This is an interesting take on quantitative research:

I was perusing some stock charts and noticed this chart:

Citigroup appeared to be making some sort of parabolic or logarithmic bottom just from visual inspection. So I decided to run a regression on the data since Oct 2007. Excel allows you to run regressions in the Data Analysis toolpak or after building a chart through the 'add trendline' option. I just used the 'add trendline' option.

There are several types of trendlines to choose from; linear, exponential, power, logarithmic, polynomial, and moving average so I decided to test several of these. Posted below are the charts with trendlines and regression equations with r-squared.

Order 3 Polynomial

Order 2 Polynomial

Exponential

Logarithmic

The logarithmic and polynomial functions appeared to have the best fit lines, however they come with different conclusions. The logarithmic function will never ultimately turn up. It will continue into infinity. Therefore I eliminated this as a useful predictive model. The polynomial functions were of the 2nd and 3rd order. The 2nd order function had a slight turn up at the end of the data which suggested that we might be seeing a bottom in citigroup stock. The 3rd order function had a slight turn down suggesting that we might get another leg down in the near future. Based on my bias that it appeared the stock is decelerate its descent I would tend to think that a bottom is relatively close and I would expect the stock to at least level off if not make a u shaped bottom.

Note the correlations on these models. All are above .8, however the usefulness of these models is based on the analysis of the model developer. Both polynomial models had correlations near .9, suggesting that the variance in price of citigroup stock over this time period could be explained by this model. It might be interesting to study other bottoms in the past to see how they differ or relate to this bottom.

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