The market went up today.
Unfortunately this market seems to be relentless in its uptrend. It is rapidly approaching the trendline from May, which currently rests at about 1322ish and which I believe represents the last line of resistance for the Minor 2 count.
On the other hand, there's always the possibility that this is actually Intermediate (B) of Primary [2], which has become an increasingly compelling count to my mind. One advantage of Intermediate (B) is that it actually would allow the SPX to breach 1370 (for, say, C=A at 1375) without invalidating the count. Bears who had capitulated and turned bullish would then be re-P3'd in Intermediate (C) down - the difference, of course, is that instead of being followed by Minor 4 and 5, it would be followed by a bull move. This would be P[3] of ending diagonal Cycle V, and would unfold in three waves.
There has been some discussion on the NDX. I personally think the NDX and Nasdaq Composite are on a different count than the SPX. In particular, to me it seems more appropriate to think of them as being in Primary [C] of Cycle b. Whether or not they're finished with that, I do not know. At any rate, the NDX looks quite weak on weekly RSI and is just about poised to make a higher high on lower monthly RSI.
P.S.: The underlying text is in fact present underneath the black bars of doom.
Yet Another Elliott Wave Analysis Blog
Wednesday, January 18, 2012
Tuesday, January 17, 2012
1/17/12
Announcement: There will be few if any posts on the week of January 23-27. The reason for this has nothing to do with certain anagrams of soap, but rather due to the fact that both my Internet access and my ability to have a stretch of uninterrupted time long enough to conduct a full analysis will be up in the air.
The market technically went up today, but relative to its gap-up open on what frankly I consider to be absurd ebullience. I find it amusing that the word "ebullience" has "bull" in the middle.
The move up from 1202 looks like this now. Notice that each successive high occurs on an increasingly shallower slope, and that we are once more under the thick orange line that had stopped most of the previous retracements of this move. Yes, we gapped over it today, but failed to hold it. This indicates that the market no longer thinks that line is important.
Today's high went above the 1301 target. That's okay, because it is still within the .786 retracement range of 1301-1307 - not to mention it reached this value with the help of a gap up, which results in stops triggering, shorts panicking and covering, etc. The market may want to hold on through opex earnings week, but I think this reversal - even though we closed higher - means that risk isn't exactly as on as it was during the festive holiday season. Yes, we rallied late in the day, but we also hit short-term oversold conditions, so that wasn't so surprising.
Several of the banks are not looking good. C gapped down and crapped. It topped on the 12th, but is showing improving 10-minute technicals and therefore probably should correct fairly soon. BAC closed down ($6.48). MS closed down. WFC closed up - it should be worth noting that Wells Fargo's reaction to the 2008 decline was quite interesting. They were trading at around $30/share until it happened, blipped down to $7 a share and then skyrocketed back up to around $30/share where they still trade. (I.e., they recovered much better, but I'm not sure how much of that is due to absorbing Wachovia.) Goldman Sachs, the bank everyone loves to hate, was down as well.
I think we could be done here. I think.
The market technically went up today, but relative to its gap-up open on what frankly I consider to be absurd ebullience. I find it amusing that the word "ebullience" has "bull" in the middle.
The move up from 1202 looks like this now. Notice that each successive high occurs on an increasingly shallower slope, and that we are once more under the thick orange line that had stopped most of the previous retracements of this move. Yes, we gapped over it today, but failed to hold it. This indicates that the market no longer thinks that line is important.
Today's high went above the 1301 target. That's okay, because it is still within the .786 retracement range of 1301-1307 - not to mention it reached this value with the help of a gap up, which results in stops triggering, shorts panicking and covering, etc. The market may want to hold on through opex earnings week, but I think this reversal - even though we closed higher - means that risk isn't exactly as on as it was during the festive holiday season. Yes, we rallied late in the day, but we also hit short-term oversold conditions, so that wasn't so surprising.
Several of the banks are not looking good. C gapped down and crapped. It topped on the 12th, but is showing improving 10-minute technicals and therefore probably should correct fairly soon. BAC closed down ($6.48). MS closed down. WFC closed up - it should be worth noting that Wells Fargo's reaction to the 2008 decline was quite interesting. They were trading at around $30/share until it happened, blipped down to $7 a share and then skyrocketed back up to around $30/share where they still trade. (I.e., they recovered much better, but I'm not sure how much of that is due to absorbing Wachovia.) Goldman Sachs, the bank everyone loves to hate, was down as well.
I think we could be done here. I think.
Sunday, January 15, 2012
A Couple Long-Term Count Possibilities
The long term count possibilities, as I see them, are as follows:
First of course is the Prechterian or pseudo-Prechterian "P[3]" count. The main thrust of this count is that 2007 marked a Cycle-degree top of some kind, and that the May 2011 high was Primary [2] of a Cycle-degree impulse down. It could, in fact, actually have been Primary [B] of a Cycle-degree correction where the top is 2007 and the March 2009 low is P[A] - the salient point is the same: we are ultimately headed for a low below 666.70 before breaching 1370 to the upside.
What happens after that point is up for debate and depends on the exact count used. A P[3] count proper would have us wallowing in deflationary misery in P[4] followed by things deteriorating even further in P[5]. A P[C] count of course would take us to new highs (though these new highs may be aided by inflation). The "Minor 3" count presupposes the larger P[3/C] count, as would a higher degree count that has us at Intermediate (3).
An alternative count, which still has a significant bear move down but which does not take us to new lows, is as follows:
This is a sketch of the "medium term bear, long term bull" count, which is my alternate. This has us in or having just finished Intermediate (B) of Primary [2] of Cycle V. This Cycle V would be an ending diagonal (3-3-3-3-3), which accounts for the move up from 2009 being in three waves.
The next step down in such a count is an Intermediate (C), which would look a lot like a Minor 3. The difference is in the targets--an Intermediate (C) would probably make it at least to sub-1000 before reversing upward; a potential target I would be watching is 878, the .618 retracement of the move from 666 to 1370. A Minor 3 might stop at the same places, but would be followed by a tepid Minor 4 that probably won't get above 1100. An Intermediate (3) of P[3] would almost certainly take us to 665 or below...
...unless it's of a leading diagonal.
While in the near-term this count is less bearish than the Prechterian P[3], further afield it is worse. A leading diagonal is, well, leading, and presupposes a Cycle III/c down in the still-distant future. In other words, at least the traditional "P[3]" count has a large-scale bull market (even if just a corrective bull market) begin sooner.
First of course is the Prechterian or pseudo-Prechterian "P[3]" count. The main thrust of this count is that 2007 marked a Cycle-degree top of some kind, and that the May 2011 high was Primary [2] of a Cycle-degree impulse down. It could, in fact, actually have been Primary [B] of a Cycle-degree correction where the top is 2007 and the March 2009 low is P[A] - the salient point is the same: we are ultimately headed for a low below 666.70 before breaching 1370 to the upside.
What happens after that point is up for debate and depends on the exact count used. A P[3] count proper would have us wallowing in deflationary misery in P[4] followed by things deteriorating even further in P[5]. A P[C] count of course would take us to new highs (though these new highs may be aided by inflation). The "Minor 3" count presupposes the larger P[3/C] count, as would a higher degree count that has us at Intermediate (3).
An alternative count, which still has a significant bear move down but which does not take us to new lows, is as follows:
This is a sketch of the "medium term bear, long term bull" count, which is my alternate. This has us in or having just finished Intermediate (B) of Primary [2] of Cycle V. This Cycle V would be an ending diagonal (3-3-3-3-3), which accounts for the move up from 2009 being in three waves.
The next step down in such a count is an Intermediate (C), which would look a lot like a Minor 3. The difference is in the targets--an Intermediate (C) would probably make it at least to sub-1000 before reversing upward; a potential target I would be watching is 878, the .618 retracement of the move from 666 to 1370. A Minor 3 might stop at the same places, but would be followed by a tepid Minor 4 that probably won't get above 1100. An Intermediate (3) of P[3] would almost certainly take us to 665 or below...
...unless it's of a leading diagonal.
While in the near-term this count is less bearish than the Prechterian P[3], further afield it is worse. A leading diagonal is, well, leading, and presupposes a Cycle III/c down in the still-distant future. In other words, at least the traditional "P[3]" count has a large-scale bull market (even if just a corrective bull market) begin sooner.
Friday, January 13, 2012
1/13/12
The market went down today.
Obviously, it turned out that 1292 was not the Minor 2 top after all. I have updated my "Targets for Minor 3" count to adjust for this assuming that 1296.66 is the top as I have it here.
It may not be - in particular, if the market were to hit 1301.26-43, it would be pennies away from an interesting Fibonacci confluence: 1301.26 is the log-scale .786 retracement of the move from 1370.74-1074.77, and a 3/C = 1.618*1/A move from 1301.43 would, on a log scale, put a target at 878.00, which just so happens to be the .618 retracement log-scale of the entire move from 666.70-1370.74. This would work well with a "medium term bear, long term bull, super long term bear" count in which we are in or have just finished Intermediate (B) of Primary [2] of a Cycle V ending diagonal.
However, we dropped below the channel line that had heretofore limited our retracements, and failed to get back above it. Notwithstanding the permabulls' or neo-bulls' cries that the fact that we retraced the opening's down move means we are in a New Bull Market, it looks more like a mini-wave 2 than anything else. Not to mention the fact that it stopped at just about the .618 retrace of today's down move (1289.41; 1289.34 would have been exact. The .786 is at 1292.56), and the fact that the 5-minute chart is showing bearish RSI divergence on this afternoon's up move already.
The main downside for bears is that there was a gap down, which may want to fill and would do so dangerously close to the high (above 1295.50). Still, in late July the first wave after the interim top at 1347.00 retraced to roughly 1346.99.
Obviously, it turned out that 1292 was not the Minor 2 top after all. I have updated my "Targets for Minor 3" count to adjust for this assuming that 1296.66 is the top as I have it here.
It may not be - in particular, if the market were to hit 1301.26-43, it would be pennies away from an interesting Fibonacci confluence: 1301.26 is the log-scale .786 retracement of the move from 1370.74-1074.77, and a 3/C = 1.618*1/A move from 1301.43 would, on a log scale, put a target at 878.00, which just so happens to be the .618 retracement log-scale of the entire move from 666.70-1370.74. This would work well with a "medium term bear, long term bull, super long term bear" count in which we are in or have just finished Intermediate (B) of Primary [2] of a Cycle V ending diagonal.
However, we dropped below the channel line that had heretofore limited our retracements, and failed to get back above it. Notwithstanding the permabulls' or neo-bulls' cries that the fact that we retraced the opening's down move means we are in a New Bull Market, it looks more like a mini-wave 2 than anything else. Not to mention the fact that it stopped at just about the .618 retrace of today's down move (1289.41; 1289.34 would have been exact. The .786 is at 1292.56), and the fact that the 5-minute chart is showing bearish RSI divergence on this afternoon's up move already.
The main downside for bears is that there was a gap down, which may want to fill and would do so dangerously close to the high (above 1295.50). Still, in late July the first wave after the interim top at 1347.00 retraced to roughly 1346.99.
Wednesday, January 11, 2012
1/11/12 - Looking at Divergences
I know there are some people who don't like using divergences, but...
The market still looks like we're in a complicated topping process. In particular, the wave count since Dec. 29 is quite tricky to figure out. So I have instead decided to look at RSI divergences in various markets. These are all RSI(13), the Fibonacci value I typically post in my charts, not RSI(14). I look at XLB mostly because I am now long SMN, but that's beside the point.
Bearish RSI divergences (bullish for the VIX) are present at the 60- and 30-minute levels on all of these. Many of the highest values occurred in the powerful New Year's thrust up. The two markets I looked at that have yet to make a new high on lower 10-minute RSI are the SPX and RUT. The SPX closed today at 1292.48, four points below its high set yesterday morning of 1296.46.
This may suggest marginally higher highs tomorrow morning before a selloff - I'd be highly amused if the market topped at 1299.99. Many of these indices are very close to their late October Minute [w] (or Minor W) highs and will not need much more to get above them.
The market still looks like we're in a complicated topping process. In particular, the wave count since Dec. 29 is quite tricky to figure out. So I have instead decided to look at RSI divergences in various markets. These are all RSI(13), the Fibonacci value I typically post in my charts, not RSI(14). I look at XLB mostly because I am now long SMN, but that's beside the point.
Bearish RSI divergences (bullish for the VIX) are present at the 60- and 30-minute levels on all of these. Many of the highest values occurred in the powerful New Year's thrust up. The two markets I looked at that have yet to make a new high on lower 10-minute RSI are the SPX and RUT. The SPX closed today at 1292.48, four points below its high set yesterday morning of 1296.46.
This may suggest marginally higher highs tomorrow morning before a selloff - I'd be highly amused if the market topped at 1299.99. Many of these indices are very close to their late October Minute [w] (or Minor W) highs and will not need much more to get above them.
Monday, January 9, 2012
1/9/12
The broader market decided to stay still today, much as it did Friday. It's probably tracing out a triangle of some sort. About the only thing that seems clear to me about the past couple of days with respect to the SPX is that the move from 1283.06 (Thursday 1:40 p.m.) to 1274.55 (today 11:15 a.m.) looks a lot like a flat. To which I have to say: Pick a direction, market, and go in it.
So instead I'm going to look at Netflix, which has been explosive the past couple of days, rising nearly 14% today alone.
The weekly chart for the past year does not look particularly good. From this it looks as if the recent surge, powerful though it may have been, is simply a backtest of the 200-week SMA which it gapped through in October.
Speaking of gaps, NFLX's history is full of them. Let's take a look at the daily chart, highlighting the gaps. (Blue = gap up, red = gap down.)
Currently it looks as though the stock is trying to fill the massive (largest on this log scale) gap it left when it plunged overnight from 115 to under 80 a share. NFLX is already daily overbought (RSI(13) at 75), but may have a little more room to run. An operative question is whether this dramatic upturn is the C wave of a correction, or 3 of A (or 3 of 1 of the new NFLX bull).
IF the broader market is about to have a major crash, I would find it hard pressed for NFLX to continue double-digit daily rises. On the other hand, if such a crash is still a few days or weeks away (market making a topping process ultimately to reach the 1310-1330 range), NFLX may power through to at least fill the gap at 115. I find it difficult to believe it would fill the higher gap at ~200 soon, though, as the 200-day SMA is at 185.60 (about the bottom of that gap) and declining. If the market is still ascending, NFLX may, however, try to challenge this SMA in a wave 2/B.
On the other hand, if a crash is due, now (or soon) would be a good time for NFLX to reverse. Of course, it is always possible that the stock may hold up through Minor 3 (i.e. not go below 77 causing 4/1 overlap), rise in a 5 of A during the broader market's Minor 4 filling the gap at 115, fall in a B-wave during the broader market's Minor 5, and rise to meet its 200-day SMA somewhere in the 150s (?) during Intermediate (2) before filling the gap in the lower 50s during Intermediate (3).
NFLX is severely overbought hourly, but the structure suggests that even if this is NFLX's C wave, there still needs to be a 4 and 5 of C. A pullback of some kind is likely; it's just a matter of how strong and long-lasting this pullback will be. I may consider buying shares of NFLX in the near future, possibly within the next 72 hours.
So instead I'm going to look at Netflix, which has been explosive the past couple of days, rising nearly 14% today alone.
The weekly chart for the past year does not look particularly good. From this it looks as if the recent surge, powerful though it may have been, is simply a backtest of the 200-week SMA which it gapped through in October.
Speaking of gaps, NFLX's history is full of them. Let's take a look at the daily chart, highlighting the gaps. (Blue = gap up, red = gap down.)
Currently it looks as though the stock is trying to fill the massive (largest on this log scale) gap it left when it plunged overnight from 115 to under 80 a share. NFLX is already daily overbought (RSI(13) at 75), but may have a little more room to run. An operative question is whether this dramatic upturn is the C wave of a correction, or 3 of A (or 3 of 1 of the new NFLX bull).
IF the broader market is about to have a major crash, I would find it hard pressed for NFLX to continue double-digit daily rises. On the other hand, if such a crash is still a few days or weeks away (market making a topping process ultimately to reach the 1310-1330 range), NFLX may power through to at least fill the gap at 115. I find it difficult to believe it would fill the higher gap at ~200 soon, though, as the 200-day SMA is at 185.60 (about the bottom of that gap) and declining. If the market is still ascending, NFLX may, however, try to challenge this SMA in a wave 2/B.
On the other hand, if a crash is due, now (or soon) would be a good time for NFLX to reverse. Of course, it is always possible that the stock may hold up through Minor 3 (i.e. not go below 77 causing 4/1 overlap), rise in a 5 of A during the broader market's Minor 4 filling the gap at 115, fall in a B-wave during the broader market's Minor 5, and rise to meet its 200-day SMA somewhere in the 150s (?) during Intermediate (2) before filling the gap in the lower 50s during Intermediate (3).
NFLX is severely overbought hourly, but the structure suggests that even if this is NFLX's C wave, there still needs to be a 4 and 5 of C. A pullback of some kind is likely; it's just a matter of how strong and long-lasting this pullback will be. I may consider buying shares of NFLX in the near future, possibly within the next 72 hours.
Thursday, January 5, 2012
1/5/12 - A Tale of Three Indices
Let's look at the Dow Jones Industrial Average, the S&P 500, and the Nasdaq Composite all together, shall we?
The primary count in the SPX is that we are currently in Micro [5] of v of (c) of [y] of 2. If so, the SPX should not go much above 1288.50 and the DJIA should close no higher than 12,467. Unless the DJIA and SPX are on separate counts, which is not out of the question, and assuming the primary is the correct count, Micro [5] on the DJIA should truncate, terminating below Micro [3] (Tuesday's high).
On the Nasdaq we do have a new high above Tuesday's high. Micro [3] on the Nasdaq is longer than Micro [1] (88 vs. 86 points), so Micro [5] is not limited in how high it can go before invalidating the wave count (well, besides 2887.75, its May 2 top).
On the SPX and DJIA, we had negative RSI divergence with respect to the December 27 and January 3 highs. The Nasdaq did not confirm this, as its January 3 high had higher RSI than Dec. 27, but we have lower RSI on a higher high for it here. All three indices have lower MACD highs (though it's hard to see on the Nasdaq so I have helpfully included the values).
What does this mean? It means the market's tired. At the very least, it will likely undertake a significant correction soon (down to the lower 1200s at least). More bearishly it means we may be only a matter of hours before Minor 3.
The above chart adds credence to this view by suggesting that the entire move from May 2 so far is fractaling the action from May 2 through the end of July. In such a case, we are at the equivalent of Point 5. In July, the market topped and then began to oscillate near its top making steadily lower highs and lower lows before finally collapsing to point 6.
The primary count in the SPX is that we are currently in Micro [5] of v of (c) of [y] of 2. If so, the SPX should not go much above 1288.50 and the DJIA should close no higher than 12,467. Unless the DJIA and SPX are on separate counts, which is not out of the question, and assuming the primary is the correct count, Micro [5] on the DJIA should truncate, terminating below Micro [3] (Tuesday's high).
On the Nasdaq we do have a new high above Tuesday's high. Micro [3] on the Nasdaq is longer than Micro [1] (88 vs. 86 points), so Micro [5] is not limited in how high it can go before invalidating the wave count (well, besides 2887.75, its May 2 top).
On the SPX and DJIA, we had negative RSI divergence with respect to the December 27 and January 3 highs. The Nasdaq did not confirm this, as its January 3 high had higher RSI than Dec. 27, but we have lower RSI on a higher high for it here. All three indices have lower MACD highs (though it's hard to see on the Nasdaq so I have helpfully included the values).
What does this mean? It means the market's tired. At the very least, it will likely undertake a significant correction soon (down to the lower 1200s at least). More bearishly it means we may be only a matter of hours before Minor 3.
The above chart adds credence to this view by suggesting that the entire move from May 2 so far is fractaling the action from May 2 through the end of July. In such a case, we are at the equivalent of Point 5. In July, the market topped and then began to oscillate near its top making steadily lower highs and lower lows before finally collapsing to point 6.
Wednesday, January 4, 2012
1/4/12
The market went to the right today. I think, if it were to have gone to the left, we would have more to worry about on our hands than even a Submillennial-degree downturn.
The count I described previously remains intact, with a necessary truncation on the Dow and a possible truncation on the SPX. I added to my short position today.
Extremely small-scale intraday waves can be difficult to count and are more prone to breaking rules. The point is that the market seems to be struggling even as social mood has become quite relieved. What Eurozone crisis? What China slowdown? This is what you expect at the tip-top of wave 2.
Provided 1288.50 does not break in the SPX, the market can make a new high above where I have Micro [3]. The preference is for the DJIA to go no higher than 12,468.71, only fifty points from its close today. But this is doable; the Dow stocks could, for instance, start a tumble "early" while things like AAPL and GOOG lag it - the Nasdaq, unlike the Dow and SPX, is still under its daily Bollinger band. (The Dow is also weighted by share price, not by market capitalization; this might have an effect.)
The count I described previously remains intact, with a necessary truncation on the Dow and a possible truncation on the SPX. I added to my short position today.
Extremely small-scale intraday waves can be difficult to count and are more prone to breaking rules. The point is that the market seems to be struggling even as social mood has become quite relieved. What Eurozone crisis? What China slowdown? This is what you expect at the tip-top of wave 2.
Provided 1288.50 does not break in the SPX, the market can make a new high above where I have Micro [3]. The preference is for the DJIA to go no higher than 12,468.71, only fifty points from its close today. But this is doable; the Dow stocks could, for instance, start a tumble "early" while things like AAPL and GOOG lag it - the Nasdaq, unlike the Dow and SPX, is still under its daily Bollinger band. (The Dow is also weighted by share price, not by market capitalization; this might have an effect.)
Tuesday, January 3, 2012
1/3/12
The market went slightly up today.
1288.50 did not break, and therefore my count remains. Additionally, we have lower 30- and 60-minute RSI and MACD than earlier in this seasonal rally despite the shell-shocker of an opening, suggesting it may be just about to peter out.
One argument against the immediate bearish case is that what would be the fifth wave on the Dow Jones Industrial Average is now longer than what would be the third wave (which was shorter than the first), meaning this may just be Micro [3] of Submin iii instead of Submin v itself. That may or may not be the case. If it is, and the SPX confirms, the indices could make a 4-5-4-5 pattern, topping at around SPX 1301-07, which is where the 78.6% logarithmic retracement of 1370-1074 is.
On the other hand, indices need not always confirm, and there is a third option as well: Micro [5] of v on the DJIA could truncate, finishing below today's intraday high of 12,478.86 and - critically - no higher than the v=iii point of 12,468.71 (yes, just 10 DJIA points lower).
As for the new bull market scenario? Certainly, it's a possibility, but a lot of this talk has been from aggressive (perma)bulls and/or capitulating bears. My preferred bull-market scenario is that P[1] up ended in May 2011 and we are currently in Intermediate (B) of P[2] (Int. (A) was the trip to 1074). The (C) wave of this move would probably look very similar to wave 3 down in the bear counts; its bottom has the potential to be a significant bear trap.
1288.50 did not break, and therefore my count remains. Additionally, we have lower 30- and 60-minute RSI and MACD than earlier in this seasonal rally despite the shell-shocker of an opening, suggesting it may be just about to peter out.
One argument against the immediate bearish case is that what would be the fifth wave on the Dow Jones Industrial Average is now longer than what would be the third wave (which was shorter than the first), meaning this may just be Micro [3] of Submin iii instead of Submin v itself. That may or may not be the case. If it is, and the SPX confirms, the indices could make a 4-5-4-5 pattern, topping at around SPX 1301-07, which is where the 78.6% logarithmic retracement of 1370-1074 is.
On the other hand, indices need not always confirm, and there is a third option as well: Micro [5] of v on the DJIA could truncate, finishing below today's intraday high of 12,478.86 and - critically - no higher than the v=iii point of 12,468.71 (yes, just 10 DJIA points lower).
As for the new bull market scenario? Certainly, it's a possibility, but a lot of this talk has been from aggressive (perma)bulls and/or capitulating bears. My preferred bull-market scenario is that P[1] up ended in May 2011 and we are currently in Intermediate (B) of P[2] (Int. (A) was the trip to 1074). The (C) wave of this move would probably look very similar to wave 3 down in the bear counts; its bottom has the potential to be a significant bear trap.
Friday, December 30, 2011
Why Cycles Aren't That Easy
It's easy to understand why one might think cycles are easy to figure out. Let's take a simple sine wave and call it Figure 1.
Actually, the equation used here (and for subsequent figures) was negative cosine, rather than sine, because I wanted the cycle to be at a bottom at timestamp 0. This cycle behaves as any such sinusoidal wave should: it bottoms at 0, 100, 200, 300 etc. at a value of -10, reaches its top at 50, 150, 250, 350, etc. at a value of +10, and passes through zero at 25, 75, 125, 175, etc.
Now let's suppose I add a 50-year cycle, with the same amplitude and with its phase set so that its bottom is also at timestamp 0:
Now, at timestamp 0, the value of the "market" (if this is to represent the stock market) is -20. The 100-unit and 50-unit cycles, both at their respective bottoms, exhibit constructive interference and so our "market" is down much further. The subsequent top actually occurs a little later than timestamp 25 as would be expected, because while the 50-unit cycle is going down, the 100-unit cycle is still rising. The same effect occurs in reverse at about timestamp 70, resulting in an earlier peak than expected (while the 50-unit is still rising, the 100-unit is falling). At timestamp 50, the 100-unit cycle is at a top, while the 50-unit cycle is at a bottom - we get destructive interference and a "market" value of zero (+10-10).
Now, for fun and to illustrate how tricky cycles can become even when there are just a handful, I combine cycles of 100, 64, 36, 16, and 9 units. They are all of the same amplitude (10) and are all in phase at time unit 0.
Okay. You can, for the most part, see what's going on. Obviously at timestamp 0 they all undergo constructive intereference with each other and the "market's" value is -50. The prominent "triple top" observed by the market has its highs at about timestamps 22, 40, and 58 - these highs, in fact, are 9-unit cycle highs that occur, for the most part, during the "high" phases of the 100- and 64-unit cycles. Similarly, the high in timestamp upper 80s can be attributed to the juxtaposition of the 64-unit and 16-unit cycles approaching peak and the 9-unit and 36-unit ones just past it.
But would you have been able to figure those cycles out if I hadn't already told you what they were, and if so, how long would it have taken?
Now let's make things more complicated by putting the cycles out of phase at timestamp 0.
In this instance I have helpfully included the magnitude of the phase shifts. Notice how the graph has changed compared to Figure 3 - there's no true "triple top" anymore. Now, what happens if I mess with the cycles' amplitudes, and add a secular "bullish" linear trend y=0.25*t, where t is the timestamp?
Notice how suspiciously like a continuation head and shoulders pattern this looks like. There is a strong "bull" move up in timestamp 35-40 where, if this were a market, fortunes could easily be made on the long side (depending on what the actual market values of this would be). Similarly, after an extensive topping process including a "bull trap" from about timestamp 53-67, there is an equally powerful "bear" move down from positive 36 or thereabouts to about negative 11.
Now, to further complicate things, let's add some noise. Using Random.org, I generate for each time stamp a uniformly distributed random number between -15 and +15, and add it to the cycles. I do this with four different sets of random numbers, which you can consider to refer to different market indices. These random numbers are supposed to represent smaller variations in the market. Take their cause how you will - smaller-scale cycles, earnings reports, fundamentals, the psychology of the collective investors, the whims of central bankers, etc.
Clearly the prominent larger trends remain intact--there is a strong "bull" move, for instance, at timestamps in the late 30s and a strong "bear" move in the late 50s/early 60s. But they don't equate--there is significant non-confirmation, for instance, in index I (which peaks at timestamp ~55) relative to indices II, III, and IV (which peak at timestamp ~40).
Obviously, you'd need to use a smoothing algorithm to determine the time cycles from this; the questions, of course, are (1) would you get the right period for the cycles? (2) would you be able to tell which are of the greatest magnitude? (3) would your smoothing algorithm catch cycles that aren't there (or ignore cycles that are)? And it might create more problems if the "noise" is patterned (e.g. Elliott waves) rather than purely random.
Now take into account that I have:
Fig. 1: Sinusoidal wave with wavelength 100 units, amplitude 10. |
Actually, the equation used here (and for subsequent figures) was negative cosine, rather than sine, because I wanted the cycle to be at a bottom at timestamp 0. This cycle behaves as any such sinusoidal wave should: it bottoms at 0, 100, 200, 300 etc. at a value of -10, reaches its top at 50, 150, 250, 350, etc. at a value of +10, and passes through zero at 25, 75, 125, 175, etc.
Now let's suppose I add a 50-year cycle, with the same amplitude and with its phase set so that its bottom is also at timestamp 0:
Fig. 2: 50-unit and 100-unit cycles combined |
Now, for fun and to illustrate how tricky cycles can become even when there are just a handful, I combine cycles of 100, 64, 36, 16, and 9 units. They are all of the same amplitude (10) and are all in phase at time unit 0.
Fig. 3: Several cycles, all in phase, all same amplitude. |
But would you have been able to figure those cycles out if I hadn't already told you what they were, and if so, how long would it have taken?
Now let's make things more complicated by putting the cycles out of phase at timestamp 0.
Fig. 4: Like figure 3, but cycles out of phase. |
In this instance I have helpfully included the magnitude of the phase shifts. Notice how the graph has changed compared to Figure 3 - there's no true "triple top" anymore. Now, what happens if I mess with the cycles' amplitudes, and add a secular "bullish" linear trend y=0.25*t, where t is the timestamp?
Fig. 5: As graph title implies. |
Now, to further complicate things, let's add some noise. Using Random.org, I generate for each time stamp a uniformly distributed random number between -15 and +15, and add it to the cycles. I do this with four different sets of random numbers, which you can consider to refer to different market indices. These random numbers are supposed to represent smaller variations in the market. Take their cause how you will - smaller-scale cycles, earnings reports, fundamentals, the psychology of the collective investors, the whims of central bankers, etc.
Fig. 6: As graph titles imply. |
Obviously, you'd need to use a smoothing algorithm to determine the time cycles from this; the questions, of course, are (1) would you get the right period for the cycles? (2) would you be able to tell which are of the greatest magnitude? (3) would your smoothing algorithm catch cycles that aren't there (or ignore cycles that are)? And it might create more problems if the "noise" is patterned (e.g. Elliott waves) rather than purely random.
Now take into account that I have:
- assumed that the cycles are all sinusoidal in nature
- assumed that the amplitude, phase, and wavelength of each separate cycle are all constant
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