Professor Engle's Contribution
From Toby Baxendale:
As a businessman with a degree in economics, and trying in my spare time to keep up with contemporary developments, I read in my LSE Alumni magazine, that the 2003 Nobel Prize winner, Professor Engle from NYU Stern School of Business, a fellow old Alumni recently spoke at the School. The blurb on Professor Engle says the following: "Professor Engle was cited for his methods of analyzing economic time series with time-varying volatility, a discovery which was a major breakthrough. He found that the concept of autoregressive conditional hetroskedasticity (ARCH) accurately captures the properties of many time series, and then developed methods for statistical modeling of time-varying volatility."
Well, I can hardly pronounce "autoregressive conditional hetroskedasticity," can anyone tell me what it is? What value does the understanding of it have for humanity? Any hints or explanations would be gratefully received.
Comments (9)
Anyone with the cojones to tackle a subject that somehow relates to the Non-constancy of the variance of a measure over the levels of the factor under study should also consider posting the same answer to wikipedia, since they don't know what it is either.
Published: January 27, 2004 4:29 PM
What a coincidence! I just encountered the subject of heteroskedasticty while studying CFA II Quant last night (no joke!). Here's a quick summary.
For any linear regression model, the general equation is
Yi = b0 + b1Xi + ei
Where:
Yi = the ith observation of the dependent variable, Y
Xi = the ith observation of the independent variable, X
b0 = the Y-axis intercept
b1 = the slope coefficient
and ei = the error residual for each observation.
The line of best fit will minimize the sum of the squared errors [min SUM(ei^2)].
Among the many assumptions of linear regression are that the relationship between the dependent and independent variable is, in fact, linear...
the expected value of the error term is zero... E(e) = 0
and the distribution of error terms has a constant variance... s(e)^2 = k
If the variance of the error terms is in fact constant, then the error terms are described as homoskedastic. A violation of this assumption is known as heteroskedasticity.
This is just the basics of the subject. I won't pretend to have a clue about "Autoregressive conditional heteroskedasticity".
Reference: Schweser Study Notes for the 2003 CFA Exam.
Published: January 27, 2004 5:37 PM
CFA II ugh...now you reminded me what I have to look forward to this winter/spring. I've glanced at the books (the pile of books that is) and haven't had the heart to begin the journey just yet.
Published: January 28, 2004 1:25 AM
Here's how I would interpret it:
Autoregressive - Using historical data to predict future data.
Conditional - Dependent on another variable
Heteroskedastic - The variations in the data over time are not uniform.
So Autoregressive Conditional Heteroskedasticity means something like:
Using the past behavior of an independent variable to predict the future variablitily in values of another dependent variable over time.
Basically it's a fancy way of saying what the other sentences in the article say. For instance, "methods of analyzing economic time series with time-varying volatility"
As and example, how much you drink may predict how extreme your mood swings are. Doesn't sound so fancy anymore does it.
If I get a chance I'd like to read about what his methods are.
Published: January 28, 2004 10:45 AM
Let me try a more intuitive explanation:
When trying to reduce a complex relationship into a simple cause and effect type relationships such as the relationship between say, driving speed and the number of car accidents, statisticians might use a model that predicts that an increase in factor X (driving speed) by 1% causes Y (accidents per mile driven) to increase by B%.
In order to estimate B, they would typically assume the difference between the prediction equation and reality is a unpredictable random number that is evenly distributed across odd and even numbers (maybe even distributed like a bell curve). They will also typically assume a constant (expected) variance. Here variance represents the level of dispersion: the greater the variance, the greater the average absolute error and the worse the model performs in predicting reality.
ARCH modeling relaxes the constant variance assumption and models the dispersion of the error term with a second equation. Engel was a pioneer in the coming up with such models in a manner that made the equations somewhat easy to estimate by simply assuming the possible dispersion each period (say in this example, driving each week) is positively related to observed dispersion during the last period.
In this example, weather that has greater variance in winter months than in summer months might create such a correlation in dispersion, and if the statistician did not have a reliable statistic on weather, ARCH modeling could perform the same role—especially if the main goal is to simply estimate B.
This example is very simple and the model is sparse, relative to how it could be formulated, but I hope you get the idea.
Engel’s contributions were even greater in financial modeling were the time variation in dispersion is an important subject in its own right, in the sense that dispersion and risk are related. ARCH modeling has proven itself to be amazingly powerful in capturing time varying risk in financial markets.
Published: January 28, 2004 6:53 PM
Actually your question bears on one of the central issues separating the Austrian School of economics from the so called mainstream approach to 'economic science.' Most of the economics profession is committed to the notion that economics is an empirical science must as physics and chemistry are empirical. For this reason, activities such a econometrics are held in high regard, particularly by academic economists. Needless to say Engle's Nobel Prize is in the field of econometrics.
The Austrian School views this work with disdain and largely disavows the empirical method. Rather than treating human beings as atomic particles or one-celled organisms, the Austrian School stresses the fact that real human being are not automatons but are acting individuals with subjectively selected goals, egos, a capacity for fallibility, and the ability to adapt and change preferences in the face of changing circumstances. The Austrian School believes that human action can be interpreted as rational but insist that this rationality can only be interpreted in the context of the individual's subjectively chosen goals.
One of the best efforts to debunk econometrics by a respected Austrian economist can be found in a paper by Mario Rizzo (Professor of economics at NYU). It appeared in a 1978 book of readings edited by Louis Spadaro. The book is titled New Directions in Austrian Economics. The paper requires a slow reading but gets to the heart of the matter.
Published: January 29, 2004 9:31 AM
While Austrian economists are busy musing in the cloisters on human action, human actors in the real world are using the tools of time series econometrics developed by those nasty lowlife mainstream economists. See Campbell and Lo's classic text on financial econometrics - this stuff is used everyday on Wall Street and the City by financial engineers.
Published: January 30, 2004 3:12 PM
Yes, and humans are minding the models and tweaking the inputs all day long to make sure their trades don't deviate from goals that humans set.
This is not the practice of economics, it's finance: how to aquire money on the markets.
How is it that we still have business cycles?
Published: January 30, 2004 4:40 PM
Austrian economists are not per se disqualified from using econometrics. Only from doing so to TEST economic axioms. There is nothing to prevent an Austrian economist from running regressions the aim of which is to do other than test principles of economics. Yes, few do, but this is due to specialization and comparative advantage, not to any necessary incompatibility. Few Austrian economists play handball. (Some do). This does not mean that there is any necessary incompatibility between praxeology and this particular sport.
Published: January 30, 2004 5:31 PM