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In: Statistics and Probability

Hi, Which value of α do you prefer? (Round your answers to 2 decimal places.). It...

Hi,

Which value of α do you prefer? (Round your answers to 2 decimal places.). It is question C.

Daily Spot Exchange Rate, U.S. Dollars per Pound Sterling
Date Rate Date Rate Date Rate
1-Apr-04 1.8584 13-Apr-04 1.7860 23-Apr-04 1.7874
2-Apr-04 1.8363 14-Apr-04 1.7752 26-Apr-04 1.7857
5-Apr-04 1.8140 15-Apr-04 1.7785 27-Apr-04 1.7925
6-Apr-04 1.8474 16-Apr-04 1.8104 28-Apr-04 1.7720
7-Apr-04 1.8410 19-Apr-04 1.8255 29-Apr-04 1.7656
8-Apr-04 1.8525 20-Apr-04 1.7816 30-Apr-04 1.7744
9-Apr-04 1.8422 21-Apr-04 1.7620 3-May-04 1.7720
12-Apr-04 1.8558 22-Apr-04 1.7794 4-May-04 1.7507
5-May-04 1.7732 13-May-04 1.7754 21-May-04 1.7880
6-May-04 1.7641 14-May-04 1.7692 24-May-04 1.7808
7-May-04 1.7942 17-May-04 1.7595 25-May-04 1.7535
10-May-04 1.7693 18-May-04 1.7695 26-May-04 1.8542
11-May-04 1.7644 19-May-04 1.7727 27-May-04 1.7769
12-May-04 1.7743 20-May-04 1.7610 28-May-04 1.7730

Click here for the Excel Data File

(b) Perform simple exponential smoothing (using Excel’s Data Analysis or other software such as Minitab) using α = .05, .10, .20, and .50.

The degree of smoothing  (Click to select)  varies  does not vary  dramatically as α is increased.

(c) Which value of α do you prefer? (Round your answers to 2 decimal places.)

α =

(d) Is exponential smoothing appropriate for this kind of data?

(Click to select)  Yes  No

Solutions

Expert Solution

b)

Rate ES(0.05) = αAt+(1-α)Ft ES(0.1) = αAt+(1-α)Ft ES(0.2) = αAt+(1-α)Ft ES(0.5) = αAt+(1-α)Ft ES(0.05) Error^2 = (Actual-Predicted)^2 ES(0.1) Error^2 = (Actual-Predicted)^3 ES(0.2) Error^2 = (Actual-Predicted)^4 ES(0.5) Error^2 = (Actual-Predicted)^5
1.8584 1.8584 1.8584 1.8584 1.8584 0 0 0 0
1.8363 1.8584 1.8584 1.8584 1.8584 0.00048841 0.00048841 0.00048841 0.00048841
1.814 1.857295 1.85619 1.85398 1.84735 0.001874457 0.001779996 0.0015984 0.001112223
1.8474 1.85513025 1.851971 1.845984 1.830675 5.97568E-05 2.0894E-05 2.00506E-06 0.000279726
1.841 1.854743738 1.8515139 1.8462672 1.8390375 0.00018889 0.000110542 2.77434E-05 3.85141E-06
1.8525 1.854056551 1.85046251 1.84521376 1.84001875 2.42285E-06 4.15137E-06 5.30893E-05 0.000155782
1.8422 1.853978723 1.850666259 1.846671008 1.846259375 0.000138738 7.16775E-05 1.99899E-05 1.64785E-05
1.8558 1.853389787 1.849819633 1.845776806 1.844229688 5.80913E-06 3.57648E-05 0.000100464 0.000133872
1.7732 1.853510298 1.85041767 1.847781445 1.850014844 0.006449744 0.005962569 0.005562392 0.00590052
1.7641 1.849494783 1.842695903 1.832865156 1.811607422 0.007292269 0.006177316 0.004728647 0.002256955
1.7942 1.845225044 1.834836313 1.819112125 1.787853711 0.002603555 0.00165131 0.000620614 4.02754E-05
1.7693 1.842673791 1.830772681 1.8141297 1.791026855 0.005383713 0.003778891 0.002009702 0.000472056
1.7644 1.839005102 1.824625413 1.80516376 1.780163428 0.005565921 0.0036271 0.001661684 0.000248486
1.7743 1.835274847 1.818602872 1.797011008 1.772281714 0.003717932 0.001962744 0.00051579 4.07348E-06
1.786 1.832226104 1.814172585 1.792468806 1.773290857 0.002136853 0.000793695 4.18455E-05 0.000161522
1.7752 1.829914799 1.811355326 1.791175045 1.779645428 0.002993709 0.001307208 0.000255202 1.97618E-05
1.7785 1.827179059 1.807739794 1.787980036 1.777422714 0.002369651 0.000854966 8.98711E-05 1.16054E-06
1.8104 1.824745106 1.804815814 1.786084029 1.777961357 0.000205782 3.11831E-05 0.000591266 0.001052266
1.8255 1.824027851 1.805374233 1.790947223 1.794180679 2.16722E-06 0.000405047 0.001193894 0.0009809
1.7816 1.824101458 1.80738681 1.797857778 1.809840339 0.001806374 0.00066496 0.000264315 0.000797517
1.762 1.821976385 1.804808129 1.794606223 1.79572017 0.003597167 0.001832536 0.001063166 0.00113705
1.7794 1.818977566 1.800527316 1.788084978 1.778860085 0.001566384 0.000446363 7.54288E-05 2.91508E-07
1.7754 1.816998688 1.798414584 1.786347983 1.779130042 0.001730451 0.000529671 0.000119858 1.39132E-05
1.7692 1.814918754 1.796113126 1.784158386 1.777265021 0.002090204 0.000724316 0.000223753 6.50446E-05
1.7595 1.812632816 1.793421813 1.781166709 1.773232511 0.002823096 0.001150689 0.000469446 0.000188582
1.7695 1.809976175 1.790029632 1.776833367 1.766366255 0.001638321 0.000421466 5.37783E-05 9.82036E-06
1.7727 1.807952366 1.787976669 1.775366694 1.767933128 0.001242729 0.000233377 7.11126E-06 2.27231E-05
1.761 1.806189748 1.786449002 1.774833355 1.770316564 0.002042113 0.000647652 0.000191362 8.67984E-05
1.7874 1.803930261 1.783904102 1.772066684 1.765658282 0.00027325 1.22213E-05 0.000235111 0.000472702
1.7857 1.803103748 1.784253691 1.775133347 1.776529141 0.00030289 2.09181E-06 0.000111654 8.41047E-05
1.7925 1.80223356 1.784398322 1.777246678 1.78111457 9.47422E-05 6.56372E-05 0.000232664 0.000129628
1.772 1.801746882 1.78520849 1.780297342 1.786807285 0.000884877 0.000174464 6.88459E-05 0.000219256
1.7656 1.800259538 1.783887641 1.778637874 1.779403643 0.001201284 0.000334438 0.000169986 0.000190541
1.7744 1.798526561 1.782058877 1.776030299 1.772501821 0.000582091 5.86584E-05 2.65787E-06 3.60308E-06
1.772 1.797320233 1.781292989 1.775704239 1.773450911 0.000641114 8.63596E-05 1.37214E-05 2.10514E-06
1.7507 1.796054221 1.78036369 1.774963391 1.772725455 0.002057005 0.000879935 0.000588712 0.000485121
1.788 1.79378651 1.777397321 1.770110713 1.761712728 3.34837E-05 0.000112417 0.000320027 0.000691021
1.7808 1.793497185 1.778457589 1.77368857 1.774856364 0.000161219 5.48689E-06 5.05724E-05 3.53268E-05
1.7535 1.792862326 1.77869183 1.775110856 1.777828182 0.001549393 0.000634628 0.000467029 0.00059186
1.8542 1.790894209 1.776172647 1.770788685 1.765664091 0.004007623 0.006088268 0.006957447 0.007838607
1.7769 1.794059499 1.783975383 1.787470948 1.809932045 0.000294448 5.0061E-05 0.000111745 0.001091116
1.773 1.793201524 1.783267844 1.785356758 1.793416023 0.000408102 0.000105429 0.000152689 0.000416814
Forecast value 1.792191448 1.78224106 1.782885407 1.783208011
MSE MSE 0.0017 0.0011 0.0008 0.0007

the degree of smoothing does not vary  dramatically as α is increased (there is a little change, not much)

c)

MSE of ES(0.5) is less than others, so prefer ES(0.5)

d)

yes

orchestra answered 1 year ago
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