As a further illustration of the ARCH effect, Figure 22.8 presents monthly percentage change in the NYSE (New York Stock Exchange) Index for the period 1952-1995.24 It is evident from this graph that the percent price changes in the NYSE Index exhibit considerable volatility. Notice especially the wide swing around the 1987 crash in stock prices.
To capture the volatility in the stock return seen in the figure, let us considera very simple model:
where Yt = percent change in the NYSE stock index and ut = random error term.
Notice that besides the intercept, there is no other explanatory variable in the model. From the data, we obtained the following OLS regression:
What does this intercept denote? It is simply the average percent rate of return on the NYSE index, or the mean value of Yt (can you verify this?). Thus over the sample period the average monthly return on the NYSE index was about 0.0069 percent.
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