Daily Speculations
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The Sun-Baked Speculator
Tom Ryan
6/3/2005
Redundancy, by
Tom Ryan
From 'Information Theory', S. Goldman, 1953 picked up at library sale for $1
Chapters. Foundations of information & the 2 basic laws Exponential law of choice Intersymbol influence Information Entropy Information energy Noise Negative information Redundancy Reliability and probability Attention span Bandwidth Dimensionality
Redundancy. In counting, it is found that the average information per symbol in a language is always considerably less than its maximum theoretical value stipulated by L to the n power where L is the total number of letters in an alphabet and n is the length of the symbol (in letters). In effect this means that parts of messages usually tell things to the receiver that is already partly known, that is there is some repetition built into the structure of language. The partial or complete repetition of message content which occurs in language is a form of redundancy. It is likely that redundancy, has developed over time thru trial and error with feedback in order to maximize the rate of transfer of knowledge and minimize interpretation error on the part of the receiver and is therefore a fundamental property of all language (and music), .
By coding messages with some redundancy, there is a loss in the maximum rate of transfer of information. However, redundancy is a very useful property of language, for it allows individual errors in the transmission of messages to be easily identified and corrected. Redundancy, in effect, is the primary "noise reducing" mechanism in all languages. In its simplest form, redundancy employs a simple repetition of information over time. Various permutations of redundancy are also common, such as embedding a key piece of information into repeated context or the referral to a previously transmitted message in the subsequent message, which is the basis for all logic. Logic imposes structure within a stream of messages in order to constrain interpretation.
If market prices are information, and I think they are, one could expect that the messages that the market sends to have some redundancy buried within the stream.
To test this simply I looked at a market message that I follow, that is a series of price changes that lead to a 20 day low. I then rolled the tape forward from each 20 day low and looked at the time expired since the previous 20 day low. It has been noted already that the standard deviation of 1,3, and 5 day returns immediately after a new 20 day low are substantially wider than average. This volatility effect diminishes with time expired since the 20 day low, in particular volatility in the past decade has tended to return to longer run averages after about 20 days has expired from the 20 day low. So I looked for repeated messages in the period of time of t=+3 to t=+20 from the last 20 day low. Specifically, I looked at the 1, 3, and 5 day returns during that t+3....20 day period whenever the previous 3 day return was less than 90% (arbitrary) of the 3 day return that had transpired when the 20 day low was set. In other words the market goes down and sets a 20 day low. I noted the 3 day return (obviously quite negative) on that day. Then for the period of 3 to 20 days afterwards I screened for times when the three day return dropped near or below that previously noted negative 3 day return that had occurred when the 20 day low was set.
1997- present, S&P cash
Average 1 day return all days .03% stdev 1.22% Average 1 day return when redundant message received .30% stdev 1.3%
Average 3 day return all 3 day periods (overlapping) .09% stdev 2.1% Average 3 day return when redundant message received .65% stdev 2.2%
Average 5 day return all 5 day periods (overlapping) .15% stdev 2.6% Average 5 day return when redundant message received .87% stdev 2.9%
Maybe I just haven't been listening to the market although like most of the systems I test, there are quite a few knobs to turn and tune on this.
Andrew Moe responds:
Some relevant quotes from Shannon's Mathematical Theory of Communication (1948) follow:
"The redundancy of ordinary English, not considering statistical structure over greater distances than about 8 letters, is roughly 50% ... This has the advantage of allowing considerable noise in the channel. A sizable fraction of the letters can be received incorrectly and still be reconstructed by the context. In fact, this is probably not a bad approximation to the ideal in many cases, since the statistical structure of English is rather involved and the reasonable English sequences are not too far from a random selection."
"An approximation to the ideal would have the property that if the signal is altered in a reasonable way by the noise, the original can still be recovered ... This is accomplished at the cost of a certain amount of redundancy in the coding. The redundancy must be introduced in the proper way to combat the particular noise structure involved. However, any redundancy in the source will usually help if it is utilized by the receiving point. In particular, if the source already has a certain redundancy and no attempt is made to eliminate it (in encoding), the redundancy will help combat noise."
As we are all too well aware, the signals and patterns generated by the markets are rife with noise. Dr. Ryan shows us that repetition can help eliminate some of the noise. I have always considered redundancy to mean confirmation in the form of several different patterns telling me the same thing simultaneously. Perhaps bonds have spiked higher as stocks reach 20 day lows (see late April). We know from Chair's work in thermodynamics that the moves between stocks and bonds are correlated on a weekly basis. Thus, we have confirmation or redundancy from different signals telling us to be bullish.
