Positive Economic News - Giving You Something Positive About Our Economy
Saturday 23rd July, 2011.
It doesn't look like American companies will lose out in the economy's soft patch. Business
profits are looking better than expected so far in 2nd qtr
earnings season. Strong
showings from large companies such as Apple, Coca-Cola and
McDonald's have put the quarter on track to set a new record for
operating earnings."The
corporate sector's in great shape," says Joseph LaVorgna, chief U.S.
economist at Deutsche Bank. "The economy is a little healthier than we
thought it was."Aside from
companies' continuing stubbornness about hiring more workers, the early
results are good news for investors and anyone worried that the
debt-limit standoff in Washington or the financial crisis in Europe
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willingness to spend on fast food, electronic gadgets and other items
has helped fuel better-than-expected quarterly results. Among the
standouts: Apple Inc. more
than doubled its profit to $7.31 billion on an 82 percent jump in
revenue, further testimony to the runaway popularity of the iPhone and
iPad. Coca-Cola Co. more than tripled net income
to $5.77 billion as the world's largest drink maker increased its
strength in emerging markets, such as Latin America, India and China,
while sales held stable in the U.S. and Europe. Harley-Davidson Inc. more than doubled its profit to $191 million,
posting an increase in U.S. motorcycle sales for the first time since
2006 and expanding its market share overseas. McDonald's Corp. increased net income 15 percent to $1.4 billion on a
16 percent jump in revenue, attracting more customers for its broadening
menu and array of coffee drinks even as it raised prices. Companies
in several other industries also blew past Wall Street's expectations
this week, including credit card issuer American Express Co., toy maker
Hasbro Inc., oil services company Halliburton Co., computer company IBM
Corp., chipmaker Intel Corp. and health insurer UnitedHealth Group Inc. All
told, 148 companies in the SP500 index have
reported earnings and 73 percent have beaten the expectations of financial analysts. So with all the doom and gloom we hear, when looking at the facts you can actually see a lot of large companies improving their businesses. Source: Yahoo Finance
Tuesday 9th August, 2011.
Well it does seem hard to shed positive light on recent financial news given the USA has for the first time lost its coveted AAA rating from standards and poors rating agency. This news hasn't been well received by the American public and in particular the financial markets. The dow jones has slid very hard the day the stock market opened for trading on Monday. Most industries and sectors have been sold off by investors and the news has been very negative. Now to offer something positive; As president Obama said, "it doesn't matter what some agency says, the USA always has been and always will be a AAA country" and we agree with him. Since ratings should all be relative, when comparing to other countries, the USA is still widely regarding as the safest place in the world to store money, it still has the most trusted government and ethical investment community. Hedge funds in America are very safe place to invest for consistent returns and low risk in your portfolio. Most of these trading firms use very sophisticated trading software to find the best trades in real time. These trading applications use predefined trading strategies largely based around pair trading. In addition to these trading software applications, many investment banks have very experienced floor traders who will manually generate trading signals for their managers based off technical analysis of the stock charts. So before you get negative about the downgrading of America's credit rating, it's best to step back and take a holistic look at the whole global economy, and instead of looking at America in a vacuum, compare it to other economies such as Russia, India, China, etc.......where would you rather keep your life savings? I'll let you decide.
Joseph Fourier (1768-1830) (pronounced "fooryay'') was a French mathematician and inventor of
Fourier analysis. His work helped show the way to expressing periodic curves or functions by a sum of sines and cosines. These simple functions are easy for our computer to evaluate and project into the future. Many natural physical phenomena are oscillatory, that is repeating over and over again, much like the Markets.
The Markets are not a function in the mathematical sense, but do seem to go up and down over and over again. During the late 1960's a number of Fast Fourier Transforms methods were divised to 'transform' time dependent data, such as the daily market close, to frequency. The frequency Vs. amplitude squared is referred to as the 'Power or Transformation Spectrum'. A typical plot of a 'Transformation Spectrum' is shown in Figure 1. The plot shows which frequency has the most relative impact on daily (weekly, monthly) closes.
FAST FOURIER TRANSFORM WITH DATA PREPROCESSING
The program Fourier Analysis, included in this issue, was developed on two microcomputers: the Radio Shack (Tandy) Color ComputerTM, and the Apple ][TM. The original Fast Fourier Transform Algorithm (Cooley-Tukey 1965) was supplied to us by one of the co-authors, James W. Cooley, at the IBM Thomas J. Watson Research Center, and we would like to express our gratitude to him. Most of the microcomputers on the market today operate with a BASIC interpreter developed here in the Seattle area by a prominent company called MicrosoftTM. (This includes the Apple as well). Transferring this BASIC program, or almost anything written in BASIC, to another machine would not be a programming problem since the microcomputer BASIC's are so similar.
With this Fourier routine one must translate significant frequencies into cycle length by hand (see below under WHAT IS IT). The method behind the FFT is a mathematical operation known as the Discrete Fourier Transform (DFT). Each daily close is used as a discrete data point. If each and every daily close was used to compute the 'Transformation Spectrum' (see Dr. Warren's aritcle) you would get half as many frequencies as daily closes. In addition an "FFT Composite" graph using the total spectrum would pass through the daily closes exactly (i.e. the process is reversible).
ABOUT THE PROGRAM OPERATION
The program presented here will take all the data from any column, truncate any leading or trailing zeros (possibly from prior studies), detrend, level and apply a 'window' to the data (see Dr. Warren's article). Then the data array length is doubled by adding zeroes to increase the output resolution. An optimized Discrete Real Fast Fourier Transform is performed that is about eight times faster than the original Compu Trac transform. This speed increase is possible because we have reduced the number of computations (multiplication and division) in the innermost (time critical) programming iteration and the fact that we use a REAL-FFT rather than a COMPLEX-FFT such as Compu Trac's version). FFT Power (this is the amplitude squared) or Amplitude is computed in terms of Percentage of TOTAL Power (or
FIGURE 1:
amplitude) and stored in the Study column for the Compu Trac system to graph.
In an effort to save time we have implemented a high speed algorithm for computing the discrete Fourier transfrom known as the Real Fast Fourier Transform (FFT). The term 'Real' refers to the type of data used as input (i.e. Real Vs. Complex). Speed is a real problem, so some shortcuts have been made. The number of days of data used has been limited to those that equal powers of 2 (i.e. 4, 8, 16, 32, 64, 128 & 256 etc.). This is a great help in speeding up the computation from a two hour wait to less than two minutes.
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The program is comprised of a number of subroutines written in BASIC. Although the program was designed to be used from within the Compu Trac System, it may be modified to run on any computer. The Compu Trac System runs on an Apple ][TM computer and contains many thousands of lines of programming code similar to the program included in Dr. Warren's article (refer elsewhere in this issue). When using the Compu Trac System, the program is accessed through the Study (2.) Menu and followed by User Study Program (A.). At this point the Compu Trac system will prompt you for a Study Number.(We have used 30)
STUDY NO.: 30
and proceed to 'EXEC', the BASIC computer routine stored on your Data Disk (as a 'T' type sequential text file named STUDY.30).
Because of the size of this program it will take about 50 seconds to load Fourier Analysis into the Compu Trac system. This slow loading could be eliminated only at the expense of added program complexity. It will become clear in future issues of Technical Analysis that this Fourier Analysis tool has a myriad of applications including selection of moving average lengths and evaluation of other trading systems.
The following line will then appear at the Command line:
1:O 2:H 3:L 4:C 5:V 6:OI 7:S :
This is your prompt to choose which COLUMN of data you wish to run Fourier Analysis against.
1 = 1:O Open Mean open trade price 2 = 2:H High Highest trade price 3 = 3:L Low Lowest trade price 4 = 4:C Close Last trade or bid price 5 = 5:V Volume Number of shares or contracts traded 6 = 6:OI Open Interest Total contracts or optioned shares 7 = 7:S Study Last Study results
Fourier Analysis will preprocess the data in the matrix column of your choice, do the Fast Fourier Transform, and then ask:
1:Power 2:Amplitude Vs. Frequency
This is the prompt for you to specify the type of plot i.e. 1) for Power or 2) for Amplitude (square root of power). The transform result is stored in the Study column. The Compu Trac System then takes over and graphs the Fourier Transform from the study column.
WHAT IS IT (THE FOURLER TRAMFORM)?
1) The X-Axis (from RIGHT to LEFT i.e. 0 to N/2) is the Frequency (complete cycles).
Days in Cycle= N , Frequency
N = Length of FFT series
NOTE: This RIGHT to LEFT graphing method is just the reverse of text book examples, but works best from within the Compu Trac System. To determine the most prominent Frequency, use (from within Compu Trac) Tool Menu (3.) and then Vertical Line (B.). This feature displays the number of points between the right margin (0) and any Frequency plotted to the left by using the Arrow keys or Game Paddle control.
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2) The Y-Axis is the Percent (%) of TOTAL Discrete Fast Fourier Transform Power or Amplitude present at that Frequency. This is a direct relative measure of the detrended data's cyclical price movement as a function of Frequency.
EXAMPLES → INTERPRETATION SUGGESTIONS
A major application of the Fourier Transform is in the design and verification of filters, such as a moving average. With this tool one may 'design' a filter that enhances large component cycles and suppresses minor aberrations or random market noise. Refer to Figure 2 for an example showing the effect of a seven day simple linear moving average on the Fourier Analysis plot output. By comparing this with the raw data Fourier Analysis plot (Figure 1) the moving average filtering effect is apparent.
Figure 3 is a three dimensional representation of a series of Fourier Transforms using different quantities of data. By using the new FFT program we may display one slice of this graph at a time. Each slice is shown as a cut at the WEEKS (of daily data) axis 29, 32, ... ,50, and 53. It is apparent that for this security (IBM prior to September 16, 1982) as the number of weeks of daily data is increased the long cyclical content of the closing prices which were used completely over-powers the effect of shorter cycles.
Let us briefly examine a concrete example, using Fourier Analysis, and propose a few applications and point out a pitfall or two. Look again at Figure 1, the approximate mean highest line in Area A. is a peak area of cycle strength (i.e. 256/21 = 12.2 Day Cycle). This means one of the cycles prominent in this data is about 12 days in length.
USE OF THE AMPLITUDE PLOT:
The relative importance of individual cycles may be approximated by adding the heights of adjacent
histogram bars on either side of the peak. If the Amplitude plot option is used this will be in percent of the total cyclic price movement. The total of all histogram bars has been normalized to equal 100% prior to plotting with both the Power and Amplitude plot options. With the Compu Trac system one may center the 'live cursor' above the peak and review the Fourier study data by using the systems hidden command 'P'. By pressing 'P' the screen will display seven days of historical data centered around the live cursor position. In this case adding the Fourier study results shows about 28% of the cyclic price motion is centered about a 12 Day Cycle. Actually, Area A. encompasses cycle lengths of between 9 to 15 days centered at about 12 days. The 9 to 15 day AREA A. is 28% of the total price motion.
GENERAL RULE:
The Higher The Frequency The More Likely The Cycle Is Important.
That is, when a peak, located AWAY from the right side of the screen. occurs. This means the data has oscillated over and over a number of times in the past. Thus the probability that that cycle is significant is increased the further the peak is located, on our plot, to the left. The fact that we have detected a larger (to the left) frequency of that cycle implies that statistically our sample size, of cycles, is larger and therefore more likely to continue into the future.
For example suppose a peak was found located at 2 lines from the right, on our plot, with N = 256 this would suggest a 128 Day Cycle. But, with the Technical Analysis Fourier program, to obtain an N= 256 we could have used as few as 65 Days of data (see Dr. Warren's article). To have a peak located at a 128 Day Cycle our data would have to be 'shaped' something like Figure 4.
Since Fourier Analysis indiscriminately interprets ANY data as a cycle, this 'Cycle' would
be the most significant (128 days). It should be obvious that, although one could imagine a cycle of this shape (Figure 4) repeating itself, it is hardly statistically important. For Stock or Commodity analysis we need more cycles samples in our data to infer any cyclic continuity into the future. The practical crux of this is that PLOTTED PEAKS IN THE 1 TO (about) 6 FREQUENCY RANGE SHOULD BE USED ONLY WITH A GREAT DEAL OF CAUTION. At a later date we will write about filters and detrending that may be used to help alleviate part of this problem (Highpass, Bandpass, etc.).
A NOTE ABOUT THE EXISTING COMPU TRAC FOURIER ANALYSIS(U.) PROGRAM
The Compu Trac program will Fourier Transform a quantity of daily (weekly, monthly) data equal to a
power of two up to seven (i.e. 27 = 128). Thus N can equal 4, 8, 16, 64 or 128 days of data. If more data is available only the last 128 days will be used. The program allows transformation of the daily close column. This restriction may be circumvented by moving the data, such as the study column, to the close column just prior to Fourier Transform with Tool Menu (3.) and then Move column (G.).
NO DATA PREPROCESSING IS PROVIDED PRIOR TO THE FOURIER TRANSFORMATION.
Without at least some sort of detrending preprocessing the Transform results could be severely skewed toward the long cycle end of the frequency spectrum in a trending market. Thus the system should only be used on sideways markets or one of the oscillatory systems. such as Relative Strength, these are already detrended. The Amplitudes that are displayed are those with the greatest magnitude. The technique used to graph the derived cycles and extrapulate a forecast is an appealing visual experience.
Our routine does not provide its own graphics, but relies on the standard Compu Trac 'Histogram' graphics routine.
Please note that the Compu Trac Fourier Analysis Study has been released for many months. It is much easier for us to revise and improve on an existing idea than research and produce the original.
1. Brigham, E. Oran, The Fast Fourier Transform. Englewood Cliffs, N.J.: Prentice-Hall, 1974.
2. Cooley, J.W., P.A.W. Lewis, and P.D. Welch, "The Fast Fourier Transform and Its Applications," IEEE Trans. Education, Vol. E-12, pp. 27-34, March 1969.
3. Hurst, J.M., The Profit Magic of Stock Transaction Timing. Englewood Cliffs, N.J.: Prentice-Hall, 1970.
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