In: Statistics and Probability
Marge N. O’Hara, a senior analyst for a large stock brokerage has been tasked to forecast the weekly closing stock prices for this blue-chip stock for the first four weeks of next year. You are assigned to provide technical support to Ms. O’Hara. Weekly closing stock prices for all 52 weeks of this year for this blue-chip stock are reported in units of dollars ($). use mititab or excel 11. Prior to attempting ARIMA modeling, Ms. O’Hara wants to verify that differencing will make the weekly closing stock price data stationary. a. Present a time series plot of the first differences of the weekly closing prices. b. Does this plot appear to show horizontality? Explain why? c. Does this plot appear to show constant variance? (That is, overall, are the first differences of the weekly closing prices confined within a band?) Explain why? d. Can it be concluded that the first differences of the weekly closing prices stationary or nonstationary? Explain why? week, t stock price, y 1 267 2 267 3 268 4 264 5 263 6 260 7 256 8 256 9 252 10 245 11 243 12 240 13 238 14 241 15 244 16 254 17 262 18 261 19 265 20 261 21 261 22 257 23 268 24 270 25 266 26 259 27 258 28 259 29 268 30 276 31 285 32 288 33 295 34 297 35 292 36 299 37 294 38 284 39 277 40 279 41 287 42 276 43 273 44 270 45 264 46 261 47 268 48 270 49 276 50 274 51 284 52 304
Solution a). The first difference time series plot is give below which is drown using excel
b). Yes, horizontality means the general tendency of the data to be parallel to time axis . Here on average the data has mean zero ( an estimation) I.e. the data has a general tendency to cluster round the x axis.
c). Yes the data of first difference show constant variance. We can easily observe from the plot that the spreadness of the data is fairly constant as we move on time as axis.
d). A stationary time series is one with constant mean and variance. Since here also aur data plot shows constant i.e. horizontal mean and faiirl constant variance. So we can interpret the series ( first difference) is stationary.