Anon

164 The Basics of financial economeTrics

Let’s illustrate the robustness of regression through another example.
Let’s create an equally weighted index with the daily returns of 234 Japanese
firms. Note that this index is created only for the sake of this illustration;
no econometric meaning is attached to this index. The daily returns for the
index for period 1986 to 2005 are shown in Figure 8.1.
Now suppose that we want to estimate the regression of Nippon Oil on
this index; that is, we want to estimate the following regression:

RNO = β 0 + β 1 RIndex + Errors

Estimation with the standard least squares method yields the following
regression parameters:

R^2 : 0.1349

Adjusted R^2 : 0.1346

Standard deviation of errors: 0.0213

Beta t-Statistic p-Value

β 0 0.0000 0.1252 0.9003

β 1 0.4533 27.6487 0.0000

0

–0.2

–0.15

–0.1

–0.05

0

0.05

0.1

0.15

500 1000 1500 2000 2500

Days

Returns

3000 3500 4000 4500 5000

FIGURE 8.1 Daily Returns of the Japan Index: 1986–2005