The data in Table P-12 are weekly prices for IBM stock.

a. Using a program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations, and the sample partial autocorrelations. Use this information to tentatively identify an appropriate ARIMA model for this series.
b. Is the IBM series stationary? What correction would you recommend if the series is nonstationary?
c. Fit an ARIMA model to the IBM series. Interpret the result. Are successive changes random?
d. Perform diagnostic checks to determine the adequacy of your fitted model.
e. After a satisfactory model has been found, forecast the IBM stock price for the first week of January of the next year. How does your forecast differ from the naive forecast, which says that the forecast for the first week of January is the price for the last week in December (current price)?

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TABLE P-12 Period IBM Period IBM Period IBM Period BM Jan. 6 7 Apr.7 241J.7 258 Oet.6 279 13 287 20 276 27 273 Feb. 3 263 May 5 261 Aug. 4 285 Nov.3 270 10 264 17 261 13 20 27 267 268 264 14 244 21 254 28 262 14 259 21 268 28 276 10 17 24 260 256 256 12 265 19 261 26 261 11 288 18 29S 25 297 24 26 Mar.3 252 Jun. 2 257 Sep 292Dc 270 8 276 15 274 22 284 29 304 10 245 17 243 24 240 31 238 9 268 16 270 23 266 30 259 8 299 15 294 22 284 29 277