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In fact, the optimal gold-stock composition depends on the spectral density of each stock market index, where a stock market index with a stable. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance. A system according to claim 17, wherein the power spectral density is determined by multiplying the square of the fund cumulative growth by the fund. CEMEX IPO PRICE Then choose the largest to the cloud, virtualization either of wheels of demand в important to highlight to point it out in and login. One is policies will. The interface in this.
But ASD by itself is meaningless unless one specifies the impedance of the noisy source. Of course, ASD may be represented as either voltage or current noise; which one is preferred depends on the output impedance: if the source is a voltage source, i. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge.
Create a free Team Why Teams? Learn more. Amplitude spectral density vs power spectral density Ask Question. Asked 1 year, 4 months ago. Modified 11 months ago. Viewed 1k times. Improve this question. Rotos S. Rotos 9 9 silver badges 24 24 bronze badges. Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Improve this answer.
Semoi Semoi 7, 1 1 gold badge 12 12 silver badges 29 29 bronze badges. The long version has deep roots in mathematics i. Do you agree? Sign up or log in Sign up using Google. Sign up using Facebook. The power spectral density analysis provides a clear indication of comparative mutual fund performance. Provisional Patent Application Ser. The present invention relates to selecting and tracking mutual funds and, more particularly, to a method and system for comparing mutual funds according to a power spectral density that incorporates fund growth and stability.
There are three basic factors that affect the performance of a mutual fund, including fund management, market conditions and fund investment strategy. Thus, market timing is often the difference between gain and loss, between one fund and another. Whether this success or failure is a matter of skill or luck is not as important as the results achieved. A profile of the fund manager is, therefore, an important piece of information that should be considered when selecting a mutual fund.
Some of the better known managers are documented in mutual fund research reports, such as Mutual Fund Forecast, Ruykeyser Report, and financial newspapers Wall Street Journal, Investor's Business Daily, etc. The fund manager should have had experience managing the fund under consideration for at least three years, in order to establish a definable record.
Clearly, the real value of stocks had not suffered to that extent from either technical nor fundamental considerations. Newspapers and TV e. Fundamental market analysis refers to the study of corporation profits, debt, cash flow, market share, growth in sales, etc. Mutual fund managers will apply these analyses to whole sectors e. A fund manager must have this flexibility if it is to out-perform most other mutual funds.
Investment strategy applies to each mutual fund and can be discerned from the mutual fund prospectus. Strategies vary from aggressive growth stock funds to U. Government bond funds. Each investment type carries a measure of risk—ALL investments have some degree of risk to the principal amount of investment. Even bank accounts that are insured carry a finite amount of risk—risk that the insurance fund will have sufficient funds to pay off in the event of failure of the bank.
Bank failures occurred frequently in and again in The issue that must be addressed is the amount of risk that one is willing to take with the investment. To reduce the inherent risk in investing in stocks, bonds, real estate, etc. It is not uncommon for a fund to contain several hundred to a thousand stocks at any one time. This is part of the strategy to reduce risk to the investor. It is important to understand the investment strategy of the fund objective and of the manager performance.
The strategy of the fund and the manager is best determined by the annual performance total return on investment relative to the performance of similar funds comparison tends to eliminate variances that all funds experience because of market conditions. This fact should be used to temper frequent swapping of mutual funds, which occurs when a fundamentally sound mutual fund experiences some losses. This is especially true when one changes the investment from a mutual fund to money market funds; being out of the market may mean missing one or more of the big up days that occur without warning.
Unlike stocks, most mutual funds trade only at the closing price each day. It is an objective of the present invention to provide a vehicle for determining which mutual fund s to choose and when to make changes to personal investment strategy. Given that these decisions can be highly emotionally charged, since life savings are involved, it is important to find an approach that can be followed using predetermined decisions, i. The trick to successful investing is to bias the ups and downs in your favor.
Ideally, you want to choose investments that best satisfy two criteria:. To evaluate mutual funds against these criteria, a statistical analysis must be performed. In the 18 th and 19 th centuries, the German mathematician Karl Gauss formulated statistical applications based on the probability theory invented in the 17 th century by Blaise Pascal and Pierre de Fermat. This method consists of calculating the average annual growth of the fund over at least a ten 10 year period, and calculating the standard deviation of that growth over the same period.
Three standard deviations plus the average would not occur more than 0. Using probability of occurrence as a measure of risk associated with an investment, one can determine performance limits of a fund that correspond to a desired level of risk. For younger investors, higher levels of risk are more appropriate than they are for older investors, simply because they have more years ahead of them in which to recover from temporary set backs.
Thus, three standard deviations 3 sigma might be more appropriate at retirement and one sigma when first employed. This is the foundation of the method according to the invention to evaluate mutual funds and determine appropriate investments.
Reference: The World Book Encyclopedia. When selecting mutual funds, most analysts recommend investing in no more than five 5 funds, as more funds will not reduce risk because of the broad number of stocks that each fund owns. For example, a balance of an aggressive growth stock fund and a balanced equity fund will lower overall risk of a down market where growth stocks suffer the most and equity funds—those that invest in stable, dividend-paying stocks and bonds—suffer the least.
This invention is unique in at least two respects. First, this invention incorporates a power spectrum engineering analysis technique that may not be apparent to most personnel in the financial world e. Bridging the gap from engineering to financial domains is an important aspect of the invention.
Second, this invention incorporates probability and statistical analysis in a way not heretofore documented or disclosed. The utility of probability and statistical analysis as claimed herein provides investors with specific guidance that is useful in the timing of buying and selling investments for near-optimum results—investments of all types, not just mutual funds.
In accordance with an exemplary embodiment of the invention, a method of comparing mutual funds includes determining a power spectral density PSD of respective mutual funds according to fund cumulative growth G and fund stability S. The mutual funds are ranked from highest to lowest power spectral density. The method may further include tracking a selected mutual fund according to upper and lower control limits that are determined based on a standard deviation of the selected mutual fund performance average.
Similarly, the second track is preferably a current track of one to three years in daily increments, wherein the method further includes determining upper and lower control limits for the current track based on a standard deviation of the selected mutual fund daily performance average over multiple days of performance data. The upper and lower control limits may be determined based on two standard deviations of the selected mutual fund performance average, and timing of an investment or divestment in the selected mutual fund can be determined according to a price of the selected mutual fund relative to the upper and lower control limits.
In accordance with another exemplary embodiment of the invention a method of comparing mutual funds includes determining a power spectral density PSD of respective mutual funds according to a product of a principle factor squared times fund stability S. In accordance with yet another exemplary embodiment of the invention, a system for comparing mutual funds includes structure for determining a power spectral density PSD of respective mutual funds according to fund cumulative growth G and fund stability S , and structure for ranking the mutual funds from highest to lowest power spectral density.
These and other aspects and advantages of the present invention will be described in detail with reference to the accompanying drawings, in which:. In the description below, as would be apparent to those of ordinary skill in the art, the described calculation and graphical representations are performed by a computer or other automated means. In accordance with the present invention, a power spectral density analysis is applied to mutual fund historical data to compare, rank, select and track mutual funds.
A power spectrum of density is created from data such as annual growth performance of a mutual fund and plotted over the entire fund-spectrum to determine peak occurrences. As used in communications and structures, the spectrum of frequency is created to locate via peaks in the power spectral density plot resonant frequencies. As applied to mutual fund data, key attributes of mutual funds such as cumulative growth and stability over the spectrum of possible mutual funds are used to locate the best performing fund s.
Preferably, the principal factor is cumulative growth G of the fund since the inception of the fund or over some other predetermined period of time. Stability S is also an important factor in determining the power spectral density. In the context of a mutual fund, stability equals the average annual growth of the fund over a set period of time, preferably at least a ten year period, minus a standard deviation of that growth over the same period.
Two periods are examined: a 17 year long term and the most recent five years. Comparing results from those two periods indicates consistency of performance, especially when compared with similar analysis for other funds.
Thus, one can expect that Magellan will not achieve more than a In fact, Magellan exceeded It achieved less than 4. Both occurrences are well within the determined limits. Ultimately, this is the only factor that matters at retirement; but, along the way, many investors drop out of the investment when large negative performance occurs. It is this reason that Gaussian statistics are so important—they forecast ahead of time what to expect, especially on the downside, so that the investor does not become unduly discouraged and drop-out.
Looking at the most recent five years for comparison, note that the average increased approx. Applying this rule would have resulted in switching from Magellan to a better performing fund in Fund size influences performance. NOTE: Magellan changed fund managers again in June ; since then, its performance has improved considerably. Applying the PSD analysis to a number of highly regarded mutual funds gives the best recommendation of which fund s to own, with least risk.
See FIG. As shown in FIG. Fidelity Select-Computers and Janus 20 funds are very similar in holdings to Electronics. The Fidelity ContraFund is currently closed to investors, keeping that fund limited in size so that it can continue to achieve its excellent record of growth without having the fund become too large.
Remember, fund size affects performance. The next best fund, after ContraFund, is the Fidelity Magellan fund, which has returned to high performance since changing its management. The Merrill Lynch Growth fund has been another top performer over the years. Even the best of funds can make mistakes, and thus, it is important to track fund performance, to observe unexpected changes in time to make adjustments before losing significant value.
A time-history comparison of funds is an important tool used to spot those funds that are performing poorly compared to other funds that are rising with the market. When that happens, it may be time for a change. The basis for tracking investments developed using the method according to the invention is also a statistical analysis applied to past history of the investment. While there can be no guarantee that future performance will be indicative of past history, statistical analysis can provide the probability that the investment can repeat that history.
Normal Gaussian probability analysis can be applied to investments found in the U. This positive bias is the steady-state component of a complex total response to various market stimuli that includes a truly random component. Investments are preferably tracked on two different time scales. A global track on the one hand is the annual total return produced by the investment, tracked annually for as many years as data is available 10 or more years, if possible.
In the special case for pure real input, the amplitudes of the positive frequencies are conjugated complex values of the amplitudes of the negative frequencies. For that, only the frequencies of the positive spectrum are calculated, which means that the number of the complex output values is the half of the number of real input values.
If your input is a simple sinewave, the spectrum contains only a single frequency component. This is true for 10, , or even more input samples. All other values are zero. So it doesn't make any sense to work with a huge number of input values.
If the input data set contains a single period, the complex output value is contained in out. If the If the input data set contains M complete periods, in your case 5, so the result is stored in out. To get the power of a frequency, you have to consider the positive frequency as well as the negative frequency. However, the plan r2c delivers only the right positive half of the spectrum. So you have to double the power of the positive side to get the total power.
By the way, the documentation of the fftw3 package describes the usage of plans quite well. You should invest the time to go over the manual. As you must know, the PSD is the Fourier transform of the autocorrelation function. With sine wave inputs, your AC function will be periodic, therefore the PSD will have tones, like you've plotted. My 'answer' is really some thought starters on debugging. It would be easier for all involved if we could post equations.
You probably know that there's a signal processing section on SE these days. First, you should give us a plot of your AC function. Lastly, trying inputting white noise. You can use a Bernoulli dist, or just a Gaussian dist. The AC will be a delta function, although the sample AC will not. This should give you a sample white PSD distribution. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge.
Create a free Team Why Teams? Learn more. Calculating the Power spectral density Ask Question. Asked 7 years, 11 months ago. Modified 7 years, 11 months ago. Viewed 9k times. Improve this question. Engine Engine 5, 15 15 gold badges 76 76 silver badges bronze badges. In the first program you seem to declare time and use zeit.
This should not compile, unless your compilers knows german. Engine You are opening "sinvalues" in read mode rb and doing fwrite on it. Shouldn't you be using "wb" while doing fopen? I rewrote the program and I forgot to correct this my the sinvalues are correct thanks — Engine. How much did you 'rewrite'? As posted, it is generating a sin at the sampling rate which is identically 0 if the initial phase is 0.
Show 1 more comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. ADD-ON: Your test program generates samples of a sinusoid signal and then you read and analyse the first samples of this signal.
Improve this answer. Hartmut Pfitzinger Hartmut Pfitzinger 2, 3 3 gold badges 27 27 silver badges 48 48 bronze badges. I don't need it. It's only useful to make the number of spectral lines absolutely clear. You can skip it. It's just because you asked in a comment of your program "why only tell the half size of the window".
That's the reason. Please update the test signal creation program. You are creating values of a frequency 5 which means nothing. And you are reading the first values of it. So, you can't expect that there is an integer number of periods inside these values. You should create a test signal with e. Then, it should look as expected: one spectral line with lot of energy and the others close to 0. See my more verbose explanations in the add-on part. The time history in Figure It was also band-limited via low-pass filtering such that it has a roll-off beginning at about 85 Hz.
Filtering is covered in Section The vehicle was driven on a highway at 65 mph. An accelerometer time history from this road test is given in Figure 1. The PSD is shown in Figure The fundamental mode damping is calculated via the half-power bandwidth method in Figure 1. The Taurus auto spring-mass Frequency is 1. Common automobile natural frequencies are given in the following table. The spectral peaks in Figure 1.
The method for synthesizing a time history to satisfy a PSD are shown in Table 1. These steps are used to synthesize an acceleration time history to satisfy the Navmat P specification. The resulting broadband random time history is shown in Figure It began as white noise but was modified such that the final time history is no longer white noise. Its final, corresponding PSD is shaped and defined over a finite frequency domain, as shown in Figure White noise would have a flat PSD in contrast.
The synthesized time history satisfies the specification well within the tolerance bands. The frequency step is 2. Each of the three response time histories has a stable oscillation about its zero baseline. Each also has a brief fade in and out, which could be seen in a close-up view of the start and finish.
Solve for the acceleration response in the time domain using the synthesized base input. The numerical engine is the Smallwood ramp invariant digital recursive relationship. The response time history is shown in Figure 1. The overall response of The theoretical crest factor for this case per equation The time domain synthesis method could whimsically be referred to as a Rube Goldberg approach, after the famous inventor and cartoonist.
The base input is broadband random vibration. The response acceleration and velocity time histories are narrowband random. The SDOF system prefers to oscillate at its natural frequency. The positive slope zero cross rate is The response PSD tracks the input at the low frequency end with nearly unity gain.
The resonant response occurs at and near the Hz natural frequency. Compare Figure 1. But this is a special case of an SDOF system subjected to base excitation. A more robust method for estimating the Q value, as if this were experimental data, is to use the half-power bandwidth method shown in Figure 1. The Miles equation is widely used due to its simplicity, but its assumption of white noise over an infinite domain does not exist in physical reality.
A rule-of-thumb states that it may be used if the input PSD is flat within one-octave on either side of the natural frequency. In practice, this rule is used with some compromise. The overall response is. Real-world PSD specifications are shaped and have lower and upper frequency limits. The problem is exacerbated if the PSD is from narrowband measured data with peaks and dips. These practical characteristics can be readily accounted for by applying the power transmissibility function to the base input PSD and then by doing a point-by-point multiplication calculate the response PSD.
The overall response is then the square root of the area under the response PSD curve. The power transmissibility is equal the transmissibility squared. Equation The overall response in Figure 1. It is also very close to the time domain overall response in Table 1. The general method would yield a more accurate result if the natural frequency fell on either of the input PSD slopes.
Power Spectral Density. Figure 2. Table 2. The overall level is the square root of Power spectral density functions of measured data may be calculated via three methods:.
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