Frequency: Monthly
observation_date	S4248SM144NCEN
1992-01-01	3459
1992-02-01	3458
1992-03-01	4002
1992-04-01	4564
1992-05-01	4221
1992-06-01	4529
1992-07-01	4466
1992-08-01	4137
1992-09-01	4126
1992-10-01	4259
1992-11-01	4240
1992-12-01	4936
1993-01-01	3031
1993-02-01	3261
1993-03-01	4160
1993-04-01	4377
1993-05-01	4307
1993-06-01	4696
1993-07-01	4458
1993-08-01	4457
1993-09-01	4364
1993-10-01	4236
1993-11-01	4500
1993-12-01	4974
1994-01-01	3075
1994-02-01	3377
1994-03-01	4443
1994-04-01	4261
1994-05-01	4460
1994-06-01	4985
1994-07-01	4324
1994-08-01	4719
1994-09-01	4374
1994-10-01	4248
1994-11-01	4784
1994-12-01	4971
1995-01-01	3370
1995-02-01	3484
1995-03-01	4269
1995-04-01	3994
1995-05-01	4715
1995-06-01	4974
1995-07-01	4223
1995-08-01	5000
1995-09-01	4235
1995-10-01	4554
1995-11-01	4851
1995-12-01	4826
1996-01-01	3699
1996-02-01	3983
1996-03-01	4262
1996-04-01	4619
1996-05-01	5219
1996-06-01	4836
1996-07-01	4941
1996-08-01	5062
1996-09-01	4365
1996-10-01	5012
1996-11-01	4850
1996-12-01	5097
1997-01-01	3758
1997-02-01	3825
1997-03-01	4454
1997-04-01	4635
1997-05-01	5210
1997-06-01	5057
1997-07-01	5231
1997-08-01	5034
1997-09-01	4970
1997-10-01	5342
1997-11-01	4831
1997-12-01	5965
1998-01-01	3796
1998-02-01	4019
1998-03-01	4898
1998-04-01	5090
1998-05-01	5237
1998-06-01	5447
1998-07-01	5435
1998-08-01	5107
1998-09-01	5515
1998-10-01	5583
1998-11-01	5346
1998-12-01	6286
1999-01-01	4032
1999-02-01	4435
1999-03-01	5479
1999-04-01	5483
1999-05-01	5587
1999-06-01	6176
1999-07-01	5621
1999-08-01	5889
1999-09-01	5828
1999-10-01	5849
1999-11-01	6180
1999-12-01	6771
2000-01-01	4243
2000-02-01	4952
2000-03-01	6008
2000-04-01	5353
2000-05-01	6435
2000-06-01	6673
2000-07-01	5636
2000-08-01	6630
2000-09-01	5887
2000-10-01	6322
2000-11-01	6520
2000-12-01	6678
2001-01-01	5082
2001-02-01	5216
2001-03-01	5893
2001-04-01	5894
2001-05-01	6799
2001-06-01	6667
2001-07-01	6374
2001-08-01	6840
2001-09-01	5575
2001-10-01	6545
2001-11-01	6789
2001-12-01	7180
2002-01-01	5117
2002-02-01	5442
2002-03-01	6337
2002-04-01	6525
2002-05-01	7216
2002-06-01	6761
2002-07-01	6958
2002-08-01	7070
2002-09-01	6148
2002-10-01	6924
2002-11-01	6716
2002-12-01	7975
2003-01-01	5326
2003-02-01	5609
2003-03-01	6414
2003-04-01	6741
2003-05-01	7144
2003-06-01	7133
2003-07-01	7568
2003-08-01	7266
2003-09-01	6634
2003-10-01	7626
2003-11-01	6843
2003-12-01	8540
2004-01-01	5629
2004-02-01	5898
2004-03-01	7045
2004-04-01	7094
2004-05-01	7333
2004-06-01	7918
2004-07-01	7289
2004-08-01	7396
2004-09-01	7259
2004-10-01	7268
2004-11-01	7731
2004-12-01	9058
2005-01-01	5557
2005-02-01	6237
2005-03-01	7723
2005-04-01	7262
2005-05-01	8241
2005-06-01	8757
2005-07-01	7352
2005-08-01	8496
2005-09-01	7741
2005-10-01	7710
2005-11-01	8247
2005-12-01	8902
2006-01-01	6066
2006-02-01	6590
2006-03-01	7923
2006-04-01	7335
2006-05-01	8843
2006-06-01	9327
2006-07-01	7792
2006-08-01	9156
2006-09-01	8037
2006-10-01	8640
2006-11-01	9128
2006-12-01	9545
2007-01-01	6627
2007-02-01	6743
2007-03-01	8195
2007-04-01	7828
2007-05-01	9570
2007-06-01	9484
2007-07-01	8608
2007-08-01	9543
2007-09-01	8123
2007-10-01	9649
2007-11-01	9390
2007-12-01	10065
2008-01-01	7093
2008-02-01	7483
2008-03-01	8365
2008-04-01	8895
2008-05-01	9794
2008-06-01	9977
2008-07-01	9553
2008-08-01	9375
2008-09-01	9225
2008-10-01	9948
2008-11-01	8758
2008-12-01	10839
2009-01-01	7266
2009-02-01	7578
2009-03-01	8688
2009-04-01	9162
2009-05-01	9369
2009-06-01	10167
2009-07-01	9507
2009-08-01	8923
2009-09-01	9272
2009-10-01	9075
2009-11-01	8949
2009-12-01	10843
2010-01-01	6558
2010-02-01	7481
2010-03-01	9475
2010-04-01	9424
2010-05-01	9351
2010-06-01	10552
2010-07-01	9077
2010-08-01	9273
2010-09-01	9420
2010-10-01	9413
2010-11-01	9866
2010-12-01	11455
2011-01-01	6901
2011-02-01	8014
2011-03-01	9832
2011-04-01	9281
2011-05-01	9967
2011-06-01	11344
2011-07-01	9106
2011-08-01	10469
2011-09-01	10085
2011-10-01	9612
2011-11-01	10328
2011-12-01	11483
2012-01-01	7486
2012-02-01	8641
2012-03-01	9709
2012-04-01	9423
2012-05-01	11342
2012-06-01	11274
2012-07-01	9845
2012-08-01	11163
2012-09-01	9532
2012-10-01	10754
2012-11-01	10953
2012-12-01	11922
2013-01-01	8395
2013-02-01	8888
2013-03-01	10110
2013-04-01	10493
2013-05-01	12218
2013-06-01	11385
2013-07-01	11186
2013-08-01	11462
2013-09-01	10494
2013-10-01	11540
2013-11-01	11138
2013-12-01	12709
2014-01-01	8557
2014-02-01	9059
2014-03-01	10055
2014-04-01	10977
2014-05-01	11792
2014-06-01	11904
2014-07-01	10965
2014-08-01	10981
2014-09-01	10828
2014-10-01	11817
2014-11-01	10470
2014-12-01	13310
2015-01-01	8400
2015-02-01	9062
2015-03-01	10722
2015-04-01	11107
2015-05-01	11508
2015-06-01	12904
2015-07-01	11869
2015-08-01	11224
2015-09-01	12022
2015-10-01	11983
2015-11-01	11506
2015-12-01	14183
2016-01-01	8650
2016-02-01	10324
2016-03-01	12109
2016-04-01	11423
2016-05-01	12242
2016-06-01	13685
2016-07-01	10955
2016-08-01	12705
2016-09-01	12276
2016-10-01	11910
2016-11-01	13021
2016-12-01	14425
2017-01-01	9045
2017-02-01	10453
2017-03-01	12481
2017-04-01	11489
2017-05-01	13537
2017-06-01	14717
2017-07-01	11395
2017-08-01	13373
2017-09-01	11871
2017-10-01	12663
2017-11-01	13202
2017-12-01	14191
2018-01-01	9493
2018-02-01	10329
2018-03-01	12569
2018-04-01	11805
2018-05-01	14012
2018-06-01	14420
2018-07-01	12518
2018-08-01	14073
2018-09-01	12231
2018-10-01	13727
2018-11-01	13949
2018-12-01	15308
2019-01-01	10616
2019-02-01	10976
2019-03-01	12472
2019-04-01	13098
2019-05-01	14573
2019-06-01	14277
2019-07-01	13484
2019-08-01	14205
2019-09-01	12992
2019-10-01	14427
2019-11-01	13773
2019-12-01	16197
2020-01-01	10659
2020-02-01	11350
2020-03-01	13410
2020-04-01	12334
2020-05-01	14111
2020-06-01	16215
2020-07-01	15757
2020-08-01	15400
2020-09-01	15644

Question 1 Perform a descriptive statistical analysis of monthly sales over the period Jan2018 to Dec2019. Question 2 Generate 1-step-ahead forecasts for the last two years of your sample (2018 \& 2019) using a SMA(q) model with window lengths q=3 and q=12. Make a plot of actual against forecasted sales. Tip: Make sure to generate exactly 24 forecasts covering the period 201819, by using observations from earlier periods. Question 3 Repeat question 2 for an EWMA() model with two values for the smoothing parameter, =0.2&=0.9. Update the plot using the EWMA forecasts. Tip: To remove the initial value effect, start EWMA iterations three years earlier in the sampling period and keep the last 24 model outputs for forecasting comparison. Question 4 Make a qualitative assessment of the forecasting error for the two parametrizations of the SMA and EWMA devices: designate the periods in which models overestimate/underestimate actual sales. Do you see any systematic pattern in the alteration of the error sign across observations and predictive devices? Question 5 Make a comparson of the forecasting performance of SMA and EWMA models using the mean absolute percentage error (MAPE) criterion, where MAPE=(1/T)t=1Te^t/Yt,e^t is the forecasting error, Yt is the actual observation and T is the size of the prediction sample. Question 6 For an EWMA type of a model, make a graph of the MAPE score as a function of the parameter. Pick the value that optimizes model's performance. Question 1 Perform a descriptive statistical analysis of monthly sales over the period Jan2018 to Dec2019. Question 2 Generate 1-step-ahead forecasts for the last two years of your sample (2018 \& 2019) using a SMA(q) model with window lengths q=3 and q=12. Make a plot of actual against forecasted sales. Tip: Make sure to generate exactly 24 forecasts covering the period 201819, by using observations from earlier periods. Question 3 Repeat question 2 for an EWMA() model with two values for the smoothing parameter, =0.2&=0.9. Update the plot using the EWMA forecasts. Tip: To remove the initial value effect, start EWMA iterations three years earlier in the sampling period and keep the last 24 model outputs for forecasting comparison. Question 4 Make a qualitative assessment of the forecasting error for the two parametrizations of the SMA and EWMA devices: designate the periods in which models overestimate/underestimate actual sales. Do you see any systematic pattern in the alteration of the error sign across observations and predictive devices? Question 5 Make a comparson of the forecasting performance of SMA and EWMA models using the mean absolute percentage error (MAPE) criterion, where MAPE=(1/T)t=1Te^t/Yt,e^t is the forecasting error, Yt is the actual observation and T is the size of the prediction sample. Question 6 For an EWMA type of a model, make a graph of the MAPE score as a function of the parameter. Pick the value that optimizes model's performance