In the first few lectures in my Financial Econometrics course I emphasise that analysing financial data should be an iterative learning feedback process, where an initial idea may be modified after some statistical analysis reveals an incomplete or incorrect answer to our initial hypothesis. It is important for my students to understand that econometrics is not about producing ‘black box’ results from statistical software but is a gradual learning pathway which leads to asking the correct question using the correct empirical design and data. This enables the analyst to avoid what Kennedy called Type III errors; getting a statistically precise answer to the wrong question.
After reading Nate Silver’s excellent “The Signal and the Noise” book recently i thought i would illustrate the difficult that technical analyst (or chartists to be more derogatory) have in identifying the real information (signal) from the noise in UK stock markets.
I have taken the FTSE 100 as an example. Below are six prices series. Three of these are 1000 trading days of the FTSE100 in the 1990s, 2000s, and counting back from today. The other three are fakes, and have been generated by simply flipping a coin (actually telling STATA to pick a random series of 1s and Os).
Technical analysis is identifying the signal solely on the basis of past statistical patterns, without consideration for the historical financial characteristics of a company. You can have some sympathy for the difficult task they face in the graphs below, its really difficult to distinguishing the signal (FTSE100 series) from the noise (the fakes or random walks).
Click here to find out which graphs are the FTSE100 and how i used STATA to generate these graphs.
The first assumption of the classic linear regression model is that the dependent (or outcome) variable can be calculated as a linear function of a specific set of independent (or predictor) variables, plus a disturbance term1. This statement implies that the unknown parameters of this linear function are stable or constant over the estimation period. This assumption is particularly important when using a linear regression model to predict.
In practical terms you are assuming the effect of your predictor(s) remains unchanged over the sample period; for relationships between financial variables this may be unrealistic in the presence of large ‘landscape changing’ events. In econometric terms these large events are sometimes called break points.
This instructive video explains in more detail how to test for parameter stability, both when a break point is known and when we cannot clearly identify a break point
Click here for the do file, and here for a copy of the slides.
See Chapter 3 of Kennedy 1998 “A Guide to Econometrics” for an excellent introduction to the five assumptions underpinning classic linear regression models ↩