date / US NSA month /US SA year

1/1/2005 0:00 92 1203

2/1/2005 0:00 109 1319

3/1/2005 0:00 127 1328

4/1/2005 0:00 116 1260

5/1/2005 0:00 120 1286

6/1/2005 0:00 115 1274

7/1/2005 0:00 117 1389

8/1/2005 0:00 110 1255

9/1/2005 0:00 99 1244

10/1/2005 0:00 105 1336

11/1/2005 0:00 86 1214

12/1/2005 0:00 87 1239

1/1/2006 0:00 89 1174

2/1/2006 0:00 88 1061

3/1/2006 0:00 108 1116

4/1/2006 0:00 100 1123

5/1/2006 0:00 102 1086

6/1/2006 0:00 98 1074

7/1/2006 0:00 83 965

8/1/2006 0:00 88 1035

9/1/2006 0:00 80 1016

10/1/2006 0:00 74 941

11/1/2006 0:00 71 1003

12/1/2006 0:00 71 998

1/1/2007 0:00 66 891

2/1/2007 0:00 68 828

3/1/2007 0:00 80 833

4/1/2007 0:00 83 887

5/1/2007 0:00 79 842

6/1/2007 0:00 73 793

7/1/2007 0:00 68 778

8/1/2007 0:00 60 699

9/1/2007 0:00 53 686

10/1/2007 0:00 57 727

11/1/2007 0:00 45 641

12/1/2007 0:00 44 619

1/1/2008 0:00 44 627

2/1/2008 0:00 48 593

3/1/2008 0:00 49 535

4/1/2008 0:00 49 536

5/1/2008 0:00 49 504

6/1/2008 0:00 45 487

7/1/2008 0:00 43 477

8/1/2008 0:00 38 435

9/1/2008 0:00 35 433

10/1/2008 0:00 32 393

11/1/2008 0:00 27 389

12/1/2008 0:00 26 377

1/1/2009 0:00 24 336

2/1/2009 0:00 29 372

3/1/2009 0:00 31 339

4/1/2009 0:00 32 337

5/1/2009 0:00 34 376

6/1/2009 0:00 37 393

7/1/2009 0:00 38 411

8/1/2009 0:00 36 418

9/1/2009 0:00 30 386

10/1/2009 0:00 33 396

11/1/2009 0:00 26 375

12/1/2009 0:00 24 352

1/1/2010 0:00 24 345

2/1/2010 0:00 27 336

3/1/2010 0:00 36 381

4/1/2010 0:00 41 422

5/1/2010 0:00 26 280

6/1/2010 0:00 28 305

7/1/2010 0:00 26 283

8/1/2010 0:00 23 282

9/1/2010 0:00 25 317

10/1/2010 0:00 23 291

11/1/2010 0:00 20 287

12/1/2010 0:00 23 326

1/1/2011 0:00 21 307

2/1/2011 0:00 22 270

3/1/2011 0:00 28 300

4/1/2011 0:00 30 310

5/1/2011 0:00 28 305

6/1/2011 0:00 28 301

7/1/2011 0:00 27 296

8/1/2011 0:00 25 299

9/1/2011 0:00 24 304

10/1/2011 0:00 25 316

11/1/2011 0:00 23 328

12/1/2011 0:00 24 341

1/1/2012 0:00 23 335

2/1/2012 0:00 30 366

3/1/2012 0:00 34 354

4/1/2012 0:00 34 354

5/1/2012 0:00 35 370

6/1/2012 0:00 34 360

7/1/2012 0:00 33 369

8/1/2012 0:00 31 375

9/1/2012 0:00 30 385

10/1/2012 0:00 29 358

11/1/2012 0:00 28 392

12/1/2012 0:00 28 399

1/1/2013 0:00 32 446

2/1/2013 0:00 36 447

3/1/2013 0:00 41 444

4/1/2013 0:00 43 441

5/1/2013 0:00 40 428

6/1/2013 0:00 43 470

7/1/2013 0:00 33 375

8/1/2013 0:00 31 381

9/1/2013 0:00 31 403

10/1/2013 0:00 36 444

11/1/2013 0:00 32 446

12/1/2013 0:00 31 433

1/1/2014 0:00 33 443

2/1/2014 0:00 35 420

3/1/2014 0:00 39 405

4/1/2014 0:00 39 403

5/1/2014 0:00 43 451

6/1/2014 0:00 38 418

7/1/2014 0:00 35 402

8/1/2014 0:00 36 456

9/1/2014 0:00 37 470

10/1/2014 0:00 38 476

11/1/2014 0:00 31 442

12/1/2014 0:00 35 497

1/1/2015 0:00 39 515

2/1/2015 0:00 45 540

3/1/2015 0:00 46 480

4/1/2015 0:00 48 502

5/1/2015 0:00 47 502

6/1/2015 0:00 44 480

7/1/2015 0:00 43 506

8/1/2015 0:00 41 518

9/1/2015 0:00 35 456

10/1/2015 0:00 39 482

11/1/2015 0:00 36 504

12/1/2015 0:00 38 546

1/1/2016 0:00 39 509

2/1/2016 0:00 45 515

3/1/2016 0:00 50 526

4/1/2016 0:00 55 571

5/1/2016 0:00 53 560

6/1/2016 0:00 50 558

7/1/2016 0:00 54 639

8/1/2016 0:00 46 584

9/1/2016 0:00 44 567

10/1/2016 0:00 46 577

11/1/2016 0:00 40 571

12/1/2016 0:00 39 561

1/1/2017 0:00 45 585

2/1/2017 0:00 51 597

3/1/2017 0:00 61 631

4/1/2017 0:00 56 589

5/1/2017 0:00 57 613

6/1/2017 0:00 56 620

7/1/2017 0:00 48 565

8/1/2017 0:00 45 560

9/1/2017 0:00 50 638

10/1/2017 0:00 49 627

11/1/2017 0:00 50 712

12/1/2017 0:00 45 657

1/1/2018 0:00 48 622

2/1/2018 0:00 54 637

3/1/2018 0:00 66 662

4/1/2018 0:00 61 637

5/1/2018 0:00 62 657

6/1/2018 0:00 56 613

7/1/2018 0:00 52 617

8/1/2018 0:00 47 598

9/1/2018 0:00 46 596

10/1/2018 0:00 43 552

11/1/2018 0:00 44 614

12/1/2018 0:00 38 564

1/1/2019 0:00 49 637

2/1/2019 0:00 57 665

3/1/2019 0:00 68 700

4/1/2019 0:00 64 664

5/1/2019 0:00 56 600

6/1/2019 0:00 66 726

7/1/2019 0:00 55 661

8/1/2019 0:00 57 706

9/1/2019 0:00 56 726

10/1/2019 0:00 55 706

11/1/2019 0:00 50 696

12/1/2019 0:00 49 731

1/1/2020 0:00 59 774

2/1/2020 0:00 63 716

3/1/2020 0:00 59 612

4/1/2020 0:00 52 570

5/1/2020 0:00 64 698

6/1/2020 0:00 79 840

7/1/2020 0:00 85 979

8/1/2020 0:00 81 977

9/1/2020 0:00 77 965

10/1/2020 0:00 78 965

11/1/2020 0:00 61 857

12/1/2020 0:00 62 919

1/1/2021 0:00 73 948

2/1/2021 0:00 64 775

Let's practice time-series forecasting of new home sales. Click here (https://www.census.gov/construction/nrs/historical_data/index.html) to see the newest data in the first table: Houses Sold (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2005, so delete the earlier observations, and use the data through February 2021. Keep only the US data, both the seasonally unadjusted monthly (column B) and the seasonally adjusted annual (column G). Make a new column of seasonally adjusted monthly by dividing the annual data by 12. Make a column called "t" where t will go from 1 (Jan. 2005) to 194 (Feb. 2021); make a t² column too (since, if you look at the data, you can see sales are U-shaped; hence the quadratic). Also make a column "D" that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with straight lines) of both. Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Run four regressions: 1) seasonally unadjusted monthly as the dependent, and t and t² as the independents, 2) seasonally unadjusted monthly as the dependent, and t, t², and D as the independents, 3) seasonally adjusted monthly as the dependent, and t and t² as the independents, and 4) seasonally adjusted monthly as the dependent, and t, t², and D as the independents. Discuss your findings, and determine which of the four models is the best for forecasting new home sales. When interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001. State the equation that would be used to forecast sales.