Are Artificial Neural Networks useful tools to analyze stock market performance?

[phk]

In general neural networks serve two important functions. First as pattern classifiers and as second as nonlinear adaptive filters via a "black-box" non-linear regression.

Advantages:
    * A neural network can perform tasks that a linear program can not.
    * When an element of the neural network fails, it can continue without any problem by their parallel nature.
    * A neural network learns and does not need to be reprogrammed.
    * It can be implemented in any application.
    * It can be implemented without any problem.

Disadvantages:
    * The neural network needs training to operate.
    * The architecture of a neural network is different from the architecture of microprocessors therefore needs to be emulated.
    * Requires high processing time for large neural networks.

[Free Trade is managed by the invisible hand.]

what is a non-linear regression?

I am just asking because econometrics/Mathematical economics is perhaps the hardest thing to understand, and I don't even know where to start.

[phk]

what is a non-linear regression?

I am just asking because econometrics/Mathematical economics is perhaps the hardest thing to understand, and I don't even know where to start.

To know what a non-linear regression is we need to know what a linear regression is first.

The purpose of running a linear regression is to find values for a slope and intercept (in high school algebra it was presented as y = mx+b) that can help one fit a line through your observational data.

More formally in Econometrics it is specified as:
Yi = B0 + B1Xi + Ui  

i = [1,n]
Yi is the independent variable.
Xi is the dependent variable.
B0 + B1Xi is the population regression function.
B0 is the intercept of the line.
B1 is the slope of the line.
Ui is the error term.

More precisely, the linear regression program finds values for the slope and intercept that define the line that minimizes the sum of the square of the vertical distances between the points and the line.


An example of Econometrics using a linear regression is Okun's law which shows the relationship between the GDP growth and change in unemployment is approximately linear. This data set shows the law in application to US quarterly data.

However many relationships in economics and other feilds (like biology for example) do not follow a straight line. The relationship is either logarithmic, quadratic, hyperbolic... etc. This is where non-linear regression comes into the picture.

Nonlinear regression is a general technique to fit a curve through your data. It fits data to any equation that defines Y as a function of X and one or more parameters just as above. It finds the values of those parameters that generate the curve that comes closest to the data (minimizes the sum of the squares of the vertical distances between data points and curve). Again the same as above.

The generalized model is Yi = X'iB + Ui. But can take forms like ln(y) = ln(a) + bx.

i is a (row) vector of predictors for the ith of n observations, usually with a 1 in the first position
representing the regression constant.

B is the vector of regression parameters to be estimated.

Ui is a random error.

[Free Trade is managed by the invisible hand.]

how could we use vector auto regression to figure out the effect of monetary policy?

[Beet]

First you need some data about change in money supply, then you need some data about what "effect" you want to measure, for example GDP, price level, unemployment, etc.

Then you need to figure out what equation you want to try to "fit" to the data. In a linear regression, this is done by finding the line such that the total distance squared of the points of your data from the line is minimized. For more complicated regressions you could use a program like Stata to do the fit for you.

[Free Trade is managed by the invisible hand.]

First you need some data about change in money supply, then you need some data about what "effect" you want to measure, for example GDP, price level, unemployment, etc.

Then you need to figure out what equation you want to try to "fit" to the data. In a linear regression, this is done by finding the line such that the total distance squared of the points of your data from the line is minimized. For more complicated regressions you could use a program like Stata to do the fit for you.

Change in the money supply and asset price inflation.

In any event this paper has been somewhat difficult for me because not all the symbols are understandable.
http://www.mitpressjournals.org/doi/pdfplus/10.1162/rest.91.1.1