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 coefficient. Make model adjustments accordingly to improve 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
12/31/19964883.40826182.709-1299.30080.794976792.86872919235.59870750.0774251950.661521157
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
6/30/19996053.81986592.3579-538.53810.2213945090.55613274455.73407620.0369784940.315944389
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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MaryTemi
assignment_6__project_part_3.docx
