of the peaks and valleys in my graphs. It seems unrealistic that there would not be some contraction or expansion of the period and amplitude of any given frequency over time. How to incorporate this in the algorithm I use could be a headache.
Thus, I'm inclined to follow your idea of doing a one frequency fit to get the long cycle and do the short cycle frequency fit only for more recent data. That way, the short frequency cycle would have a more up-to-date frequency and period. This would also permit me to add even shorter cycles, effectively producing an n-frequency fit, possibly giving rise to a good trading indicator.
Regarding residuals, the assumption has been that since these are best-fit curves, they accurately find the dominant two cycles in the smoothed data. Any residuals are thus considered to be noise for this analysis.(I hope this also answers Jack Black above.) I agree with you in general about curve fitting being dangerous business, which is why I emphasize in my posts that these results are suggestive only. I also say that one should not project forward more than one or even one-half of the shorter period using this approach (though my graphs show much longer projections, just to emphasize that having an underlying equation allows for prediction of the future.)
I view this as another tool for technical analysis. Many chart patterns such as triangles and head and shoulders can be easily "explained" by adding cycles of different periods and phases. Hence, why not try to uncover these cycles? Rather than waiting to see if a triangle is going to have an upside or a downside breakout, you can make a very good guess ahead of time using extracted cycles. It will be interesting to assess the accuracy of my results for $GOLD, $SPX, and $USD in three to six months.
One of my motivations in doing this work is that technical indicators tend to either lag the data or are at best concurrent with the data. If this curve fitting, which seems to give a hint as to future direction, is consonant with, for example, the MACD and the ADX indicators as they develop after the the last data point used for the fit, that would be a strong argument in its favor.
Hear! Hear! to muniman and cwinsor.
I have uploaded a "study" of $USD, similar to what I have previously uploaded for $GOLD and $SPX. (Incidently, those two both seem to be accurate at this point, correctly predicting the turn, though it may be too early to evaluate the results or the methodology.) This amounts to doing a two frequency sine-cosine curve fit to the 10 week centered MA for $USD. The price series from Oct 1, 2006 to Oct 1, 2009. I have included a separate graph of the two sinusoidal frequencies as well as a graph of the full curve fit with the long term trend and the two frequency graphs represented in a single mathematical curve which can be used to predict future behavior of the index. I should caution that there are good arguments against this type of curve fitting. This curve fit represents the "best fit" in terms of frequencies, amplitude, and phase. A possible weakness is the fact that I used a least squares *linear* regression for the long term trend. This is standard practice but, in this case, it tends to lower future estimates perhaps more than necessary. (Notice that the bottom of the current downtrend is at 72. I'm inclined to think it is around 74.5 base on extending a trend line on an OHLC graph from the previous low at 72.) If it turns out that we are in a bull phase for the $USD, it would be perhaps better to use a quadratic regression for the long term trend.
The tick marks on the t-axis are in units of three months on the "USD Oct06 to Oct09" graph. Oct 1, 2009 represents t=12 and Jan 1, 2010 represents t=13.
I am also including a Stockcharts version of the original data curve at
http://tinyurl.com/yfxb94q
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This appeared in today's Zerohedge. See
http://tinyurl.com/yjwjn6o
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Gold bugs are an interesting crowd. They tend to be driven (almost exclusively) by fundamental data points and emotionally laden personal opinions. With gold in a secular bull market since late-September 1999, we at Fibozachi believe that the shiny, yellow metal will see much, much higher prices years down the road. Our long-term personal belief out of the way, the synthetic-cash asset of gold remains the only commodity (if not the only non-cash asset) to have escaped the guillotine over the past two years/ one decade.
Our intermediate-term personal belief, which is far from the hard right edge (the next bar on a chart, coined by Alan Farley), is that the spot PoG (price of gold) will be heavily depressed by the next all-encompassing round of deflationary pressures. We think that a monstrous DX/ $USD rally combined with an “all-the-same-markets” deleveraging of assets across the board will depress gold back toward prior inflection points between 760 and 660 over the next 21 months … before precious metals (as a collective group, denominated in all G-8 currencies) resume their long-standing date with destiny in Q3 of 2011, during the next leg of the fiat currency death spiral. Again, this is merely off-peak anal-ysis, which, at the end of the day, is nothing more than semi-educated personal speculation.
Such personal opinion and off-the-cuff anal-ysis during off-peak hours has absolutely nothing to do with either the Identification, Isolation, Timing, Execution and Management of actual trading signals during peak-hours or the Probabilistic Nature of Trading. Fundamental data points and fevered speculation (albeit warranted) about blatant central bank manipulation versus technical indicators and actual trading signals; we’ll leave the emotionally laden adjectives to others, recommend that any trader read/ re-read Mark Douglas’ seminal work, “Trading in the Zone”, and continue to focus on things that will actually make us money (technicals and price action).
http://tinyurl.com/ye69hwd
I posted a chart like this one before, but it occurred to me to use envelopes whose lengths are derived from my best fit sine-cosine wave analysis. Based on the periods of the two frequency curve fit for gold I posted previously (posted again here for easy reference) I took one half of each period and built the Hurst envelopes around those (using centered MA's). The results are more satisfactory than before.
I used period lengths of one-half the indicated sine-cosine wave periods because that allows those cycles to show through clearly. In general, cycles whose periods are twice as long as the MA will have their amplitudes reduced by half by the MA. Cycles that are less than twice as long become progressively harder to see and can even be inversed by the MA (MA decreasing while prices are increasing, for example). I have also included a chart where the prices are almost transparant so that the centered MA cross-overs display some of their cyclic behavior:
http://tinyurl.com/yjsdcd6
I have also used the slope of the MACD in these charts. Note that it gives earlier signals than the MACD crossover themselves! I got this idea from the following, accessible to members of Stockcharts:
http://tinyurl.com/yepzwq8
DYODD
I have taken a graph of the S&P 500 from Oct 1, 2006 to Oct 1, 2009 which shows weekly data as dots along with a *centered* 10 week SMA.
http://stockcharts.com/h-sc/ui?s=$SPX&p=W&st=2006-10-01&id=p41417974435&a=184541871
I have also attached a graph in pdf format showing the 10 week average represented as little circles and the two frequency trigonometric curve fit as a red curve. Since the curve fit is the graph of an equation, it can be used to predict the future of $SPX. The little circles represent 13 equally spaced data points of the 10 week MA from Oct 1, 2006 to Oct 1, 2009. Thus the interval between data points is 3 months. Oct 1, 2009 is represented by the last little circle. Note that the spread of the data points above and below the centered moving average is about 50 to 100 points on the Stockcharts graph, so this trigonometric curve may very well miss the top or bottom by that amount.
In general, with this method, you should only use it to predict as far as one half of the shorter period. Half of the shorter period is about 1.8 months or about 11 weeks.
This is only meant to be suggestive and there are a lot of possible objections to this approach. Comments and criticisms are welcome. DYODD.
I posted a graph of the 10 week *centered* moving average for $GOLD in the beginning of November. At the time I was unable to plot a graph of this 10 week MA with the mathematically defined curve that I had come up with. What I have done in the attached graph is to plot selected points of the 10 week centered moving average with the sine-cosine curve fit shown as a continuous curve. The curve was based on the period from Oct 2006 to Oct 2009. This represents 36 months. Since I had 13 equally spaced data points, the first data point, numbered 0 in the graph shown represents 1 Oct 06, and the last data point, numbered 12 represents 01 Oct 09. Thus the Oct 09 value for $GOLD is $1025. Extrapolating forward, since each tick mark on the x-axis represents 3 months, the sine-cosine curve is indicating a high for the 10 week moving average of around $1200 end of December beginning January. Since there appears from the graph of the 10 week average that prices vary between $50 above and below the 10 week MA, that means we might be looking at a high of either $1250 at that time or of $1200 about right now. But then markets always overshoot at extremes
Whether this will play out is anybody's guess. However, this is yet another tool in the tool box that is suggestive of where things could go. I have not backtested this curve fit at this point, but in making predictions using this approach, it is best not to advance further than one half period for the shorter frequency. The short frequency curve has a period of 3.5 months which equals about 15 weeks. Thus, you could go as far as say 7 weeks from Oct 1 which would put you at tick mark 13.5 or mid November. DYODD
Comments always appreciated. I hope this is useful for you. I will be doing a similar analysis for the S&P 500.
fjd10595, you talk about cutting teachers' salaries. Do you really think teachers are overpaid? I can see demanding improved performance and educational standards for teachers, but cutting their pay is not a good long term solution. It is already hard to attract intelligent, competent people to teaching who are passionate about their subject--this is true especially in the hard sciences and math. Lower salaries just exclude the best candidates for teaching and reinforce the mediocrity we currently have in our educational system. The pay structure in this country reflects the values of this country--high pay for athletes and pure money makers à la Goldman, JPM; low pay for dedicated public servants such as teachers, police, fireman, all three of which risk their very lives each day. The crisis we are in now reflects not only the corruption of the best (Ausrottung der Beste, as in the collapse of the Roman empire) but also the ignorance of the plebian class, if I may stretch the Rome thing a little. Education of youth is a form of infrastructure and we should promote it by hiring the best money can buy (I am not optimistic on that score). Not all public sector employees are equal.
Thanks for your comments and your work, Quasi! I would like to explore the Paint Net option as it seems to be a good way to go. I also appreciate your idea of using Excel with the downloaded data. Pardon me for my mistake in saying when the data begins. The t=12 chart should start 1 Nov 06 (not 07 as I mistakenly said) and should end 29 Oct 09. Notice that the Stockchart data was made to start in Jan 07. That means that in overlaying the t=12 chart over the actual price data, you would have anchor the left end of the chart really on 1 Nov 06 (equivalent to anchoring t=1 at 1 Jan 07) and stretch the other end until it coincides with 29 Oct 09. That should cause things to line up very well with the *centered* 10 week MA. Notice that the curve fitting did distort the two humps in March and mid-June of 2008, making the first hump lower than the second. In fact the first hump doesn't really show as a hump but rather as a simple rise.
Likewise, the 20 week chart would need to be stretched so that the first highest bump would occur slightly after 1 Nov 09. By the way, I also noticed that I did not include the quadratic trend in my equation on my last post:
y = -1.6*t^2+48*t+636+38.89*cos(.9517*t)-45.82*sin(.9517*t)+(-19.87*cos(2.259*t)+.5502*sin(2.259*t))
It is possible that the two curve fits would require some vertical stretching as well so that the scales line up.
With this first effort of generating a two frequency curve fit, I was mostly interested in just applying the algorithm and trying to get a general idea of how the results would pan out. If you would like to use Paint Net to adjust the overlays, that would be great to see. I'm going to try to arrive at a similar result using a spreadsheet. I don't have Excel for the Mac at this point, so I'm going to check out the Appleworks program I have, or I may find a way to do the same thing in Maple. What would really be nice is to overlay the curve fits on a standard Open High Low Close chart of $GOLD.
Meanwhile, the spreadsheet I developed does allow you to simply change the data set for any other price series and get an instantaneous set of parameters for generating a two frequency sine-cosine best curve fit.
One further consideration is how to make the curve fit more accurate for prediction. I'm inclined to think that for any single trig curve generated, it would be best just to predict a half-period ahead of the current date. One could do a single frequency curve fit on the longer term data and then zero in on the more recent data to do another single frequency curve fit of shorter period, which might be better than having the shorter frequency curve be fit all the way back to Nov 06. It would actually suffice to fit one complete period only for each curve. These could be easily updated as the period, amplitude, or phase changes with the data.
(Pardon me I hit the save button by mistake.) Then I subtracted from the 10 week centered MA a quadratic regression curve to "detrend" the data. I was not surprised to see that the trend curve was very slightly concave down. I then computed the sine-cosine regression and obtained using a spreadsheet and a mathematical program (Maple) the following curves. The t=12 curve runs from Oct 07 to the current date. The t=20 curve extends the curve beyond the current date. Each t-value represents three months. The equation for the curve fit is
38.89*cos(.9517*t)-45.82*sin(.9517*t)+(-19.87*cos(2.259*t)+.5502*sin(2.259*t))
Unfortunately, at this point, I am unable to overlay the mathematically obtained curves over the Stockcharts 10 week MA. I hope someone can suggest to me a method for doing that.
Note that the mathematical curve gives a very good fit to the data, but it is not perfect. There are undoubtedly smaller cycles that can be obtained that will give an even better fit. Note also that this algorithm predicts the future 10 week average, not the data itself which jumps above and below the 10 week MA.
Note also that in making predictions, one is generally safer using near-term predictions on the order of a half period and no more that a full cycle for the higher frequency component.
Comments and criticisms are always appreciated. You may have to view the attached PDF files using a program such as Preview if you have a Mac. Something similar for the PC.
As I mentioned previously, I was going to do a least squares sine-cosine curve fit to $GOLD. I did a two frequency fit. The algorithm I use finds the best frequency fit as well as the best amplitude and phase fit. First, I took a 10 week moving average from Nov 07 to the present. That can be seen on the following chart:
I just watched the Frank Holmes interview on Yahoo. He's saying that gold will go to $2000 or $2300. I read a book on gold by him and another writer whom I've forgotten, and found that he had very good things to say, particularily wrt how mining companies leverage the gold price and how it's also important to look at the currency of the country of origin for a miner. What I don't understand is why it is only now, now that gold is over $1000 that we hear from him. Is it because he would not have been offered an interview by Yahoo in March or last December? Or is it because now that gold is so high, he thinks that he will have more of an audience for what he has been thinking all along? It seems like we only hear what a great investment gold or anything else is only after a prolonged rise in the price. Does anyone know who might have said the S&P was a great bargain at 666 in March and would rise in six months to practically 1100? (I'm sure Bill said something about the market being very oversold in March, but perhaps I wasn't paying enough attention myself.) I just find it frustrating to hear about these great investments *after* a prolonged rise in price.
What saddened me was the terrible human cost shown by those pictures. Yes the pollution is terrible, but that can be remedied. The damage to all those innocent people is forever. Thankfully, there are those poor folks who are adopting those unwanted defective children--heroism in the midst of misery.
What saddened me was the terrible human cost shown by those pictures. Yes the pollution is terrible, but that can be remedied. The damage to all those innocent people is forever. Thankfully, there are those poor folks who are adopting those unwanted defective children--heroism in the midst of misery.
Thanks for posting this, baz22. I found it one of the most well-reasoned and informative things I've read recently. It's also nice to have a more long-term perspective as well as a perspective on global factors that factor into the price of gold.
Quasi, I looked at your revised chart and agree that using PPO vs MACD and using a log chart makes a lot more sense. Thank you for your input. With regard to the MACD being a coincident indicator to the moving averages used to construct the envelopes, I see your point. However, the RSI is also a coincident indicator, and yet if you look at the RSI on the chart, it is giving signals that do not coincide with the inner cycle hitting the bottom or top of the large envelope the way the MACD or the PPO do. Therefore, I'm not sure I see a reason not to use the PPO as a way to extend the envelope to the point in time when they both show a crossover.
Ultimately, as I've mentioned before, I will make best fit sine wave approximations to the two centered moving averages and attempt to project forward one period using the equation for the composite wave, just to see how that works. Actually, the method I will use gives a best fit for the periods of the cycles as well. When I get that done, I will certainly upload it here. Meanwhile, I'm going to do a Hurst wave fit to the S&P 500.