title: ‘AAEC 5484: Applied Economic Forecasting’ author: “Kush Jenkins” date: 02-23-2025 Homework #2 - Spring 2025 olib ```

Question 2: Assessing Seasonality

  1. Use the ggseasonplot(), ggsubseriesplot(), and ggAcf() functions to explore possible seasonality in the following time series: writing, fancy, a10, h02.

It might be useful to set the max lag in the ACF to 36 so that you can see a fair bit of the patterns in the correlogram.

  1. What can you say about the seasonal patterns?

Seasonality is a characteristic of time series data and refers to periodic and genrally regular and predictable changes that occur over a year. Using the seasonal plot we see that Writing drops in August. Concerning the data Fancy, the data increases in November. Concerning the a10 data, the data falls in February. Finally, concerning the data h02, the data falls in February also. Using the seasonal subseries plot concerning writing and fancy the sesonal subseries data appears to reinforce the results of the sesonal plot. With the variable Writing we see a decline in August and with Fancy we see an increase in the data in November. As far as A10 and H02, we see an increase in Janaury data. Although the seasonal data showed a decrease in February, maybe the research is looking at a seasonal increase in January. The Autocorrelation Function graph further supports the findings for Writing and Fancy, that there is an increase in the outputs beginning in November and exacerbated in Decemeber. As it concerns A10 autocorrelation formula, one can see that the data is showing both trend and seasonality. Finally, H02 autocorrelation function shows the seasonality in the data.

  1. Can you identify any unusual years?

Using the Autocorrelation function, yes. In the Writing data we see some unusual outcomes between 24 and 36 months. The same is the outcomes for the Fancy data. Finally, there are some unusual outcomes for 3 months between the 24th and 36th month for H02.

Question 3: White Noise

goog contains closing stock prices of Google Inc., now Alphabet Inc. (GOOG), from the NASDAQ exchange, for 1000 consecutive trading days between 25 February 2013 and 13 February 2017.

  1. Plot this series and its ACF. Comment on any pattern noticed in both. Does this series look like white noise?

No, because we expect 95% of the spikes in the autocorrelation function to lie within +-1/the square root of T. Here we see the data lies beyond that boundary.

  1. Now, use dgoog <- diff(goog) to compute the daily changes in the index.

  2. Produce an autoplot of dgoog and its ACF. Do the changes in the Daily Google Stock prices look like white noise? A simple yes will not suffice. You will need to explain your conclusion.

Yes, because 95% of the spikes in the ACF lie within the blue dotted lines, meaning they are within +-2/the square root of T.