Exam 3 – Sampled Reading QuestionsIn Nigerian Gold Rush, Lead Po.docx

Exam 3 – Sampled Reading Questions
In Nigerian Gold Rush, Lead Poisons Thousands of Children
http://www.npr.org/blogs/health/2012/10/03/161908669/in-
‐the-‐wake-‐of-‐high-‐ gold-‐prices-‐lead-‐poisons-
‐thousands-‐of-‐children
· Which organization is treating patients in the area?
· The level of lead considered “dangerous” by the U.S. Center
for Disease Control and Prevention
· Two ways of earning a living in Nigeria
· What caused lead poisoning?
· What is the role of lead in the process of extracting gold?
· Others World’s largest Dead Zone Suffocating Sea
http://news.nationalgeographic.com/news/2010/02/100305-
‐baltic-‐sea-‐algae-‐ dead-‐zones-‐water/
· Where is this “Suffocating Sea”
· Why Eagle was endangered?
· What is overfishing to do with the algae issue?
· What is the meaning of “brackish water”?
· Proposed strategy to combat the algae problem is to phase out
?
· Earth youngest sea?
· Others Vast Tracts in Paraguay Forest Being Replaced by
Ranches
http://www.nytimes.com/2012/03/25/world/americas/paraguay
s-‐chaco-‐forest-‐ being-‐cleared-‐by-
‐ranchers.html?pagewanted=all&_r=0
· Why it is called “green hell”?
· Where did those ranchers originally come from?
· Mennonite’s religious affiliation.
· Beef exported to?
Assignment 6 Project Part 3 -- The ARIMA Forecast. This

assignment is due by midnight Nov 4th. The assignment is
worth a maximum of 2.5 extra credit points and may serve as
the project ARIMA section. This assignment is due by midnight
Nov 4th. No late submissions will be graded.
(Again -- 1. Do not show failed models in business reports.
Share your failures with your family if you wish and not with
your boss or instructor.and 2.Never use Y hold out data
observations in any forecast model.)
Complete each of the following sections.
a) Examine the Y data (excluding the hold out period) to
determine if it needs to be differenced to make it stationary.
Show a time series plot of the raw Y data and autocorrelation
functions (ACFs).
The time series plot shows increasing trend along with seasonal
variation.
ACFs are significant till 4 lag and the series in not stationary as
can be seen from ACF plot
b) From your time series data plot and AFCs determine if you
have seasonality. If you do, use seasonal differences to remove
it and run the ACFs and PACFs on the non seasonal Y data
series.
Yes, seasonality can be seen, we take 1st difference to remove
the seasonal difference and then plot ACFs and PACFs

the first difference makes the data stationary as can be seen
from the ACF and PACF.
c) Fill out the ARIMA seasonal menu (P,D,Q) appropriately. If
you have no trend as shown by the seasonally differenced ACFs
run the ARIMA model and note the significance of each
coefficient. Make model adjustments accordingly to improve
results.
P= 1, D=1. Q=0

d) If it requires differencing for trend to make it stationary do
so and run another time series plot and ACFs on the differenced
data. If this requires differencing again do so but run time series
plots and ACFs each time you do.
e) Run and show the PACFs on your stationary data series and
identify the appropriate ARIMA model and show the initial
ARIMA non seasonal menu section (p,d,q) filled out
appropriately and any seasonal (P,D,Q) components in the
seasonal menu filled out.
f) Run the ARIMA model and note the significance of each
results shown by the residual MSE.
g) Calculate the two error measures that you used in other
model analysis and comment on the acceptability of the size of
the measure.

h) Note the LBQ associated P values for the selected lags. They
should each be significant (above .05) to qualify the residuals
as potentially random. If they are not random select an
alternative ARIMA model form that has random residuals.
i) Run an ARIMA forecast for your hold out period and show a
time series plot of the residuals (Y actual and Y forecast) for
the 8 quarter hold out period.
j) Calculate the hold out period RMSE and MAPE (Refer back
to earlier chapters for the error measure formulas) and compare
them to the Fit period ARIMA error measures (from g above).
k) Plot the forecast values appended to the Y data without the
hold out to check for forecast reasonableness.
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DateCostCo Revenuefirst
differenceACF1TSTA1LBQ1PACF2TSTA2
3/31/19954307.3218-0.644357759-5.50539510531.5722659-
0.644357759-5.505395105
6/30/19953896.2384307.3218-
411.08380.301467791.90383836538.580484-0.194474235-
1.661588593
9/29/19956013.80323896.2382117.5652-0.587981317-
3.5415530865.62088559-0.855294477-7.307639211
12/29/19954383.5646013.8032-
1630.23920.8712885844.527432137125.85729560.1780925531.
521623441
3/29/19964688.69484383.564305.1308-0.574072829-
2.387123598152.39169090.1296927311.108095175
6/28/19964311.48784688.6948-
377.2070.2787201891.077891363158.7398262-0.0261045-
0.223036943
9/30/19966182.7094311.48781871.2212-0.53367315-
2.031783954182.365864-0.116726699-0.997313357
12/31/19964883.40826182.709-
1299.30080.794976792.86872919235.59870750.0774251950.66
1521157
3/31/19975238.89314883.4082355.4849-0.536840594-
1.749964915260.25313070.010478440.089527832
6/30/19974836.2295238.8931-
402.66410.2593794320.812128535266.0998823-0.066749141-
0.570304908
9/30/19976915.8744836.2292079.645-0.497043517-
1.54239228287.9161906-0.165835581-1.416899822
12/31/19975429.76326915.874-
1486.11080.7448586652.239563278337.7130596-0.053169599-
0.454281252
3/31/19985795.00595429.7632365.2427-0.498703385-
1.405957925360.4073969-0.001660004-0.014183085
6/30/19985338.08595795.0059-

456.920.2369145290.650532691365.6159308-0.049857168-
0.425979829
9/30/19987707.0225338.08592368.9361-0.458813114-
1.252593237385.4872992-0.062586279-0.534737402
12/31/19985998.07817707.022-
1708.94390.6870368471.836601885430.8260267-0.068394829-
0.584365679
3/31/19996592.35795998.0781594.2798-0.452615227-
1.157632079450.8548032-0.010516919-0.089856599
6/30/19996053.81986592.3579-
538.53810.2213945090.55613274455.73407620.0369784940.31
5944389
9/30/19998811.7756053.81982757.9552
12/31/19996943.51228811.775-1868.2628
3/31/20007736.98686943.5122793.4746
6/30/20006894.60797736.9868-842.3789
9/29/200010589.1896894.60793694.5811
12/29/20007637.277810589.189-2951.9112
3/30/20018306.30867637.2778669.0308
6/29/20017718.8958306.3086-587.4136
9/28/200111134.54987718.8953415.6548
12/31/20018466.552711134.5498-2667.9971
3/29/20029382.85168466.5527916.2989
6/28/20028616.74719382.8516-766.1045
9/30/200212296.3478616.74713679.5999
12/31/20029198.58512296.347-3097.762
3/31/200310114.16999198.585915.5849
6/30/20039543.071310114.1699-571.0986
9/30/200313689.73059543.07134146.6592
12/31/200310521.480513689.7305-3168.25
3/31/200411548.969710521.48051027.4892
6/30/200410897.240211548.9697-651.7295
9/30/200415139.30210897.24024242.0618
12/31/20041157815139.302-3561.302
3/31/200512658.077115781080.077
6/30/200511996.912658.077-661.177

9/30/200516709.93611996.94713.036
12/30/200512933.34616709.936-3776.59
3/31/200614054.57612933.3461121.23
6/30/200613273.17514054.576-781.401
9/29/200619875.22113273.1756602.046
12/29/200614151.62419875.221-5723.597
3/30/200715112.01614151.624960.392
6/29/200714659.25515112.016-452.761
9/28/200720477.2614659.2555818.005
12/31/200715809.5320477.26-4667.73
3/31/200816959.88615809.531150.356
6/30/200816613.71716959.886-346.169
9/30/200823099.88716613.7176486.17
12/31/20081639523099.887-6704.887
3/31/20091684316395448
6/30/20091580616843-1037
9/30/200922378158066572
12/31/20091729922378-5079
3/31/201018742172991443
6/30/20101778018742-962
9/30/201024125177806345
12/31/20101923924125-4886
3/31/201120875192391636
6/30/20112062320875-252
9/30/201128178206237555
12/30/20112162828178-6550
3/30/201222967216281339
6/29/20122232422967-643
9/28/201232218223249894
12/31/20122371532218-8503
3/29/201324871237151156
6/28/20132408324871-788
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Chapter 4: Chapter 4 - Assignment 4
(Remember-- 1. Do not show failed models in business reports.
your boss or instructor. and 2. Never use Y hold out data

a) Tell me why you selected the appropriate exponential
smoothing method by commenting on your Y data
characteristics. (you should use a time series plot and
autocorrelations to do this),
Exponential smoothening provides an exponentially weighted
moving average of all previously observed values. This method
revises an estimate in the light of more recent experiences. This
method is based on averaging (smoothing) past values of a
series in an exponentially decreasing manner.
b) Apply the appropriate exponential smoothing forecast
technique to your Y variable excluding the last two years of
data (8 quarter hold out period). Show the Y data, fitted values
and residuals in excel format and show your exponential
smoothing model coefficients. (Find the correct coefficient and
not just use the default values.)
The exponential smoothing provides an exponentially weighted
average of all previously observed values.
c) Evaluate the "Goodness To Fit" using at least two error
measures -- RMSE and MAPE.
RMSE is the root mean square error used to evaluate forecasting

methods. It penalizes Large errors.
Sometimes it is more useful to compute forecast errors in terms
of percentages. MAPE is the mean absolute percentage error
that is computed by finding the absolute error in each period,
dividing this by actual observed value for that period. MAPE is
useful when Predicted Y values are large. MAPE has no units.
From the RMSE and MAPE, we can see that the model well as
shown by the residual plots where the data fits the best
d) Check the "Fit" period residual mean proximity to zero
and randomness with a time series plot; check the residual time
series plot and autocorrelations (ACFs) for trend, cycle and
seasonality.
e) Evaluate the residuals for the "Fit" period by indicating the
residual distribution using a histogram (normal or not and
random or not),
f) Comment on the acceptability of the model's ability to pick
up the systematic variation in your Fit period actual data.
g) Develop a two year quarterly forecast (for the hold out
period).
h) Evaluate the "Accuracy" of the forecast for the "hold out
period" using RMSE and MAPE error measures used from
forecast period residuals and comment them.
i) Do the forecast period residuals seem to be random relative to
the hold out period data? Check the forecast period time series
plot of the residuals.
j) Did the error measures get worse, remain the same or get
better from the fit to the hold out period? Do you think the
forecast accuracy is acceptable?
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DateCostCo Revenuefirst
differenceACF1TSTA1LBQ1PACF2TSTA2
3/31/19954307.3218-0.644357759-5.50539510531.5722659-
0.644357759-5.505395105
6/30/19953896.2384307.3218-
411.08380.301467791.90383836538.580484-0.194474235-
1.661588593
9/29/19956013.80323896.2382117.5652-0.587981317-
3.5415530865.62088559-0.855294477-7.307639211
12/29/19954383.5646013.8032-
1630.23920.8712885844.527432137125.85729560.1780925531.
521623441
3/29/19964688.69484383.564305.1308-0.574072829-
2.387123598152.39169090.1296927311.108095175
6/28/19964311.48784688.6948-
377.2070.2787201891.077891363158.7398262-0.0261045-
0.223036943
9/30/19966182.7094311.48781871.2212-0.53367315-
2.031783954182.365864-0.116726699-0.997313357
12/31/19964883.40826182.709-
1299.30080.794976792.86872919235.59870750.0774251950.66
1521157
3/31/19975238.89314883.4082355.4849-0.536840594-
1.749964915260.25313070.010478440.089527832
6/30/19974836.2295238.8931-
402.66410.2593794320.812128535266.0998823-0.066749141-
0.570304908
9/30/19976915.8744836.2292079.645-0.497043517-
1.54239228287.9161906-0.165835581-1.416899822

12/31/19975429.76326915.874-
1486.11080.7448586652.239563278337.7130596-0.053169599-
0.454281252
3/31/19985795.00595429.7632365.2427-0.498703385-
1.405957925360.4073969-0.001660004-0.014183085
6/30/19985338.08595795.0059-
456.920.2369145290.650532691365.6159308-0.049857168-
0.425979829
9/30/19987707.0225338.08592368.9361-0.458813114-
1.252593237385.4872992-0.062586279-0.534737402
12/31/19985998.07817707.022-
1708.94390.6870368471.836601885430.8260267-0.068394829-
0.584365679
3/31/19996592.35795998.0781594.2798-0.452615227-
1.157632079450.8548032-0.010516919-0.089856599
6/30/19996053.81986592.3579-
538.53810.2213945090.55613274455.73407620.0369784940.31
5944389
9/30/19998811.7756053.81982757.9552
12/31/19996943.51228811.775-1868.2628
3/31/20007736.98686943.5122793.4746
6/30/20006894.60797736.9868-842.3789
9/29/200010589.1896894.60793694.5811
12/29/20007637.277810589.189-2951.9112
3/30/20018306.30867637.2778669.0308
6/29/20017718.8958306.3086-587.4136
9/28/200111134.54987718.8953415.6548
12/31/20018466.552711134.5498-2667.9971
3/29/20029382.85168466.5527916.2989
6/28/20028616.74719382.8516-766.1045
9/30/200212296.3478616.74713679.5999
12/31/20029198.58512296.347-3097.762
3/31/200310114.16999198.585915.5849
6/30/20039543.071310114.1699-571.0986
9/30/200313689.73059543.07134146.6592
12/31/200310521.480513689.7305-3168.25

3/31/200411548.969710521.48051027.4892
6/30/200410897.240211548.9697-651.7295
9/30/200415139.30210897.24024242.0618
12/31/20041157815139.302-3561.302
3/31/200512658.077115781080.077
6/30/200511996.912658.077-661.177
9/30/200516709.93611996.94713.036
12/30/200512933.34616709.936-3776.59
3/31/200614054.57612933.3461121.23
6/30/200613273.17514054.576-781.401
9/29/200619875.22113273.1756602.046
12/29/200614151.62419875.221-5723.597
3/30/200715112.01614151.624960.392
6/29/200714659.25515112.016-452.761
9/28/200720477.2614659.2555818.005
12/31/200715809.5320477.26-4667.73
3/31/200816959.88615809.531150.356
6/30/200816613.71716959.886-346.169
9/30/200823099.88716613.7176486.17
12/31/20081639523099.887-6704.887
3/31/20091684316395448
6/30/20091580616843-1037
9/30/200922378158066572
12/31/20091729922378-5079
3/31/201018742172991443
6/30/20101778018742-962
9/30/201024125177806345
12/31/20101923924125-4886
3/31/201120875192391636
6/30/20112062320875-252
9/30/201128178206237555
12/30/20112162828178-6550
3/30/201222967216281339
6/29/20122232422967-643
9/28/201232218223249894
12/31/20122371532218-8503

3/29/201324871237151156
6/28/20132408324871-788
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Sheet11972 01158.74431972 02162·84061972 03165·21911972
04166·26691972 05168.01681972 06166·40961972
07165.97411972 08165·74741972 09166.1781972
10165·73651972 11164·77501972 12163·18791973
01160.36671973 02164·16061973 03162.1621973
04162·47211973 05161·93651973 06161.05421973
07161.14621973 08160·32891973 09158.57611973
10161·29581973 11160·21871973 12158.53151974
01156.27851974 02159.87091974 03156·87491974
04156·66941974 05155·88791974 06153·64001974
07153.61711974 08152.1861974 09149·91811974
10150·70931974 11149.9781974 12149.25431975

01147.99681975 02150.31711975 03148.67661975
04148.02391975 05146.66211975 06147.35169999991975
07145·88051975 08144·38651975 09144·91741975
10145·69051975 11144.88791975 12144.47351976
01144·08931976 02144.07341976 03144·08481976
04141.4131976 05142.22691976 06141·67841976
074142·24271976 08141·93191976 09142.59361976
10141·10141976 11141.33721976 12140.98381977
01137.38571977 02142·32591977 03141.461977
04142.40521977 05141.17861977 06141.5811977
07141.57521977 08144·94261977 09147·81941977
10149.44151977 11149.52231977 12147.92161978
01145.66071978 02145·96351978 03151·69771978
04153·23821978 05153.36171978 06153.44511978
07152.09981978 08152.09151978 09152·83061978
10153·13971978 11151·73181978 12150.35081979
01147.03541979 02148.06031979 03149·27141979
04148·41231979 05149·25011979 06146·40071979
07144·97151979 08148.15531979 09147·72191979
10149·36281979 11151·59291979 12149·16461980
01150·06911980 02150.56291980 03150.42061980
04150·10001980 05149·30441980 06147·86111980
07147.75611980 08145.3571980 09148.99011980
10147.48731980 11146.85221980 12148·73831981
01147.54231981 02148·65221981 03148.81571981
04147·80941981 05146.79721981 06148.90341981
07146·65171981 08148.13931981 09148·49731981
10147.77841981 11148·10541981 12148·08031982
01146.48981982 02149.92241982 03149·37951982
04147·98971982 05149·59431982 06149.02081982
07149·07531982 08148.65481982 09149·84041982
10149·83271982 11149·86731982 12148.09851983
01149.72141983 02150·84421983 03149.80641983
04151·10601983 05148·63131983 06149·22561983
07148.64371983 08149.35281983 09151·15561983
10150·91051983 11150.9461983 12144.35281984

01152.65741984 02152·68731984 03149·34711984
04152.39011984 05153.99221984 06152.23041984
07152·77141984 08151·55061984 09154·57831984
10153.10631984 11154·36191984 12152.96551985
01150·26061985 02155·17381985 03156·29411985
04155.58551985 05156.9431985 06155.08651985
07153.79541985 08151·48001985 09153.99951985
10154·29541985 11153·22381985 12155.2591986
01179.37261986 02180.13331986 03177.05271986
04174.02731986 05173.8191986 06169.82911986
07170·29611986 08164·75431986 09163.74611986
10165.92761986 11165.61031986 12164·25551987
01167·12091987 02165·11461987 03166.69791987
04167·34691987 05164·16411987 06163·04071987
07162.51141987 08161·68641987 09161·61981987
10164·70811987 11165·32501987 12163·76291988
01162·43501988 02164.88891988 03164.8851988
04163·20041988 05162·04411988 06160·89311988
07158.33321988 08159.11891988 09155·50711988
10158.01251988 11158·02191988 12156·40931989
01156.31961989 02153·38931989 03149·17651989
04153·04951989 05153.92751989 06150.1481989
07146·59691989 08148·57121989 09148·63871989
10146·76531989 11148·40611989 12144.48171990
01148.60521990 02147.64281990 03146·38551990
04145·87031990 05144.3191990 06139.93521990
07141·26511990 08143·49821990 09142·26181990
10148·52821990 11145·46751990 12144.50341991
01147·70051991 02150·39941991 03148·60721991
04147·86741991 05145.90141991 06144·16071991
07144.68491991 08144·07801991 09145·09171991
10146·46421991 11144·30661991 12143·73861992
01144.95281992 02145·50441992 03144·71171992
04143·61241992 05141·17281992 06141·14711992
07140.43421992 08136·31201992 09138.44591992
10140.3291992 11138·32791992 12139·88561993

01137·08471993 02136·72261993 03137.34341993
04135.51571993 05134.83891993 06133·81171993
07131·71731993 08133.08351993 09132.17371993
10134·67731993 11136·11081993 12135.0461994
01134·24271994 02133·32901994 03132.84261994
04130.21391994 05131·71141994 06130.18441994
07128.02311994 08128·87621994 09130·14941994
10131·11681994 11130·53441994 12133·11951995
01131·59501995 02133.80721995 03129.98551995
04130.05041995 05130.55531995 06129·55751995
07127.00081995 08126·95791995 09126.35841995
10126·45161995 11129.68911995 12128·59791996
01127.91621996 02129·52141996 03129·41661996
04126·90841996 05125.92121996 06127.18561996
07124.81981996 08125.25851996 09127.65571996
10127·63751996 11127.5321996 12128·13141997
01126·08571997 02128·29531997 03127.06981997
04126.85851997 05127·50781997 06126·86741997
07126.23061997 08125·01001997 09127·73751997
10127.37061997 11127·21591997 12128·63101998
01128.81791998 02127·54291998 03126·20281998
04127.68231998 05125.0061998 06123.43831998
07122.00011998 08122·16401998 09114·01061998
10120·97551998 11120·92331998 12119·02341999
01117.44051999 02117.49291999 03115.85021999
04115.95911999 05115.71041999 06113·47351999
07114·21291999 08113.85991999 09114.33371999
10117.13991999 11117·40871999 12117.36822000
01113·93212000 02115·26322000 03116·5791129.98552000
04115.3144129·55752000 05115.1705126.35842000
06114.7095128·59792000 07113·0623129·41662000
08114·0381127.18562000 09113.427127.65572000
10114·4357128·13142000 11114·9013127.06982000
12115.3433126·86742001 01114·2369127·73752001
02113·8665128·63102001 03115·8387126·20282001
04115.4896123.43832001 05114·8312114·01062001

06113·5779119·02342001 07113.2403115.85022001
08112.7838113·47352001 09112·4551114.33372001
10113.1854117.36822001 11115.8539116·57912001
12115·9758114.70952002 01115.6986113.4272002
02115.8462115.34332002 03115.9421115·83872002
04115.1269113·57792002 05116·3212112·45512002
06115.9143115·97582002 07113·2844115.94212002
08114·1707115.91432002 09106·5915106·59152002
10105·5464112.712002 11110.7756114.23112002
12112.71111·39302003 01113·2423110·38832003
02113·7797109.62752003 03114.2311110·49902003
04112.6964106·38462003 05111.4821699.99012003
06111·3930108.42612003 07108·2205110.23822003
08109.6957107.6742003 09110·3883183·10372003
10110.4747898·18722003 11109·1446399.03162003
12109.6275101.6262004 01109·8755999.06712004
02109.7014102.16972004 03110·4990100.51812004
04109.4122399·92312004 05109.3073696.55472004
06106·3846100.6512004 07107·9235102·25502004
08104·7824101.13512004 09699.9901378.33282004
10101.745100.66082004 11106.707102·76172004
12108.4261103·96222005 01107.2923109.57762005
02108.3525107·38792005 03110.2382108.63062005
04109.5702106·07802005 05108·4478110.50462005
06107.674110·62292005 07103.406110·51552005
08102.8145110.16652005 09183·1037110·36392005
10389·7490119·01002005 11495.6144124.48022005
12898·1872122.69862006 01100·1933129·04232006
02499·1271139.39372006 03399.0316141.21742006
04100.0654142.65432006 05101·43842006 06101.6262006
07100·30502006 08199.23462006 09999.06712006
10100.59212006 11399·75482006 12102.16972007
01100·55982007 02101.0262007 03100.51812007
04101·93472007 05102.53242007 06399·92312007
07199·22652007 0898.19382007 09696.55472007
10799.56332007 11899·31652007 12100.6512008

01100.65532008 02101.55182008 03102·25502008
04101·51442008 05101·36342008 06101.13512008
07102·05842008 08698·63632008 09378.33282008
10493·30622008 11100·17022008 12100.66082009
01101·26352009 02103.23962009 03102·76172009
04104.12182009 05106.0512009 06103·96222009
07106·40492009 08105.90272009 09109.57762009
10108·72292009 11106.13312009 12107·38792010
01106·38112010 02109.28842010 03108.63062010
04105.95792010 05106.36692010 06106·07802010
07104.69052010 08107.27672010 09110.50462010
10110.26772010 11109.51862010 12110·62292011
01108·43492011 02106·35672011 03110·51552011
04109.54542011 05110·89432011 06110.16652011
07106·74162011 08111.41882011 09110·36392011
10116.16952011 11118·55662011 12119·01002012
01120·93952012 02122.58682012 03124.48022012
04123.70642012 05124.16972012 06122.69862012
07125·79202012 08124.12252012 09129·04232012
10136·48892012 11138.91992012 12139.39372013
01138.52292013 02140.25592013 03141.21742013
04144·51812013 05143·72892013 06142.65432013
07147·96452013 08147.74752013 09153·45402013 10152·9212
Sheet4Anova: Single
FactorSUMMARYGroupsCountSumAverageVarianceColumn
11579928.09995328.53999333331105973.22986101Column
21541329327552.866666666720078634.6952381ANOVASource
of VariationSSdfMSFP-valueF critBetween
Groups3704405220.6227713704405220.62277349.72610621072
.34310189399229E-174.1959718186Within
Groups296584510.9513872810592303.9625496Total400098973
1.5741529
Sheet2DateCostCo RevenueWalmart
RevenueExportsIPIC3/31/19954307.32182044064349129.98554
307.32186/30/19953896.2382272364855129.55753896.2389/29/
19956013.80322291368943126.35846013.803212/29/19954383.

5642755169071128.59794383.5643/29/19964688.694822772697
97129.41666/28/19964311.48782558771056127.18569/30/1996
6182.7092564470553127.655712/31/19964883.40823085672842
128.13143/31/19975238.89312540977050127.06986/30/199748
36.2292838678889126.86749/30/19976915.8742877779287127.
737512/31/19975429.76323538679038128.6313/31/19985795.0
0592981978812126.20286/30/19985338.08593352176961123.43
839/30/19987707.0223350977179114.010612/31/19985998.078
14078578382119.02343/31/19996592.35793471778243115.8502
6/30/19996053.81983847079070113.47359/30/19998811.77540
43282718114.333712/31/19996943.51225139484983117.36823/
31/20007736.98684298587277116.57916/30/20006894.6079461
1290549114.70959/29/200010589.1894567691981113.42712/29
/20007637.27785655690260115.34333/30/20018306.308648052
88714115.83876/29/20017718.8955279985265113.57799/28/20
0111134.54985273877286112.455112/31/20018466.5527642107
8180115.97583/29/20029382.85165212679613115.94216/28/20
028616.74715627182705115.91439/30/200212296.34755241828
93106.591512/31/20029198.5856640081686112.713/31/200310
114.16995671882944114.23116/30/20039543.071362637848101
11.3939/30/200313689.73056248086399110.388312/31/200310
521.48057449490699109.62753/31/200411548.96976476396472
110.4996/30/200410897.24026972294993106.38469/30/200415
139.3026852098543699.990112/31/20041157882217102571108.
42613/31/200512658.07771680104752110.23826/30/200511996
.976697106652107.6749/30/200516709.93675397107166183.10
3712/30/200512933.34688418113482898.18723/31/200614054.
57679676118875399.03166/30/200613273.17585430122446101.
6269/29/200619875.22184467123774999.067112/29/200614151
.62499078128544102.16973/30/200715112.01686410132823100
.51816/29/200714659.25592999136453399.92319/28/20072047
7.2691865141627696.554712/31/200715809.5320477.26147152
100.6513/31/200816959.88617209.849151927102.2556/30/2008
16613.71717034.8749163317101.13519/30/200823099.8871674
0.06437153641378.332812/31/20081639521191.9402111320121
00.66083/31/20091684317834.0820633125990102.76176/30/20

091580617140.32461899128456103.96229/30/20092237816206.
297385697135643109.577612/31/20091729920526.4892157091
144001107.38793/31/20101874218267.2467647127148646108.6
3066/30/20101778018599.5740294138151418106.0789/30/2010
2412518025.8722088241156049110.504612/31/2010192392229
5.2616626472166177110.62293/31/20112087520155.878498794
2174342110.51556/30/20112062320659.2635496382173180110
9/30/20112817820633.8790648915181172110.363912/30/20112
162825914.7637194674179118119.013/30/20122296722914.029
1158402186505124.48026/29/20122232422951.1087347521185
218122.69869/28/20123221822512.1326204256186829129.0423
12/31/20122371529306.2397861277188686139.39373/29/20132
487125392.3719358383184578141.21746/28/20132408325027.4
115807515190528142.6543
New folder/Eco 309 03W 82819 Fall 2013 Syllabus.docx
Economics 309 03W 82819
Economic Forecasting
Fall 2013
(See your specific section syllabus in Doc Sharing)
Professor: Stanley Holmes
Email: [email protected]
Phone: 903-468-6029 (Commerce) 903- 365-7190 (Home
Office)
Office Hours:: 11:00 A.M. to 12:00 P.M. and 1:00 P.M. to 4:00
P.M. Central Time Tuesdays and Thursdays and Wednesdays
10:00 A.M to 12:00 P.M. Central Time or by appointment (BA
Room 102 TAMU Commerce). We may also meet online at our
Classlive website by appointment.
Text:Business Forecasting 9th ed., Hanke and Wichern.
Pearson/Prentice Hall, Inc, ISBN: 139780132301206
Software: You need to rent the student version of MINITAB 16
for 6 months at

http://www.minitab.com/en-US/academic/
Important Dates: Please refer to the academic calendar at:
http://www.tamu-
commerce.edu/registrar/pdfs/academicCalendar09.pdf
CLASS Online lectures will be held on Tuesdays from 6:30
P.M. until 9:30 P.M. central time. During the lectures we the
will cover specific chapters and examples mentioned in the
syllabus. You may use the BA computer lab or the library
computers at TAMUC as an alternative to your personal
computer. I suggest that you download a copy of Minitab to
enable you to follow examples during the lecture.
COURSE OBJECTIVE
Objectives of this course is to introduce the student to the
basics of quantitative methods and their application to real
business situations as well as the use of current software
available for forecasting. After taking this course the students
will be able to apply different forecasting techniques to
empirically test economic theories and business policy analysis
and professionally present the results of their analysis.
COURSE OUTLINE
Chapter 1 Introduction to Forecasting
Chapter 2 Review of Basic Statistical Concepts
Chapter 3 Data Patterns and Forecasting Techniques
Project Part 1 (Proposal- 5 points) Due 9/16
Chapter 4 Moving Averages and Smoothing Methods
Project Part 2A (5 extra credit points) Due 10/14
Chapter 5 Time-Series and Their Components
Project Part 2B (5 extra credit points) Due 10/21
—Chapters 1,2,3,4, 5 (25 points) Due 10/24-10/26
Chapter 9 Box-Jenkins (ARIMA) Type Forecasting Models and
Combining Forecast Methods

Project Part 3 (5 extra credit points) Due 11/4
— Chapter 9 (25 points) Due 11/7-11/9
Chapter 6 Simple Linear Regression
Chapters 7& 8 Multiple Regression Analysis/Time Series
Project Part 4 (5 extra credit points) Due 11/25
—Chapters 6,7 and 8 (25 points) 12/5=12/6
Completed Class Project Part 5 (20 points) Due 12/2
NOTE: This outline is subject to change! Check your e-mail
multiple times every day, check our class eCollege website and
attend the class regularly.
GRADES AND ADMINISTRATIVE MATTERS:
Grades will be based on 2 exams (25 points each), a 5-part
formal class project (total of 25 points.), and a comprehensive
final exam (25 points). Project Parts must be completed and
submitted on time to earn credit. No late work will be
accepted. Plan in advance for the exams: there will be no early
exams and no make-up exams. An exam that is missed will be
considered an F, unless your professor is notified prior to the
exam and the excuse is a legitimate medical one or officially
approved. Regardless of the excuse, if you miss two tests you
will automatically fail the class. Again, late assignments and
projects will not be accepted. Course grades will be assigned as:
90 – 100 % A
80 – 89 % B
70 – 79 % C
60 – 69 % D
Below 60 % F
See the student evaluation criteria below.
HELPFUL HINTS Since this is an enhanced course, you need to
follow your school emails regularly. You will have regular
announcements and uploads posted in the class eCollege
website. For each chapter assigned, you need to read your book,

make sure you understand the key concepts and apply the
concepts using MINITAB. Reading the assigned materials,
working the assigned exercises, using office hours, being in
frequent communication with your instructor, and checking the
class website regularly are very important learning tools. A
textbook will be placed on 2 hour reserve in the library on
campus in case the dog ate yours. It can be checked out from
the circulation desk. Unfortunately, there is not a similar online
opportunity.
All assignments must be submitted to the appropriate
assignment dropbox in the course eCollege website. Each
submission should have a filename with your first initial
followed by your last name, eco 309 and assignment number
(assign#).
EXAMS: Each exam will be online and can be found on our
class eCollege website. Each exam is subject to a time limit.
You will have to upload your answers to exam problems by the
specified deadline. Late work will not be accepted.
PROJECT PARTS: You will have to upload your project
proposals and projects to BOTH turn-it-in.com and the relevant
dropbox folder on e-College by midnight of the specified due
date. Each submission should include a summary page of what
you had done, how you have done it and interpretations of the
results. Plots and output without interpretation will be
considered incomplete and will not be graded. Please submit
everything in Word format, cite and LABEL your variables. The
class id for turn-it-in is 2769279 and your enrollment password
is ECO309.
CLASS, LAB/ WORKSHIP AND OFFICE HOURS: I strongly
recommend using all options. Do not miss a class lecture
session and if you have any questions contact me for further
explanations via the email.

RULES, REGULATIONS AND OTHER STUFF
All students enrolled at the university shall follow the tenets of
common decency and acceptable behavior conducive to a
positive learning environment.
The College of Business and Technology at Texas A&M
University-Commerce students will follow the highest level of
ethical and professional behavior. Actionable Conduct includes
illegal activity, dishonest conduct, cheating, and plagiarism.
Failure to abide by the principles of ethical and professional
behavior will result in sanctions up to and including dismissal
from the university.
PLAGIARISM Plagiarism represents disregard for academic
standards and is strictly against University policy. Plagiarized
work will result in an “F” for the course and further
administrative sanctions permitted under University policy.
Guidelines for properly quoting someone else’s writings and the
proper citing of sources can be found in the APA Publication
Manual. If you do not understand the term “plagiarism”, or if
you have difficulty summarizing or documenting sources,
contact your professor for assistance.
STUDENT WORKLOAD University students are expected to
dedicate a minimum of 90 clock hours during the term/semester
for a 3SH course.
Students with Disabilities:
The Americans with Disabilities Act (ADA) is a federal anti-
discrimination statute that provides comprehensive civil rights
protection for persons with disabilities. Among other things,
this legislation requires that all students with disabilities be
guaranteed a learning environment that provides for reasonable
accommodation of their disabilities. If you have a disability
requiring an accommodation, please contact:

Office of Student Disability Resources and Services
Texas A&M University-Commerce
Gee Library
Room 132
Phone (903) 886-5150 or (903) 886-5835
Fax (903) 468-8148
[email protected]
Student Evaluation Criteria
Criteria
1(Unsatisfactory)
2 (Emerging)
3 (Proficient)
4 (Exemplary)
Understanding of time series data and components using various
statistical and graphical tools.
Student can’t demonstrate understanding of the components.
Student can identify some components.
Student can identify most components using most of the tools.
Student can identify all components using all the tools.
Understanding of Regression Analysis and application to both
time series and cross section data.
Student cannot demonstrate an understanding of regression
analysis.
Student demonstrates an understanding of some regression
concepts but cannot apply it.
Student demonstrates an understanding of the concept of
regression and can apply those concepts.
Student demonstrates an understanding of the concept of

regression and can apply to time series and cross section data.
Understanding and application of different univariate time
series models including but not limited to Smoothing,
Decomposition, and ARIMA.
Student cannot demonstrate an understanding of univariate
methods.
Student demonstrates an understanding of some/ all of the
univariate time series models but can’t apply.
Student demonstrates an understanding of some/ all univariate
time series models and apply some of them successfully.
Student demonstrates an understanding of all univariate time
series models and apply them successfully.
Identification of the best model from alternative models and
obtaining forecasts using at least one software.
Student cannot demonstrate an understanding of the model
selection processes.
Student can demonstrate an understanding of 1 out of 3 of these
processes.
Student can demonstrate an understanding of 2 out of 3 of these
processes.
Student can demonstrate an understanding of the entire
processes.
New folder/MINITAB ASSIGNMENTS/Assignment 4 Project
Part 2A.docx
Assignment 4 Project Part 2A -- The Exponential Smoothing
Forecast. Due by midnight 10/14. Get it in on time or it will
not be graded. This part of the assignment is worth up to 2.5
extra credit points and can serve as the exponential smoothing
part of your class project.
Show your work and submit it to the Chapter 4 Assignment 6
Dropbox.

This assignment addresses forecasting your selected Y data
(dependent variable) using an exponential smoothing technique.
Note: Do not use the X (independent) variables in this
exercise. Use only one exponential smoothing method -- the
best that applies. Do not use any other forecasting techniques in
this assignment. Turn in only the one best model that you
develop.
(Remember-- 1. Do not show failed models in business reports.
your boss or instructor.and 2. Never use Y hold out data
a) Tell me why you selected the appropriate exponential
smoothing method by commenting on your Y data
characteristics. (you should use a time series plot and
autocorrelations to do this),
b) Apply the appropriate exponential smoothing forecast
technique to your Y variable excluding the last two years of
data (8 quarter hold out period). Show the Y data, fitted values
and residuals in excel format and show your exponential
smoothing model coefficients. (Find the correct coefficient and
not just use the default values.)
c) Evaluate the "Goodness To Fit" using at least two error
measures -- RMSE and MAPE.
d) Check the "Fit" period residual mean proximity to zero
and randomness with a time series plot; check the residual time
series plot and autocorrelations (ACFs) for trend, cycle and
seasonality.
e) Evaluate the residuals for the "Fit" period by indicating the
residual distribution using a histogram (normal or not and
random or not),
f) Comment on the acceptability of the model's ability to pick
up the systematic variation in your Fit period actual data.
g) Develop a two year quarterly forecast (for the hold out

period).
h) Evaluate the "Accuracy" of the forecast for the "hold out
period" using RMSE and MAPE error measures used from
forecast period residuals and comment them.
i) Do the forecast period residuals seem to be random relative to
the hold out period data? Check the forecast period time series
plot of the residuals.
j) Did the error measures get worse, remain the same or get
better from the fit to the hold out period? Do you think the
forecast accuracy is acceptable?
Show your work and graphs in a Word document. Make sure
that you comment on statistics and graphs relevant to answering
the above questions. DO NOT leave statistics and graphs
stranded. If you show something write about it. Note that this
work will become part of your class project so do a good job on
it.
Part 2B.docx
Assignment 5 Project Part 2B -- The Decomposition Forecast.
Due by midnight 10/21. Get this in on time or it will not be
graded. This part of the assignment is worth up to 2.5 extra
credit points and can serve as the Decomposition part of your
class project.
Show your work and submit it to the Chapter 5 Assignment 7
Dropbox. (Again -- 1. Do not show failed models in business
reports. Share your failures with your family if you wish and
not with your boss or instructor.and 2. Never use Y hold
out data observations in any forecast model.)
a) Perform Time Series Decomposition on your project Y
variable excluding the hold out period. Show me the smoothed
Trend Values (TREN in Minitab) , Smoothed Cycle Values (use
Minitab Calculator to DESE/TREN for Cycle Factors) and

Seasonal Indexes (SEAS in Mintab).
-- note that you must use the last cycle factor and multiply each
forecast observation by it to get a cycle adjusted forecast.
Since this is a multiplicative decomposition model this must be
done Minitab result to obtain a reasonable forecast. We have
discussed this procedure in class.
b) Show the seasonal indices (SEAS in Minitab) and develop a
one year time series plot of them. Do they indicate strong
seasonality? How can you tell?
c) Evaluate the "Goodness To Fit" using RMSE and MAPE error
measures .
d) Evaluate the residuals for the "Fit" period by indicating the
residual distribution (random or not). Use a fit period residual
time series plot, residuals ACFs and a histogram to determine if
the Fit period residuals are random. If the residuals are not
random state if you detect any trend, cycle and seasonality
autoregressive characteristics. (Note: you expect to see only
cycle in the residuals -- any T or S is a signal that the model did
not use this information. You will adjust the cycle component
in the forecast by using the last cycle factor in the forecast.)
e) Develop a two year quarterly forecast (for the hold out
period) using the time series decomposition model you
evaluated in c) above and adjust the forecast with the last cycle
factor. Evaluate the reasonableness of the forecast by
appending the cycle adjusted decomposition forecast to the Y
data and developing a time series plot.
f) Evaluate the "Accuracy" of the model for the "hold out
period" using the RMSE and MAPE measures used in part b)
and comment on them. Did the error measures increase, remain
the same or decrease from the "Fit" to "Hold Out" or
forecast period?
Show your work and graphs in a Word document. Make sure
that you comment on statistics and graphs relevant to answering
the above questions. Again, this will be the decomposition
portion of your class project.

Part 3.docx
Assignment 6 Project Part 3 -- The ARIMA Forecast. This
assignment is due by midnight Nov 4th. The assignment is
worth a maximum of 2.5 extra credit points and may serve as
the project ARIMA section. This assignment is due by midnight
Nov 4th. No late submissions will be graded.
(Again -- 1. Do not show failed models in business reports.
your boss or instructor.and 2.Never use Y hold out data
Complete each of the following sections.
a) Examine the Y data (excluding the hold out period) to
determine if it needs to be differenced to make it stationary.
Show a time series plot of the raw Y data and autocorrelation
functions (ACFs).
b) From your time series data plot and AFCs determine if you
have seasonality. If you do, use seasonal differences to remove
it and run the ACFs and PACFs on the non seasonal Y data
series.
c) Fill out the ARIMA seasonal menu (P,D,Q) appropriately. If
you have no trend as shown by the seasonally differenced ACFs
run the ARIMA model and note the significance of each
results.
Note: You may not use an ARIMA model with non significant
coefficients to forecast. If the coeffcients are not signficant
derive another model that has signficant coefficents and the
lowest residual MS value.
d) If it requires differencing for trend to make it stationary do

so and run another time series plot and ACFs on the differenced
data. If this requires differencing again do so but run time series
plots and ACFs each time you do.
e) Run and show the PACFs on your stationary data series and
identify the appropriate ARIMA model and show the initial
ARIMA non seasonal menu section (p,d,q) filled out
appropriately and any seasonal (P,D,Q) components in the
seasonal menu filled out.
f) Run the ARIMA model and note the significance of each
results shown by the residual MSE.
g) Calculate the two error measures that you used in other
model analysis and comment on the acceptability of the size of
the measure.
h) Note the LBQ associated P values for the selected lags. They
should each be significant (above .05) to qualify the residuals
as potentially random. If they are not random select an
alternative ARIMA model form that has random residuals.
i) Run an ARIMA forecast for your hold out period and show a
time series plot of the residuals (Y actual and Y forecast) for
the 8 quarter hold out period.
j) Calculate the hold out period RMSE and MAPE (Refer back
to earlier chapters for the error measure formulas) and compare
them to the Fit period ARIMA error measures (from g above).
k) Plot the forecast values appended to the Y data without the
hold out to check for forecast reasonableness.
Read chapters 6 and 7. Go to assignment 10 in chapter 6.
Part 4.docx
Assignment 7 Project Part 4-- The Multiple Regression Forecast
-- This assignment is due by midnight November 25th. This
completed assignment is worth up to 2.5 extra credit points and

may serve as the multiple regression portion of the class
project. Late submissions will not be graded.
This assignment is essentially the multiple regression analysis
portion of your project. This means that I expect you to
develop a good regression model with more than one
independent variable (X). Ideally, if you made a good choice of
variables in your proposal you should be able to include all
three or more X variables in your regression equation. Be sure
to complete each part and write your responses supported by
Minitab/excel work. This assignment should be turned in to me
as a Word document. You should include excel and Minitab
tables and graphs in the Word document as required. Be sure to
comment on each of the 10 points below.
1. Run scatter plots and a correlation matrix on your project
variables and comment on their values and significance if you
have done this earlier you may use that analysis here.
2. Note any seasonality in your Y data with ACF
(autocorrelation analysis of Y) You may use ACFs that you
previously developed.
3. Determine if any of your variables require
transformation. If they do, calculate the transformed values and
create a scatter plot with a regression line and run a correlation
with Y for each transformed X. Create a table for the Y, X and
X transformed values.
4. Determine if your model requires dummy variables (e.g. for
Y variable seasonality or significant events) and include a table
of the dummy variable values for regression analysis. You may
use either Decomposition centered moving average of Y (CMA)
for Y and seasonal indices (SI) to seasonally adjust your Y
variable or use dummy X variables in regression.
5. Use regression to evaluate the variable combinations to
determine the best regression model. Note that is any seasonal
dummy variables are used all of the seasonal dummy variables
must be used. Use R square and F as primary determinants of
the best model.
Note the significance of each slope term in the model. Rule-- if

the coefficient is not significant then you may not use the model
to forecast.
7. Investigate your best model using appropriate statistics or
graphs to comment on possible:
a. Autocorrelation (Serial correlation) with the DW statistic
b. Heteroscedasticity with a residuals versus order plot (look
for a megaphone effect)
c. Multicollinearity with the VIF statistic
Determine the best remedies for any of the problems identified
in 5 above and make the appropriate changes to your regression
model if required. Rerun the model and evaluate the fit again
including error measures, R adjusted square, F value, slope
coefficient significance, DW and VIF.
6. Evaluate the best multiple regression model accuracy with 2
error measures (RMSE and MAPE) each for the fit and again for
the forecast period.
9. Evaluate the best model fit residuals and comment on their
randomness using autocorrelation functions (ACFs) , histogram
and a normality plot (You should use a four-in-one graphs as
well). Comment on the cause of the error -- trend, cycle,
seasonality and if it is statistically significant.
10. Forecast for the holdout period using your hold out X values
to forecast Y. You can use Minitab Regression - Options menu
by placing the columns for the X variables hold out values and
any dummy variable predictions in the
"Minitab/Regression/Options/Prediction intervals for new
observations" area.
11. Evaluate the forecast error measures and residuals to
determine if the error is acceptable or has systematic
variation. Write your conclusion relative to the acceptability of
the sales forecast.
New folder/MINITAB ASSIGNMENTS/Assignment 8 -- Project

Part 5 -- Class Projec.docx
Assignment 8 -- Project Part 5 -- Class Project is due
December 2. This is worth a maximum of 20 final grade
points. No late submissions will receive a grade.
You will not be given an example for the project. Consider it a
business assignment that you have been given by an executive
to forecast the company sales (Y) variable. The projects will be
evaluated on how well you forecast the Y variable and your use
of the four alternative forecast techniques. Consider the reader
not as an economics professor but an executive that requires the
best forecast of Y. You mustnotmake this a forecasting tutorial
-- executives may take offense at this. Assume that the
executive is at least a MBA level and has basic familiarity with
statistical concepts.You mustnotuse possessive terms such as
"my", "our" or "your" when referring to data, statistics or
models in this study. This is a sign of poor professional
business report writing.You must provide statistical or graphical
support for your points in the project. Do not make assertions
without support or proof. For example, what constitutes the
"best" forecast? Why are X variables "significant" in
forecasting a Y variable. What is significant
seasonality?Remember that this is a business report and not a
Minitab exercise. As a result, each Minitab plot, table or
statistic must be appropriately narrated relative to 1) why you
are showing it and 2) what it indicates. Stand alone plots,
statistics or tables without narration will not be graded. In
essence, if it does not have narrative -- it does not exist.Never
show failed work in your report. It is a waste of the executive's
time to read about your failures. Show only your success or
best results.Never use the word "attempt" in the report. In
business either the project is accomplished or it is not.
Every project will be subject automatically to Turn-It-In so do
not use material from previous projects submitted by others. If
I detect plagiarism (a turn-it-in of 50 or more you will receive a
zero for the project and an F in the course.

You will be graded on organization, grammar and spelling as
well as content described in the project outline in Doc Sharing.
Reread and spell check your work. Your project will also be
graded on the ease of reading your material. Typically, plots
and tables close to the narrative are easier to read. However,
you may include and refer to tables in appendices as well.
Please ensure that your project is in MS Word format. The
Appendix items should be included in the document along with
appropriate data citations. Again, late projects will not receive
a grade.
Submit your project in the drop box for the class project by
midnight December 2 with your first initial, last name followed
by Eco 309 Project as the file name.
Thank you,
Stanley Holmes, Ph.D.
New folder/POWERPOINTS/chap08-09.ppt
©2007 McGraw-Hill/Irwin
Chapter 8
Combining Forecast Results
8-*
Forecasts of the Same Series (Y) Can Be Quickly and Easily
Combined
The forecast methods can be different – for example a
regression forecast can be combined with a qualitative forecast

and combined with a decomposition forecast and combined with
and exponential smoothing forecast.
You must have the forecast series along with the residuals and
RMSE to combine forecasts effectively.
Selecting the appropriate weights to give to each forecast series
can be done using several alternative methods.
8-*
McGraw-Hill/Irwin
©2007 The McGraw-Hill Companies, Inc. All rights reserved
Selecting the Appropriate Weights for each Forecast is
Important
8-*
One of the methods to assign forecast weights is the Variance-
Correlation method with a general form:
k = (ó2)2 - ρ ó1ó2
(ó1)2 - (ó2)2 - 2ρ ó1 ó2
Another method of continually adjusting weights is the Ratio of
Errors method with a general form:

ɑ1, T+1 = ∑ ε22t
ε21t + ε22t
Where:
k = the weight of Forecast 1
Ó1 = the variance of residuals of Forecast 1
Ó2 = the variance of residuals of Forecast 2
ρ = the Correlation if residuals between Forecast 1 and Forecast
2
k-1 = the weight of Forecast 2
T
t=T-v
Where:
ɑ1, T+1 = Weight assigned to Forecast 1 in time period T+1
εit = error (residual) made by forecast i in time period t
v=no of periods included in adaptive weighting procedure.
T = total number of forecast error periods
8-*
8-*
Combining a Subjective, Regression and a Decomposition
Forecast
8-*

Note combining all three forecasts produces the best results.
8-*
The General Form for Combining Forecasts With Regression
Ŷ1 is the forecast series for the best forecast method. When
compared to the observations (Y) values generates residuals that
can be summarized with the lowest RMSE.
Ŷ2 is the next best forecast series and when compared to the Y
observation values generates residuals that can be summarized
by RMSE.
Problem: what weights to apply to each forecast series to get the
best forecast results (lowest RMSE).
ŶF= β Ŷ1 + β Ŷ2
You may have more than 2 forecasts to combine. When you do
combine the stepwise through the regressions. Combine two
forecasts, then three and if necessary combine 4 in successive
regression runs.. Note the RMSE changes as well as BIC, AIC
and R square changes as you add other forecast (Ŷn) models.
Also note the t values for the coefficients of your forecasts.
8-*
Using Regression to Combine Forecasts
Make sure there is no overlap in model composition – Run
correlation coefficient(s) on the squared residuals between each

forecast Ŷ1 and Ŷ2. Correlation should be low.
Run regression with the actual observations (Y) as the
dependent variable and the forecast series (Ŷ1) as X1 and Ŷ2 as
X2.
Check the t-statistic for the intercept (constant) coefficient to
ensure that it is not significant. You want it to fail the Ho
hypothesis. If it is significant you may want to include another
forecast as X3 and check the intercept t statistic again.
Rerun the regression with the same data again and force the
intercept through the origin (no intercept coefficient). Check
the slope terms for forecasts X1 and X2 to ensure they sum to
approximately 1. The coefficients are the weights to apply to
each forecast.
Multiply each X variable forecast series by its weight
(percentage) and sum for each period for the forecast.
Check the RMSE and MAPE the ensure that it is lower than
individual forecast measures.
8-*
8-*

Solution
s to
Case Questions #2
8-*

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