10. Home sales are often considered an important determinant of the future health of the economy. Thus, there is widespread interest in being able to forecast home sales (HS). Quarterly data for HS are shown in the following table in thousands of units (c2p10): Date Home sales (000) per Quarter Mar-89 Jun-89 Sep-89 Dec-89 Mar-90 Jun-90 Sep-90 Dec-90 Mar-91 Jun-91 Sep-91 Dec-91 161 179 172 100 121 144 126 116 138 153 152 130 Mar-92 159 Jun-92 158 Sep-92 159 Dec-92 132 Mar-93 154 Jun-93 183 Sep-93 169 Dec-93 160 Mar-94 178 Jun-94 185 Sep-94 165 Dec-94 142 Mar-95 154 Jun-95 185 Sep-95 181 Dec-95 145 Mar-96 192 Jun-96 204 Sep-96 201 Dec-96 161 Mar-97 211 Jun-97 212 Sep-97 208 Dec-97 174 Mar-98 220 Jun-98 247 Sep-98 218 Dec-98 200 Mar-99 227 Jun-99 248 Sep-99 221 Dec-99 185 Mar-00 233 Jun-00 226 Sep-00 219 Dec-00 199 Mar-01 251 Jun-01 243 Mar-06 285 Jun-06 300 Sep-06 251 Dec-06 216 Mar-07 Jun-07 214 240 a. Prepare a time-series plot of THS. Describe what you see in this plot in terms of trend and seasonality. b. Calculate and plot the first 12 autocorrelation coefficients for HS. What does this autocorrelation structure suggest about the trend? Sep-01 216 Dec-01 199 Mar-02 240 Jun-02 258 Sep-02 254 Dec-02 220 Mar-03 256 Jun-03 299 Sep-03 294 Dec-03 239 Mar-04 314 Jun-04 329 Sep-04 292 Dec-04 268 Mar-05 328 Jun-05 351 Sep-05 326 Dec-05 2.78