MBA 728 – Fall AP1 2021 Project 2 Due: Sunday, September 26, 11:59 PM CST ※ Using the R script, answer the following questions. Please show all works for full credit. ※ Please install and load the following package as follows. install.packages("astsa") library(astsa) 1. Run the following code: set.seed(150) x <- arima.sim(model = list(ar = c(0.4, 0.35), ma = c(0.5, 0.7)), mean = 0, n = 150) a) [3 points] What model is this simulation about? (that is, what are p, d, and q in ARIMA(p, d, q)? ) b) [2 points] Show the first five rows of ‘x’. c) [2 points] Plot the series ‘x’ you obtained from the simulation. d) [3 points] Plot the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF). Explain how they look like. 2. Consider ‘x’ you have obtained in previous question. Suppose that you do not know what model the data ‘x’ were generated from. After looking at ACF and PACF, you decided to try to fit the following models to ‘x’ : AR(1), AR(2), MA(1), MA(2), ARMA(1, 1), ARMA(1, 2), ARMA(2, 2), and ARMA(2, 3). a) [5 points] Fit each model you have decided to run. Find the best model in terms of AIC and BIC criteria. b) [5 points] Explain about the significance of coefficients for all models. Is the best model you selected in part a) reconciled? b) [5 points] Check the residual plots of the best model you chose in part a). Explain all the plots. Are the residuals white noise or not? This material is only for the use of students enrolled in MBA 728 for purposes associated with the course and may not be retained or further disseminated. All information in this material is proprietary to Dr. Sung Ik Kim. Scanning, copying, posting to a website or reproducing and sharing in any form is strictly prohibited. 3. [25 points] Please use the following instructions. - Find ANY STOCK you want to research. You can find ticker symbol from Google, Yahoo! Finance, MSN money, and so on (i.e. The ticker symbol of Apple Inc. is “AAPL”). - Run the following steps. 1) Install package ‘quantmod’ and load it. install.packages("quantmod") library(quantmod) 2) From Yahoo! Finance, download daily prices of the stock (from Jan. 1, 2005 to Dec, 2019) you selected to research. You can run the following codes to download daily prices of the stock if you chose Apple Inc (The ticker symbol: AAPL). getSymbols("AAPL", src = "yahoo", from = ' XXXXXXXXXX', to = ' XXXXXXXXXX') Please note that you have full length of daily prices. If not, consider other stock. 3) Obtain monthly log stock returns. For instance, if you decide to do research on Apple Inc. whose ticker is “AAPL”, then you will need to run the following: AAPL.rtn <- monthlyReturn(AAPL$AAPL.Adjusted, subset=NULL, type='log', leading=TRUE) 4) Change the data type to ts. Again, for example, if you decide to do research on Apple Inc., rtn <- ts(AAPL.rtn, frequency = 12, start = c(2005,1)) - Using monthly time series data rtn you obtained above, find a best model for the series. For example, AR(1), AR(2), MA(3), ARMA(2, 3), ARIMA(2, 1, 4), or WAHTEVER. Justify your selection for a best model, using all knowledge you have learned so far in this course.