Question: Problem 1 Use the hw9-p1-p2.csv dataset for this problem. Does the time series have a trend? Does it have seasonality? Problem 2 Use the hw9-p1-p2.csv
Problem 1 Use the hw9-p1-p2.csv dataset for this problem. Does the time series
have a trend? Does it have seasonality?
Problem 2 Use the hw9-p1-p2.csv dataset for this problem. Calculate the
autocorrelation with lag = 3 using the method we discussed in the class.
Problem 3 Use the hw9-p3.csv dataset for this problem. Suppose that you forecast
the time series using the following formula:
S2 = Y1
St = * Yt-1 + (1 - ) * St-1, for t 3
Here, St is the forecast value at time t.
(1). Calculate the RMSE for = 0.1.
(2). Calculate the RMSE for = 0.5.
(3). Which one is better?
For Problem 1, use any tool and justify answer.
For Problem 2 and Problem 3, Use a spreadsheet program, such as Excel, for calculations not a data mining/analysis software or any other tool that calculates the autocorrelation and the RMSE.
hw9-p1-p2.csv
| Y | t |
| 326 | 1 |
| 248 | 2 |
| 425 | 3 |
| 412 | 4 |
| 420 | 5 |
| 505 | 6 |
| 261 | 7 |
| 193 | 8 |
| 200 | 9 |
| 203 | 10 |
| 354 | 11 |
| 307 | 12 |
| 259 | 13 |
| 206 | 14 |
| 58 | 15 |
| 140 | 16 |
| 180 | 17 |
| 199 | 18 |
| 152 | 19 |
| 223 | 20 |
| 105 | 21 |
| 136 | 22 |
| 182 | 23 |
| 111 | 24 |
| 160 | 25 |
| 149 | 26 |
| 305 | 27 |
| 163 | 28 |
| 89 | 29 |
| 73 | 30 |
| 157 | 31 |
| 158 | 32 |
| 212 | 33 |
| 163 | 34 |
| 111 | 35 |
| 157 | 36 |
| 140 | 37 |
| 162 | 38 |
| 177 | 39 |
| 152 | 40 |
| 167 | 41 |
| 172 | 42 |
| 154 | 43 |
| 203 | 44 |
| 142 | 45 |
| 143 | 46 |
| 216 | 47 |
| 177 | 48 |
| 218 | 49 |
| 174 | 50 |
| 165 | 51 |
| 192 | 52 |
| 270 | 53 |
| 214 | 54 |
| 210 | 55 |
| 273 | 56 |
| 182 | 57 |
| 178 | 58 |
| 356 | 59 |
| 304 | 60 |
| 387 | 61 |
| 290 | 62 |
| 353 | 63 |
| 165 | 64 |
| 438 | 65 |
| 338 | 66 |
| 162 | 67 |
| 320 | 68 |
| 320 | 69 |
| 286 | 70 |
| 214 | 71 |
| 296 | 72 |
| 229 | 73 |
| 319 | 74 |
| 212 | 75 |
| 366 | 76 |
| 303 | 77 |
| 213 | 78 |
| 175 | 79 |
| 262 | 80 |
| 262 | 81 |
| 431 | 82 |
| 109 | 83 |
| 571 | 84 |
| 349 | 85 |
| 315 | 86 |
| 365 | 87 |
| 438 | 88 |
| 421 | 89 |
| 174 | 90 |
| 301 | 91 |
| 354 | 92 |
| 288 | 93 |
| 393 | 94 |
| 219 | 95 |
| 416 | 96 |
| 370 | 97 |
| 222 | 98 |
| 168 | 99 |
| 182 | 100 |
| 363 | 101 |
| 443 | 102 |
| 435 | 103 |
| 267 | 104 |
| 235 | 105 |
| 286 | 106 |
| 295 | 107 |
| 419 | 108 |
| 431 | 109 |
| 569 | 110 |
| 340 | 111 |
| 244 | 112 |
| 143 | 113 |
| 542 | 114 |
| 455 | 115 |
| 454 | 116 |
| 515 | 117 |
| 594 | 118 |
| 367 | 119 |
| 450 | 120 |
| 510 | 121 |
| 708 | 122 |
| 753 | 123 |
| 600 | 124 |
| 626 | 125 |
| 465 | 126 |
| 454 | 127 |
| 509 | 128 |
| 409 | 129 |
| 734 | 130 |
| 587 | 131 |
| 570 | 132 |
| 765 | 133 |
| 632 | 134 |
| 518 | 135 |
| 568 | 136 |
| 702 | 137 |
| 550 | 138 |
| 744 | 139 |
| 827 | 140 |
| 821 | 141 |
| 646 | 142 |
| 986 | 143 |
| 968 | 144 |
| 1128 | 145 |
| 1097 | 146 |
| 1216 | 147 |
| 1025 | 148 |
| 1137 | 149 |
| 1243 | 150 |
| 1488 | 151 |
| 1292 | 152 |
| 1139 | 153 |
| 725 | 154 |
| 923 | 155 |
| 1629 | 156 |
| 1761 | 157 |
| 2038 | 158 |
| 2200 | 159 |
| 1809 | 160 |
| 1184 | 161 |
| 2047 | 162 |
| 2495 | 163 |
| 2482 | 164 |
| 2674 | 165 |
| 2841 | 166 |
| 2076 | 167 |
| 1967 | 168 |
| 2263 | 169 |
| 2744 | 170 |
| 2532 | 171 |
| 2288 | 172 |
| 2991 | 173 |
| 2721 | 174 |
| 1785 | 175 |
| 2225 | 176 |
| 3224 | 177 |
| 4464 | 178 |
| 2914 | 179 |
| 2501 | 180 |
| 1166 | 181 |
| 2845 | 182 |
| 4613 | 183 |
| 6477 | 184 |
| 5192 | 185 |
| 5356 | 186 |
| 4747 | 187 |
| 2463 | 188 |
| 3627 | 189 |
| 5675 | 190 |
| 5130 | 191 |
| 5475 | 192 |
| 4968 | 193 |
| 4677 | 194 |
| 3572 | 195 |
| 3720 | 196 |
| 5450 | 197 |
| 4985 | 198 |
| 5632 | 199 |
| 3995 | 200 |
| 4162 | 201 |
| 3760 | 202 |
| 3293 | 203 |
| 4509 | 204 |
| 5655 | 205 |
| 7424 | 206 |
| 2973 | 207 |
| 4060 | 208 |
| 3659 | 209 |
| 6135 | 210 |
| 6887 | 211 |
| 8542 | 212 |
| 3110 | 213 |
| 4358 | 214 |
| 4178 | 215 |
| 6419 | 216 |
| 7136 | 217 |
| 7635 | 218 |
| 7110 | 219 |
| 5396 | 220 |
| 4239 | 221 |
| 4906 | 222 |
| 5278 | 223 |
| 5545 | 224 |
| 5074 | 225 |
| 5657 | 226 |
| 4283 | 227 |
| 3224 | 228 |
| 2567 | 229 |
| 3987 | 230 |
| 4821 | 231 |
| 4935 | 232 |
| 4330 | 233 |
| 3750 | 234 |
| 3477 | 235 |
| 2215 | 236 |
| 3022 | 237 |
| 4222 | 238 |
| 2781 | 239 |
| 3957 | 240 |
| 2546 | 241 |
| 2270 | 242 |
| 1963 | 243 |
| 2186 | 244 |
| 2602 | 245 |
| 2982 | 246 |
| 3378 | 247 |
| 3004 | 248 |
| 1276 | 249 |
| 1319 | 250 |
| 1920 | 251 |
| 2213 | 252 |
| 2228 | 253 |
| 1949 | 254 |
| 1820 | 255 |
| 1480 | 256 |
| 967 | 257 |
| 1322 | 258 |
| 1803 | 259 |
| 1679 | 260 |
| 1822 | 261 |
| 1316 | 262 |
| 1150 | 263 |
| 1114 | 264 |
| 1788 | 265 |
| 1928 | 266 |
| 1734 | 267 |
| 1516 | 268 |
| 1428 | 269 |
| 1248 | 270 |
| 980 | 271 |
| 1553 | 272 |
| 1410 | 273 |
| 1677 | 274 |
| 1495 | 275 |
| 1281 | 276 |
| 892 | 277 |
| 1006 | 278 |
| 1413 | 279 |
| 1589 | 280 |
| 1577 | 281 |
| 1548 | 282 |
| 1508 | 283 |
| 1004 | 284 |
| 1018 | 285 |
| 1640 | 286 |
| 1857 | 287 |
| 1887 | 288 |
| 1880 | 289 |
| 1678 | 290 |
| 1103 | 291 |
| 1476 | 292 |
| 1865 | 293 |
| 2274 | 294 |
| 2301 | 295 |
| 2362 | 296 |
| 1817 | 297 |
| 1464 | 298 |
| 1683 | 299 |
| 2252 | 300 |
| 2455 | 301 |
| 2160 | 302 |
| 2263 | 303 |
| 2912 | 304 |
| 1566 | 305 |
| 2292 | 306 |
| 1938 | 307 |
| 2184 | 308 |
| 2107 | 309 |
| 1831 | 310 |
| 1376 | 311 |
| 1401 | 312 |
| 2004 | 313 |
| 1884 | 314 |
| 1962 | 315 |
| 1694 | 316 |
| 1265 | 317 |
| 1236 | 318 |
| 968 | 319 |
| 1370 | 320 |
| 1431 | 321 |
| 1452 | 322 |
| 1386 | 323 |
| 1085 | 324 |
| 812 | 325 |
| 825 | 326 |
| 1392 | 327 |
| 1260 | 328 |
| 1179 | 329 |
| 1115 | 330 |
| 786 | 331 |
| 481 | 332 |
| 718 | 333 |
| 888 | 334 |
| 1004 | 335 |
| 881 | 336 |
| 795 | 337 |
| 655 | 338 |
| 446 | 339 |
| 472 | 340 |
| 626 | 341 |
| 616 | 342 |
| 337 | 343 |
| 657 | 344 |
| 494 | 345 |
| 281 | 346 |
| 359 | 347 |
| 425 | 348 |
| 538 | 349 |
| 400 | 350 |
| 405 | 351 |
| 287 | 352 |
| 188 | 353 |
| 195 | 354 |
| 382 | 355 |
| 215 | 356 |
| 253 | 357 |
| 203 | 358 |
| 146 | 359 |
| 179 | 360 |
| 100 | 361 |
| 241 | 362 |
| 177 | 363 |
| 216 | 364 |
| 126 | 365 |
| 89 | 366 |
| 100 | 367 |
| 116 | 368 |
| 85 | 369 |
| 121 | 370 |
| 113 | 371 |
| 33 | 372 |
| 44 | 373 |
| 55 | 374 |
| 56 | 375 |
| 82 | 376 |
| 71 | 377 |
| 91 | 378 |
| 41 | 379 |
| 48 | 380 |
| 33 | 381 |
| 68 | 382 |
| 78 | 383 |
| 60 | 384 |
| 56 | 385 |
| 31 | 386 |
| 41 | 387 |
| 63 | 388 |
| 93 | 389 |
| 76 | 390 |
| 79 | 391 |
| 269 | 392 |
| 61 | 393 |
| 99 | 394 |
| 169 | 395 |
| 322 | 396 |
| 191 | 397 |
| 208 | 398 |
| 236 | 399 |
| 269 | 400 |
| 717 | 401 |
| 366 | 402 |
| 457 | 403 |
| 477 | 404 |
| 586 | 405 |
| 1243 | 406 |
| 657 | 407 |
| 598 | 408 |
| 742 | 409 |
| 844 | 410 |
| 2054 | 411 |
| 883 | 412 |
| 962 | 413 |
| 1046 | 414 |
| 1111 | 415 |
| 2587 | 416 |
| 1109 | 417 |
| 1368 | 418 |
| 1228 | 419 |
| 1182 | 420 |
| 2996 | 421 |
| 1254 | 422 |
| 1452 | 423 |
| 1373 | 424 |
| 1459 | 425 |
| 3335 | 426 |
| 1290 | 427 |
| 1400 | 428 |
| 1793 | 429 |
| 1591 | 430 |
| 4081 | 431 |
| 1557 | 432 |
| 1796 | 433 |
| 1593 | 434 |
| 1703 | 435 |
| 5484 | 436 |
| 1362 | 437 |
| 2096 | 438 |
| 1726 | 439 |
| 4752 | 440 |
| 1453 | 441 |
| 2716 | 442 |
| 1999 | 443 |
| 2024 | 444 |
| 4364 | 445 |
| 1283 | 446 |
| 1821 | 447 |
| 1885 | 448 |
| 1784 | 449 |
| 4095 | 450 |
| 1380 | 451 |
| 1448 | 452 |
| 1486 | 453 |
| 1543 | 454 |
| 3283 | 455 |
| 1184 | 456 |
| 1492 | 457 |
| 1532 | 458 |
| 1583 | 459 |
| 4466 | 460 |
| 1471 | 461 |
| 1560 | 462 |
| 1512 | 463 |
| 2815 | 464 |
| 1888 | 465 |
| 1355 | 466 |
| 1267 | 467 |
| 1343 | 468 |
| 3173 | 469 |
| 1115 | 470 |
| 1274 | 471 |
| 1432 | 472 |
| 1245 | 473 |
| 3243 | 474 |
| 1066 | 475 |
| 1290 | 476 |
| 1586 | 477 |
| 1598 | 478 |
| 4039 | 479 |
| 1397 | 480 |
| 1745 | 481 |
| 3708 | 482 |
| 5248 | 483 |
| 1848 | 484 |
| 2650 | 485 |
| 3196 | 486 |
| 2581 | 487 |
| 6801 | 488 |
| 2616 | 489 |
| 2978 | 490 |
| 5058 | 491 |
| 5497 | 492 |
| 2915 | 493 |
| 4838 | 494 |
| 5170 | 495 |
| 5179 | 496 |
| 11199 | 497 |
| 3720 | 498 |
| 5403 | 499 |
| 5472 | 500 |
| 5007 | 501 |
| 11078 | 502 |
| 4039 | 503 |
| 5133 | 504 |
| 5883 | 505 |
| 6345 | 506 |
| 13717 | 507 |
| 5531 | 508 |
| 7817 | 509 |
| 9042 | 510 |
| 10040 | 511 |
| 12983 | 512 |
| 9228 | 513 |
| 15163 | 514 |
| 21137 | 515 |
| 21397 | 516 |
hw9-p3.csv
| Y | t |
| 326 | 1 |
| 248 | 2 |
| 425 | 3 |
| 412 | 4 |
| 420 | 5 |
| 505 | 6 |
| 261 | 7 |
| 193 | 8 |
| 200 | 9 |
| 203 | 10 |
| 354 | 11 |
| 307 | 12 |
| 259 | 13 |
| 206 | 14 |
| 58 | 15 |
| 140 | 16 |
| 180 | 17 |
| 199 | 18 |
| 152 | 19 |
| 223 | 20 |
| 105 | 21 |
| 136 | 22 |
| 182 | 23 |
| 111 | 24 |
| 160 | 25 |
| 149 | 26 |
| 305 | 27 |
| 163 | 28 |
| 89 | 29 |
| 73 | 30 |
| 157 | 31 |
| 158 | 32 |
| 212 | 33 |
| 163 | 34 |
| 111 | 35 |
| 157 | 36 |
| 140 | 37 |
| 162 | 38 |
| 177 | 39 |
| 152 | 40 |
| 167 | 41 |
| 172 | 42 |
| 154 | 43 |
| 203 | 44 |
| 142 | 45 |
| 143 | 46 |
| 216 | 47 |
| 177 | 48 |
| 218 | 49 |
| 174 | 50 |
| 165 | 51 |
| 192 | 52 |
| 270 | 53 |
| 214 | 54 |
| 210 | 55 |
| 273 | 56 |
| 182 | 57 |
| 178 | 58 |
| 356 | 59 |
| 304 | 60 |
| 387 | 61 |
| 290 | 62 |
| 353 | 63 |
| 165 | 64 |
| 438 | 65 |
| 338 | 66 |
| 162 | 67 |
| 320 | 68 |
| 320 | 69 |
| 286 | 70 |
| 214 | 71 |
| 296 | 72 |
| 229 | 73 |
| 319 | 74 |
| 212 | 75 |
| 366 | 76 |
| 303 | 77 |
| 213 | 78 |
| 175 | 79 |
| 262 | 80 |
| 262 | 81 |
| 431 | 82 |
| 109 | 83 |
| 571 | 84 |
| 349 | 85 |
| 315 | 86 |
| 365 | 87 |
| 438 | 88 |
| 421 | 89 |
| 174 | 90 |
| 301 | 91 |
| 354 | 92 |
| 288 | 93 |
| 393 | 94 |
| 219 | 95 |
| 416 | 96 |
| 370 | 97 |
| 222 | 98 |
| 168 | 99 |
| 182 | 100 |
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