Time Series Analysis of Stock Market Averages: The New T-Theory

By David Corna

When purchasing a stock, the greatest risk to an investor is what professionals call “Market Risk”.  Market Risk is what is happening to the general market averages like the popular Dow Jones Industrial Average or the S&P 500 Average.  This is why investors avoid buying stocks during a bear market.  No matter how well you select a particular stock, the rise or fall of the general market averages will affect the price of your stock selection.  A rising tide raises all boats and investors are more motivated to buy stocks during bull markets.  It is therefore necessary to determine the general direction of the market when considering the purchase of a selected stock and also the possible duration of the uptrend.  Time Series Analysis is a mathematically based tool used to determine the general market direction and the time and duration the direction will persist.

 My New T–Theory is a form of Time Series Analysis that is derived from the mathematical concept of Symmetry and is so named because of the symmetry of the letter T.  Terry Laundry, an Electrical Engineering graduate of M.I.T., named the T-Theory™  at www.ttheory.com and he has been publishing work about his T-Theory™ on the web for many years.  Terry has successfully applied his T-Theory™ to his investment strategy since 1978 and has handily outperformed the market averages.

There are only three variables in Time Series Analysis; these are Price, Volume and Time.  Price and Volume are the dependent variables while Time is the independent variable.    T Theory™ links price to volume and time by identifying a time period of “cash build-up” market under performance followed by an equal amount of time of superior price appreciation.  Special oscillators based on daily up volume and down volume are used as a proxy for the daily ratio of up volume to down volume.  This oscillator is a tool used to identify oversold conditions and identify the center post of a new T. The left side of the T is a lower probability time period of price appreciation.  The right side of the T is a high probability period of exceptional price appreciation.  The key to success in following the T-Theory™ is to be invested during the time represented by the right side of the T and to either liquidate any positions or drastically reduce positions as the right side of the T expires.  

My New T-Theory addresses shorter-term market moves by applying a unique oscillator to 10-minute intra day charts.  For the swing trader, my New T-Theory provides an easily defined system for entering the market on the long side and also specific stop loss sell orders limiting market losses.  If a new center post has been discovered and a new position established in stocks and the price of the market average drops below the low price of the new center post, all positions should be immediately liquidated.   

Below is a daily chart of the S&P 500 illustrating the symmetry of T’s that are constructed by using my special oscillator that is a proxy for the up volume down volume ratio derived from the intra-day price changes.

This chart of the daily closing price of the S&P 500 average in blue and a special oscillator in orange helps to identify periods of cash build up as well as the center post of the T’s.  Examination of the right side of the T’s demonstrates the exceptional price appreciation of the market averages compared to the left side of the T.  Smaller T’s can be identified within the larger T’s and these smaller T’s are helpful for shorter term trading.  These short term T’s are confirmed by intra day charts of 10-minute periods to be shown later.  To use the New T-Theory to maximize your investment returns simply buy your favorite no load mutual fund or ETF after a new center post has been identified.  Place a stop sell order at the price shown at the bottom of the T.  Hold your position through most of the time period predicted on the right side of the T.  Before the T expires, selectively take profits in your long positions so you are totally out of the trade just before the right side of the T expires.

In the chart below you will notice a red dashed line at the bottom of each T.  This is the stop loss signal.  If a T has been identified and a long position taken in the market and the market average drops below the red dotted line all long positions should be liquidated and aggressive traders can consider a short position.  You can set up an alert on web pages like Yahoo that will notify you when a price is reached on the S&P 500, DIA or the SPY.  When you are notified that the price has dropped below the center post low, all long positions should be liquidated before the close. 

The chart below is an intra day chart of the Diamonds (DIA).  This is an ETF or exchange traded fund representing a portfolio of the stocks equivalent to the Dow Jones Industrial Averages.  One share represents 1/100^th  of the Dow averages.  The Spiders (SPY) is an exchange traded fund that represents 1/10^th of the S&P 500.  These stocks are a proxy for the market averages they represent and the price moves in close concert to the price of the underlying average. 

This 10-minute chart above of the DIA or Diamonds, demonstrates the application of the New T-Theory to the Dow Jones Averages.  The T’s are colored the same as the corresponding T’s on the daily S&P 500 above that.  This chart just takes a microscopic look at the New T-Theory applied to a different market average in different time dimensions.  This exercise demonstrates that the New T-Theory works as a fractal and its application to different averages in different time dimentions results in similar predictions.  This supports the validity of the theory.

In the future I will be posting updated charts of this New T-Theory with timely purchases and sales of ETF’s.  In order to explain in greater detail my New T-Theory, the updated charts will be accompanied by detailed explanations and execution prices of various ETF’s.

DC

Inductive Reasoning verses Deductive Reasoning and why I went wrong!

The difficulty of applying new analytic techniques to stock market analyses is the necessity of using Inductive Reasoning in our investigative process.  Inductive Reasoning is the operating mechanism of the Scientific Method.  Let me first define my terms.  Deductive Reasoning is the process we learned from Euclid when we studied Geometry. Deductive Reasoning of mathematics is an exhaustive process whereby a set of premises (givens) leads us to one and only one unique conclusion we call a Theorem.  A Theorem  is not a Theory.  A Theorem is a unique law of the universe derived through Deductive Reasoning.  A Theory, on the other hand, is a Hypothesis formulated from a series of observations in nature whereby an overwhelming series of valid arguments and experimental repetition form a body of evidence supporting the veracity of the Theory.  Any valid theory is able to predict an outcome within probability limits and demonstrates both causality and coherence. 
  
My New T Theory is based upon observations of an implied symmetry in the ten minute time-price series of The Dow Jones Industrial Average and its special underlying price oscillators.  Because of the verisimilitudes of the chart patterns, I formed a hypotheses that my new T Theory can be applied to more narrow market averages like the S&P Financial Sector average.  In my rush to judgement, I quickly concluded that if the theory worked on a more narrow market average then it could be applied to an individual commodity or a single stock.  Inductive Reasoning has led me to conclude that beyond any qualification or reservation my latest hypothesis is invalid!   DC January 19, 2010

Daily Chart Oscillators Offer a Bullish Look for January 2010

The chart above shows the basic volume oscillator using Terry Laundry's formula to calculate the function.  I have drawn the latest three (3) T's using this oscillator to determine the cash build up phase which is the time duration of the left half of the T.  The right side of the T is the time period where we expect a high probability superior market price appreciation.  As the price chart illustrates, once the middle post of the T has been discovered then the right side of the T is a rising market.  It is said that Genius is a bull market.  I say that true genius is to recognize the bull market.  T Theory cannot forecast the time when the next center post will be places, however, the right side of the center post T is hauntingly accurate at predicting the end of a bull move. My New T Theory has developed some new oscillators that help to quickly recognize a new center post placement or in plainer English, to find the bottom of the downtrend.

Upon close examination of the top chart you will notice that the cacophony of the vicissitudes characterizing the basic volume oscillator function can easily confuse anyone.  As a result, I have developed a series of derivative functions that that more clearly define the new center post placement and can clearly illustrates the cash build up phase.  The above chart illustrates three (3) functions with smoother curves that provide clear visual evidence of the new center post of each T and where the left side of the center post begins.  These new functions are a valuable tool in drawing our T's for T Theory.

The above chart shows further derivative functions that produce oscillators that form a bottom in concert and sometimes form a top simultaneously.  The horizontal lines are drawn at the level of one (1) standard deviation  of the functions. I have drawn double T's to illustrate the different tops each oscillator shows for the cash build up phase.  Both of the latest T's indicate further duration of the bullish persistence of  the Dow Jones Average.  The bullish daily T's combined with the bullish 10 minute T's confirm my bullish positions of Long DIA and BGU and short BGZ put on 1/6/2010.  The DIA is up 1% and BGU and BGZ are up 3% at todays close.

A further refinement of the New T Theory are my directional oscillators.  The oscillators in the above chart will cross each other when confirming a  uptrend.   The red and green oscillators will cross at the center post and at the end of a defined T.  These red and green oscillators are a good indicator for finding the position of a new center post and also confirms the end of a defined T.   Currently these oscillators are in bullish territory.  The outlook for January is very bullish at the present time. The only thing to worry about is a bursting of the bubble in China.  They have built a large inventory of unsold goods for export that the Chinese government is financing.  What will happen when they realize that all this inventory cannot be financed forever.  Someone in the Oxidant has to buy those goods and it is not happening. For now in the American Stock Market it is onward and upward.

Trend Indicator Oscillators

The above chart shows my trend indicator oscillators that are based on a surrogate net volume advance/decline number for every 10 minute interval of the DIA.  When the green line crosses above the red line, a bull trend begins and when the red line crosses above the green line a bearish trend begins.  Each oscillator is a derivative of my basic oscillator.  This trend indicator is more sensitive than the oscillator shown in the chart below.  The trend indicator oscillator shown below is the exact same calculation as the above chart oscillators with the 10 minute last price of the DIA substituted for a net up/down volume substitute.

The above trend indicator signals a new trend as the red line crosses the red line.  As the green line crosses above the red line a bull trend begins and visa-versa.

Terry Laundry Revisited

Terry Laundry has recently explained his concept of Bear T's or Failed T's and more recently Phantom T's.  When a Bear T is discovered, it can be used  as a tool to discover the next center post.  In the above chart, the blue line is the 10 minute last price of the DIA and below it is a derivative oscillator based on the last price.  In the chart, utilizing the price and the oscillator I drew the smallest T and since it failed, the end of the T gave us the center post for the second T.  The second T also failed and I used the end of the second Failed T to mark the center post of the current green T.  This latest green T has proven to be an exceptional Bull T.  If I have interpreted T Theory correctly with this oscillator, The current T will expire at 1:40 PM on Monday
November 16 , 2009.

DIA 10 min close November 11, 2009 with Derivitive Oscillator

DIA 10 min close October 29, 2009 Basic Volume Oscillator

I came across Terry Laundry when reading Marty Schwartz' s book in the late 1990's. Terry called the top of the market in 2000 and I made money on his advise so I became hooked. Unlike Terry, Marty is parsimonious with the details of his trading tools and methods. I have picked up bits and pieces of his details through reading Marty's published interviews. Marty digresses from Terry in that he holds sacred the amplitude of the oscillator in calling tops and bottoms. For this reason I draw the horizontal lines of my charts at each standard deviation of the oscillator. This makes it easier to judge the over-bought and over-sold state of the oscillator.

Since there is no available data to compute the net up and down volume for intra-day time periods i.e. 10 minute periods, I needed to find a unit of study that would approximate this volume data. My basic data-point for intra-day charting is the net arithmetical difference between the 10 minute close and 10 minute low less the 10 minute high and 10 minute close i.e. (close-lo)-(hi-close). (close-lo)= up volume: (hi-close)= down volume. The result is a quantity that represents the net up and down volume for this time period. This is the value I plug into Terry Laundry’s formula for his volume oscillator. You can visit Terry’s blog from my link for a complete description of his formula.

I know this process is valid because I have done extensive calculations using my daily Hi-Lo-Close unit of study and have compared this new oscillator with Terry Laundry’s daily oscillator and my new daily oscillator charts are the exact images of Terry Laundry's oscillator charts. Therefore the 10-minute calculations are valid representations of Terry's Volume Oscillator because the market is a fractal.

The problem with the intraday oscillator is that it does not define well the cash build-up period or where to place the center post of the T. As a result I had to develop a reliable oscillator in order to apply T-Theory to intra-day charts. I have investigated several oscillators that are derivatives of the new volume oscillator and found some that work well.

I will further explain the new oscillators in later posts