Part I

1.1a)

1.1b)

1.1c)

1.1d) Seasonal adjustment

Seasonal adjustment is performed to remove the influence of predictable seasonal patterns to determine the underlying trends in a data set.

1.1e) Conclusions

We can use moving averages as a type of seasonal adjustment to see trends in the data. For the J&J data, finding the moving average allows us to see the trends in the data year to year and eliminates the fluctuations we see that are due to the predictable quarterly changes that are repreating each year.

1.3a) Random walk plots

1.3b) Moving average plots

1.3c) Plot comparison

The random walk plots fluctuate much more dramatically than the moving average plots. The random walk plots are generating values that range as far as -40 to 40. We see a mix of plots with upward trends, downward trends, and plots with a mix of increasing and decreasing intervals. The variability of this data makes sense due to the completely random nature of the values that are being generated. In contrast, the moving average plots are appear to follow the same overall pattern of being centered at zero with values that all range between -3 and 3. These plots appear relatively constant with no visible increasing or decreasing trends. By taking the average of 3 Normally distributed values, we are generating a data set that is still Normally distributed and has an even smaller standard devation and thus creates plots that deviate significantly less than the random walk plots.

1.4a)

To me this graph most closely resembles a random walk plot with a positive drift value; there is a clear upward trend in the data and no visible cyclic pattern.

1.4b) Plot GDP growth rate

Both methods of calculating growth rate produce almost identical values, which is to be expected for small return values. We can see on our plot that for points near 0 both methods produce near equivalent values, while for points farther from 0, especially those above 0.03, the log model underestimates the value of the actual return since the higher-order terms that are being ignored have a larger value.

1.4c) Analyzing GDP growth rate

The plot of the GDP growth rate most closely resembles a white noise plot. It is also likely that it could be modeled as an autoregressive series, since it would be logical that the GDP growth of one year would be related to the GDP growth of the next.