Correlation and Causality

By George J. Paulos

Editor/Publisher Freebuck.com

One of the most popular investment themes being promoted for 2005 is the “Year 5 Effect”. The Year 5 Effect is based upon the observation that every year ending in 5 over the last century experienced a stock market advance. Many market analysts have used this observation as a justification for a bullish forecast for 2005. For many people this seems like a strong argument since the statistical evidence is so apparent. There are many such statistical relationships that are commonly used to make predictions about future trends. Does a statistical relationship such as the Year 5 Effect actually influence future events? Let’s examine the facts.

Humans are extraordinarily adept at pattern recognition. We can identify patterns in highly incomplete and distorted data. This is an essential survival skill that animals also possess to a lesser extent. An important type of pattern recognition is called correlation. Correlation is where there is a notable relationship between two or more patterns. A correlation may be visually apparent such an in stock market graphs or revealed by using a statistical technique called regression analysis. The statistical approach gives a quantitative measure of the correlation between different data series.

Measuring correlation via regression analysis is an extremely powerful technique to analyze trends and verify patterns. It is an excellent way to augment our own natural pattern recognition abilities and give them a rigorous methodology. It is used in science, engineering, economics, and many other fields to study data and make predictions. These techniques do have limits however and can be easily misused to make flawed analyses.

One of the most common errors of analysis occurs when correlation is assumed to imply causation. In other words, the analyst claims that because two different trends have highly similar patterns, that they have real influence over each other. Let’s take a simple example. Everybody knows that flipping a coin has a 50/50 chance of hitting heads or tails. It is possible, although highly unlikely, that a coin-flipper could hit 10 heads in a row. After such a run, the coin-flipper could conclude that it is statistically likely that the next flip of the coin would also be heads because of the previous trend. But of course that would be a false conclusion. The coin always has a 50/50 chance of hitting heads regardless of the previous results. The past history of the coin has no influence over the future. The run of 10 heads in a row was a statistical fluke and not likely to be repeated.

Statistical flukes or anomalies are common in large data sets. There is a story about an Economics PhD student who programmed a supercomputer to perform over a million regression analyses on a large data set of economic statistics. From that project, the student uncovered many strongly correlated data series including some ludicrous ones such as a high correlation between the US Dow Jones Industrial Average and milk production in Lithuania. Of course there is no causal relationship between the DJIA and Lithuanian milk, but the correlation was almost perfect. It was a classic statistical anomaly.

Market technicians are fond of doing this same kind of statistical research on financial markets looking for trends and correlations. This type of research is called data mining and is very easy using modern computers and huge market databases. The good thing is that such data mining will find many good correlations and repeating patterns in market prices. The bad thing is that most of these correlations will be statistical anomalies.

So how do we actually identify causality in the markets? There is no mathematical technique to identify whether there is influence between different markets and trends. This is a purely qualitative effort and is in the realm of fundamental analysis. The analyst must identify a mechanism where the various items under study can influence each other. If none can be identified, then the correlation is likely to be an anomaly. On the other hand, correlation can provide excellent confirmation of a suspected causal relationship. This is the essence of the scientific method: Propose a self-consistent theory and then find evidence to support or refute that theory. Statistical analysis can provide good evidence to either confirm or falsify a causal link.

In the case of the Year 5 Effect, is there any possible influence of the fifth year of a decade on stock prices? The Year 5 Effect is an exact ten year cycle. There are many multi-year cycles that are significant to markets. We know that there is a causal influence between the 4-year election cycle and economic activity because of the effect of fiscal policy. There are other yearly and seasonal cycles that are related to tax and funding deadlines. But there is no significant policy cycle that correlates to the fifth year of a decade. No natural or astronomical cycle is tied to a ten-year mid-decade cycle. It is possible that a ten-year social cycle exists, but such a cycle would not be so stable as to maintain perfect symmetry for over a century. In fact, a ten-year mid-decade cycle seems to be an orphan with little intrinsic market meaning.

Investors, however, can be influenced by such artificial cycles. Once identified, investors often tend to follow such conventions because they believe that other investors will do the same. This is not an unreasonable belief being that investors are known to be herd animals. Such reasoning can be self-fulfilling as more and more investors participate. But such a sentiment-led trend can also be self-destructing because it is by definition a market inefficiency that would eventually be arbitraged away.

We can conclude that the Year-5 Effect is probably another statistical anomaly, but one that is now in the investor psyche. If large numbers of investors attempt to play the Year 5 Effect, we can assume that they would invest early in the year then cash out late in the year for a net neutral effect.

Out of any arbitrary year, the markets are up more often than they are down. This is a result of the influence of general economic growth and inflation. From that standpoint 2005 is more likely to be up than down, but that can be said of any year. The last digit of the year has no effect on that.

Although the Year 5 Effect was highlighted in this essay, the same kind of reasoning can be applied to any statistical “fact” about markets. The ability to mine large data sets with fast computers has enabled market technicians to uncover a multitude of patterns and correlations including the Year 5 Effect. Some are meaningful but others are not. Committing money into the markets on the basis of pure statistical relationships is just speculation and is not true investing. Pure statistics do not reveal any truth about the markets and more importantly does not reduce risk. There is no substitute for understanding how markets work and how your invested money is used.

George J. Paulos is Editor/Publisher of Freebuck.com, a website devoted to wealth preservation and enhancement using alternative investing approaches including precious metals. He is also Associate Editor of The Gold Letter, a newsletter covering junior mining and natural resource stocks.

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		Correlation and Causality By George J. Paulos Editor/Publisher Freebuck.com Associate Editor The Gold Letter One of the most popular investment themes being promoted for 2005 is the “Year 5 Effect”. The Year 5 Effect is based upon the observation that every year ending in 5 over the last century experienced a stock market advance. Many market analysts have used this observation as a justification for a bullish forecast for 2005. For many people this seems like a strong argument since the statistical evidence is so apparent. There are many such statistical relationships that are commonly used to make predictions about future trends. Does a statistical relationship such as the Year 5 Effect actually influence future events? Let’s examine the facts. Humans are extraordinarily adept at pattern recognition. We can identify patterns in highly incomplete and distorted data. This is an essential survival skill that animals also possess to a lesser extent. An important type of pattern recognition is called *correlation. Correlation is where there is a notable relationship between two or more patterns. A correlation may be visually apparent such an in stock market graphs or revealed by using a statistical technique called regression analysis. The statistical approach gives a quantitative measure of the correlation between different data series. Measuring correlation via regression analysis is an extremely powerful technique to analyze trends and verify patterns. It is an excellent way to augment our own natural pattern recognition abilities and give them a rigorous methodology. It is used in science, engineering, economics, and many other fields to study data and make predictions. These techniques do have limits however and can be easily misused to make flawed analyses. One of the most common errors of analysis occurs when correlation* is assumed to imply *causation. In other words, the analyst claims that because two different trends have highly similar patterns, that they have real influence over each other. Let’s take a simple example. Everybody knows that flipping a coin has a 50/50 chance of hitting heads or tails. It is possible, although highly unlikely, that a coin-flipper could hit 10 heads in a row. After such a run, the coin-flipper could conclude that it is statistically likely that the next flip of the coin would also be heads because of the previous trend. But of course that would be a false conclusion. The coin always has a 50/50 chance of hitting heads regardless of the previous results. The past history of the coin has no influence over the future. The run of 10 heads in a row was a statistical fluke and not likely to be repeated. Statistical flukes or anomalies are common in large data sets. There is a story about an Economics PhD student who programmed a supercomputer to perform over a million regression analyses on a large data set of economic statistics. From that project, the student uncovered many strongly correlated data series including some ludicrous ones such as a high correlation between the US Dow Jones Industrial Average and milk production in Lithuania. Of course there is no causal relationship between the DJIA and Lithuanian milk, but the correlation was almost perfect. It was a classic statistical anomaly. Market technicians are fond of doing this same kind of statistical research on financial markets looking for trends and correlations. This type of research is called data mining* and is very easy using modern computers and huge market databases. The good thing is that such data mining will find many good correlations and repeating patterns in market prices. The bad thing is that most of these correlations will be statistical anomalies. So how do we actually identify causality in the markets? There is no mathematical technique to identify whether there is influence between different markets and trends. This is a purely qualitative effort and is in the realm of fundamental analysis. The analyst must identify a mechanism where the various items under study can influence each other. If none can be identified, then the correlation is likely to be an anomaly. On the other hand, correlation can provide excellent confirmation of a suspected causal relationship. This is the essence of the scientific method: Propose a self-consistent theory and then find evidence to support or refute that theory. Statistical analysis can provide good evidence to either confirm or falsify a causal link. In the case of the Year 5 Effect, is there any possible influence of the fifth year of a decade on stock prices? The Year 5 Effect is an exact ten year cycle. There are many multi-year cycles that are significant to markets. We know that there is a causal influence between the 4-year election cycle and economic activity because of the effect of fiscal policy. There are other yearly and seasonal cycles that are related to tax and funding deadlines. But there is no significant policy cycle that correlates to the fifth year of a decade. No natural or astronomical cycle is tied to a ten-year mid-decade cycle. It is possible that a ten-year social cycle exists, but such a cycle would not be so stable as to maintain perfect symmetry for over a century. In fact, a ten-year mid-decade cycle seems to be an orphan with little intrinsic market meaning. Investors, however, can be influenced by such artificial cycles. Once identified, investors often tend to follow such conventions because they believe that other investors will do the same. This is not an unreasonable belief being that investors are known to be herd animals. Such reasoning can be self-fulfilling as more and more investors participate. But such a sentiment-led trend can also be self-destructing because it is by definition a market inefficiency that would eventually be arbitraged away. We can conclude that the Year-5 Effect is probably another statistical anomaly, but one that is now in the investor psyche. If large numbers of investors attempt to play the Year 5 Effect, we can assume that they would invest early in the year then cash out late in the year for a net neutral effect. Out of any arbitrary year, the markets are up more often than they are down. This is a result of the influence of general economic growth and inflation. From that standpoint 2005 is more likely to be up than down, but that can be said of any year. The last digit of the year has no effect on that. Although the Year 5 Effect was highlighted in this essay, the same kind of reasoning can be applied to any statistical “fact” about markets. The ability to mine large data sets with fast computers has enabled market technicians to uncover a multitude of patterns and correlations including the Year 5 Effect. Some are meaningful but others are not. Committing money into the markets on the basis of pure statistical relationships is just speculation and is not true investing. Pure statistics do not reveal any truth about the markets and more importantly does not reduce risk. There is no substitute for understanding how markets work and how your invested money is used. *George J. Paulos* is Editor/Publisher of Freebuck.com, a website devoted to wealth preservation and enhancement using alternative investing approaches including precious metals. He is also Associate Editor of The Gold Letter, a newsletter covering junior mining and natural resource stocks. Email Freebuck.com Website The Gold Letter Website TO RETURN TO THE FACTS THE BROKERS, AND THE FINANCIAL REPORTERS, WONT TELL YOU! PAGE



		Enter supporting content here There are always opportunities through which businessmen can profit handsomely if they will only recognize and seize them. J. Paul Getty (1892 - 1976) PITAGORAS INTERNACIONAL SA.