Recall:
\[AR(2): y_t = b_0+b_1y_{t-1}+b_2y_{t-2}+ \text{error}\]
Process in Excel. (pls see autoregression.xlsm)
1. Since we want an AR(2), we first get the lag1 and lag2 of the original stock return as shown below.
2. From the Data Ribbon, click Data Analysis on the left side of the Ribbon.
3. Choose Regression, then click OK.
4. For the Input Y Range, choose the original series.
5. For the Input X Range, choose the lag series.
6. Remember to only choose the number of observations that both Y and X have. Unfilled Cells are disregarded. That means for the Y series, we chose B5:B100 and for the X series we chose C5:D100.
7. Click OK.
Results and Interpretation:
With 96 observations, the model resulted to an AR(2) with the linear combination of
\[ y_t = 0.00679131-0.0066908y_{t-1}-0.0486791y_{t-2}+ \text{error}\]
However, The F Statistics shows us that the value is greater than alpha of 0.05. It implies that the model does not fit to the data given. Moreover, the Adjusted $R^2=-0.01$ which implies that only -0.1% of the variance was explained. Furthermore, the betas and the coefficient are not significant as their p-values are greater than alpha of 0.05. These leads us to the analysis that even though we got the model, it is not a good model to begin with. At least we know now how to do regression in Excel. :-)
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