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I am performing regression on the financial data

(dependent variable is the MSCI AC World Financials and independent variables are the MSCI North America Financials, MSCI Europe Financials, MSCI Pacific Financials, and MSCI Emerging Markets Asia Financials).

The data is here: see the excel file online

Then I use Python to calculate cook's distance

x_data = my_data[['MSCI N AMERICA FINANCIALS', 'MSCI EUROPE FINANCIALS', 'MSCI PACIFIC FINANCIALS', 'MSCI EM ASIA FINANCIALS']]
y_data = my_data['MSCI WORLD FINANCIALS']
model = sm.ols(endog = y_data, exog = x_data)
fitted = model.fit()
influence = fitted.get_influence()
(c,p)=influence.cooks_distance
plt.stem(np.arange(len(c)), c, markerfmt=",")

enter image description here

I was expecting the 32nd data point (9/30/2002) to have a high Cook's distance because that's when the market lost its value most compared to other dates (the dependent variable was -0.14559 while the independent variables were -0.12523, -0.23832, -0.02796, and -0.16854). But it seems like, based on the picture, the most influential data point was the 7th one (8/31/2000), which does not make much sense to me.

I would greatly appreciate it if someone could explain the intuition behind this?

Thank you very much.

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... to have a high Cook's distance because that's when the market lost its value most compared to other dates

Your statement describes a data point that tend to be away from the rest of the data. This concept is not really expressed by Cook's distance, but rather by "leverage". If you make a leverage plot, you'll see that 32nd point does have a very high leverage.

Yet, high leverage is only part of the game. Just because it's an extreme point does not elevate it automatically to be an influential point that tilts the regression results. There are generally two outcomes: a high leverage point that happens to be well predicted (aka, has low residual) and a high leverage point that happens to be badly predicted (aka, has high residual.) The former one does not tend to have high Cook's distance, the latter does.

In this case, if you check the standard residual, the 32nd point is well within $\pm$1 standard deviation. It's well predicted. While the 7th point is -2 SDs away.

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  • $\begingroup$ hi penguin, thank you very much for your comment. So you are saying that although 7th point is low leverage, it is badly predicted (aka high residual)? How should I go about analyzing the 7th point? $\endgroup$ – Jun Jang Aug 15 '18 at 19:21

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