actual prices and two predictions -> ANOVA or MANOVA?

#1
Hello everybody,

I'm unsure which stats to use for the following problem:

I've got a list of prices for stocks of a certain date. In that list I also have two predictions for prices for the same date. I want to see which prediction is better and whether there is a difference in predictive power.

So I've got:
actual prices, prices according to predictor A, prices according to predictor B. (>10.000 cases)

A correlation would be unsuitable as I'm not interestet in the relationship between the predictors. My guess is that some sort of ANOVA would be the way forward. I thought about a MANOVA. Am I on the right way?

Cheers,
Paul
 
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trinker

ggplot2orBust
#2
I think what you have is a set of actual values and 2 sets of predicted values.

If so then I'd calculate the coefficient of determination.

Here's how:

\(R^2 = 1 - \frac{SS_{err}}{SS_{tot}}\)

\(SS_{tot} = \sum{(y_i-\bar{y})^2}\) each observation minus the average

\(SS_{tot} = \sum{(y_i-f_1)^2}\) each observation minus predicted

You'd do this for each model. I may go one step further and compare the coefficients of determination with each other. There was a paper written by Olkin and Finn called Correlation Redux that shows how to do this.


This might be my approach others may have different ideas. It's possible if you have an actual model that predicts to compare the models. All you said you had were two sets of predictions though.
 

noetsi

Fortran must die
#3
I would think you could simply do a t test for the mean differences between the predicted and observed values of the two predictors. But I suspect trinker's answer is a lot better:p
 
#5
Hi again,

I've checked the paper recommended by trinker. I don't really think what's explained there is what I need. (But thanks nevertheless). I don't want to know whether any of the predicted prices correlates with the actual prices but which of the list of predicted prices is the closer match to the actual prices. I'm no expert but as I understand it a correlation simply tells me whether the prediction is high/low if the actual price is high/low (or low/high in the case of a negative correlation). That means that prices can still correlate if they actually differ quite a lot in absolute terms. What I need to know is whether the predicted prices significantly differ from the actual prices and which of the two predicted prices is better. The head of my table looks like that: ID | actual price | pedicted price A | predicted price B

I thought about a MANOVA or ANOVA. What makes me unsure is that with ANOVA or MANOVA (i.e. in SPSS) the p-value tells me whether the actual and the predicted price are different. This is the case if p < .05. I actually need p<.05 if the actual and predicted price are NOT different.

Thanks for any suggestions.

Paul