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
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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
12/31/19964883.40826182.709-1299.30080.794976792.86872919235.59870750.0774251950.661521157
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_4_project_part_2a.docx
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