Task 1

Inthefirsttask,youwillanalyseandforecasttheamountofhorizontalsolarradiationreachingthegroundat aparticularlocationovertheglobe.Forthisaim,youwillworkonthemonthlyaveragehorizontalsolarradiationandthemonthlyprecipitationseriesmeasuredatthesamepointsbetweenJanuary 1960andDecember 2014.Bothseriesareattached intable below

solar	ppt
5.051729287	1.333
6.415831889	0.921
10.8479197	0.947
16.93026419	0.615
24.03079665	0.544
26.29820179	0.703
26.37065748	0.741
22.48036537	0.868
15.28125086	1.107
10.18159408	1.429
7.010803777	1.437
4.672524081	1.58
13.48152391	0.747
16.07858355	0.504
25.72149415	0.487
34.19702116	0.392
44.06678049	0.35
47.63652229	0.338
49.39733178	0.332
43.73478557	0.434
32.53640941	0.65
22.2513301	0.884
15.26416566	0.844
11.42466072	0.896
6.951181284	0.644
7.76386236	0.539
11.89204716	0.603
13.58588688	0.589
22.00316916	0.498
22.63356168	0.473
23.70440556	0.328
20.73449898	0.379
13.68008988	0.519
10.42227102	0.84
6.6880641	0.852
5.78099388	0.797
5.740027501	0.968314
8.949175965	0.732
12.37678374	0.598657
16.45492714	0.575086
21.58890089	0.533314
23.6441462	0.494286
22.79688498	0.3272
21.14347991	0.290114
17.16085926	0.347257
11.21815272	0.625229
7.931192922	0.815943
5.81279764	0.939629
5.194090344	0.531114
8.485004659	0.450257
13.18248869	0.495029
18.82105112	0.455486
23.46454445	0.561057
25.68759864	0.387314
27.24186967	0.3288
23.16407662	0.269829
16.22850324	0.380771
11.29198333	0.515314
6.208846665	0.7296
4.12980295	0.680857
1.58198238	0.834
2.40294408	0.655
4.4812716	0.602
3.72178608	0.533
4.12462602	0.293
4.49295975	0.258
3.1980174	0.209
3.49521042	0.245
3.97169152	0.358
3.50314208	0.679
2.63740488	0.74
12.78639416	0.991
5.286285484	0.583714
8.37378534	0.432686
13.03832599	0.485829
18.471224	0.497486
22.91422766	0.594229
25.2593295	0.474657
27.25072964	0.329371
24.51362599	0.260743
18.13482731	0.260657
11.90550187	0.433429
7.900462394	0.491971
5.245637526	0.599086
5.72472794	0.401257
8.12532276	0.2744
14.4113145	0.325057
16.4992484	0.495914
21.8405585	0.5332
22.6945494	0.374857
23.88742454	0.206914
21.38821198	0.167943
17.45139185	0.162914
13.0372207	0.304771
7.345377744	0.301486
5.678640576	0.428714
5.576693547	0.478543
7.6074156	0.357771
11.69349515	0.4418
16.43867936	0.597571
20.19955775	0.515829
21.96796903	0.363686
22.75210046	0.156943
20.75504919	0.103143
16.17297263	0.214829
10.62147741	0.383486
6.390607467	0.5022
4.706023011	0.487457
12.66011562	0.394
16.97024479	0.345
26.68443024	0.402
33.42071232	0.575
43.73508443	0.594
47.25108295	0.38
46.95314772	0.115
43.04624164	0.062
34.74285301	0.18
24.29064637	0.389
15.0252529	0.456
11.48226411	0.474
4.224080902	0.348743
8.625186512	0.344
13.62007732	0.414771
17.21275904	0.616886
20.94374481	0.698686
24.81104458	0.4392
26.0054901	0.130086
23.05744945	0.119571
18.17749062	0.235229
10.81015505	0.467514
5.107352742	0.460771
3.460766121	0.399943
12.7125204	0.42
17.26068776	0.398
25.48556332	0.466
32.99319352	0.616
41.87037252	0.597
47.40814123	0.354
48.54622512	0.089
45.02026963	0.06
35.56999214	0.178
26.22688278	0.35
16.4652888	0.423
12.10990032	0.467
7.5927618	0.259571
9.75901212	0.294743
14.81596872	0.416429
17.75440452	0.535857
22.00219224	0.537514
21.85383996	0.291971
23.45194152	0.086686
22.17999168	0.065229
18.16554828	0.149286
12.45335748	0.460771
9.3700584	0.421086
6.6147951	0.287829
7.038442167	0.196912
10.25157518	0.243824
14.76467505	0.306088
15.83230905	0.580294
20.96339348	0.698118
23.53030983	0.415706
24.168303	0.2575
19.4578041	0.151647
17.71037334	0.200324
12.00953342	0.476382
8.615485392	0.323206
6.511674216	0.225235
8.237723745	0.197057
11.48414063	0.223829
16.99588865	0.293286
18.20247938	0.528714
22.55450415	0.778914
28.36889404	0.743371
27.48637887	0.546114
26.37012192	0.4156
20.77461357	0.271686
13.51368105	0.435371
10.15876563	0.274086
7.317892386	0.226114
6.174697746	0.372
9.524703632	0.501771
15.79370244	0.492229
18.42159981	0.760857
23.54489449	0.753543
29.30737182	0.493257
28.55423055	0.194371
26.37343309	0.107171
21.75830714	0.1532
14.51213198	0.534429
9.883588463	0.500114
5.772445836	0.430314
5.765815289	0.84726
8.404420879	0.62509
13.67259885	0.65937
18.97639157	0.47946
24.23084697	0.32771
26.1279065	0.20697
27.43610449	0.12023
23.6799855	0.04714
17.71174085	0.19289
11.8741741	0.46791
7.34933807	0.90586
4.853285229	1.02729
5.504580698	0.813171
7.170858021	0.688314
11.41079721	0.643286
16.02435629	0.640914
21.30557078	0.427086
24.29123085	0.329343
25.20653467	0.184714
22.0310158	0.1344
15.84201393	0.399171
10.59071342	0.666343
6.759733563	0.853057
5.009374558	0.970457
3.770345942	0.358625
7.337857226	0.242937
12.42120792	0.275562
17.67308234	0.373312
21.47405024	0.41425
24.90035126	0.223313
25.71854387	0.094313
22.1256983	0.07975
16.75371842	0.029733
9.972278625	0.221333
4.817265492	0.2754
3.242056127	0.386667
5.947449811	0.405886
8.744105956	0.332114
13.3296744	0.366286
18.35911996	0.522229
23.08390895	0.487029
25.87721302	0.327086
27.58904801	0.144086
25.13684328	0.119086
19.27045009	0.175886
12.69221174	0.2952
8.181073582	0.377286
5.683866541	0.4186
8.68146936	0.444
11.0142985	0.353
15.8632037	0.366
18.02726758	0.465
23.50206682	0.447
25.05388098	0.351
25.35233004	0.068
23.67035292	0.051
19.2367271	0.121
14.73332129	0.297
9.299385216	0.386
7.72227348	0.495
7.159257994	0.399971
12.27910928	0.317429
15.76940647	0.396771
20.90475747	0.5298
25.19004442	0.537514
28.3783342	0.315771
28.97948119	0.086743
27.38615382	0.0714
22.66915112	0.116486
15.0489572	0.330171
9.930452825	0.458714
7.602672835	0.459229
15.03019332	0.72
16.30667886	0.66
25.73395686	0.569
34.89094901	0.567
44.89142784	0.462
50.20626341	0.251
54.05637956	0.159
48.6841104	0.097
38.36427642	0.157
26.47905374	0.405
16.30250602	0.592
13.13615478	0.839
6.546942116	0.414371
9.248326082	0.361429
14.75825907	0.425714
18.33325663	0.492686
24.32122277	0.457457
26.2664986	0.3126
29.16086588	0.193943
25.75712847	0.139486
20.37903271	0.1752
13.39571596	0.3774
8.30182766	0.387257
6.232334054	0.468343
7.120755666	0.371286
11.27762208	0.312971
16.57696257	0.366486
21.66961895	0.518343
26.48924174	0.421571
30.53356289	0.210771
30.78117048	0.074086
27.84631339	0.034457
23.2775449	0.087657
15.07752303	0.257657
10.06704228	0.342943
6.85849116	0.416114
6.567777336	0.41
9.02576388	0.373
13.66130003	0.514
17.328593	0.578
22.2513208	0.472
24.00157532	0.181
25.82858629	0.02
23.38603819	0.016
19.07848777	0.066
13.59599723	0.377
8.62355196	0.445
6.24303052	0.411
15.41006474	0.366714
16.27574628	0.414686
16.33814735	0.508857
15.60810148	0.643486
14.23027781	0.515571
15.47839925	0.124714
14.9944576	0.020943
14.11837588	0.005286
10.41277222	0.0782
14.73501981	0.475686
14.69851918	0.465057
12.34901215	0.435057
16.65483919	1.2158
19.46387496	1.44654
27.58004258	1.30169
32.07091901	1.20751
42.05811173	0.77137
48.92843344	0.20446
48.82618248	0.06754
43.10347816	0.04066
36.43551845	0.10806
27.77259507	0.69051
18.1097708	1.13577
14.83097917	1.39849
7.88411656	1.211
9.62898872	0.91811
16.04560862	0.81257
18.31601722	0.48843
24.57656252	0.26414
26.77884258	0.06634
27.77065363	0.02471
24.9412421	0.01591
19.69294874	0.19569
14.87402568	0.43517
9.307507608	1.12731
7.16672001	1.34366
8.065542045	0.99229
9.561993285	0.84291
15.27863529	0.72174
18.8112549	0.57623
24.53610959	0.35414
27.23666261	0.13323
28.12930012	0.03394
24.72547929	0.024
19.4442328	0.11146
14.26363116	0.42506
8.977545675	0.9104
6.947778856	1.16026
8.43287811	0.507429
10.09749164	0.380086
15.47365918	0.455429
18.11114314	0.504257
22.9123793	0.404571
25.44839384	0.251571
25.58173877	0.151971
23.65985801	0.078571
19.54147032	0.1676
14.16480967	0.340257
9.13503936	0.429514
6.88609974	0.587314
5.926395463	0.727
7.20045864	0.648
11.69900079	0.543
14.37164955	0.561
17.4788433	0.501
19.70011515	0.295
21.01327008	0.135
19.33684047	0.105
15.14581878	0.156
10.91060143	0.364
7.4933253	0.461
5.164158617	0.856
8.276500522	0.667886
12.78498298	0.500943
18.52300822	0.4746
22.49041638	0.482543
25.53736872	0.428229
30.32891938	0.220543
30.86748696	0.079486
27.8098111	0.086971
23.37526991	0.1746
15.50571705	0.443657
11.21233396	0.628971
7.595322152	0.777457
7.71501636	0.353
10.15893875	0.282
15.95038852	0.271
18.75849685	0.34
23.54974517	0.436
25.28871859	0.232
27.595664	0.069
24.93732512	0.056
20.00780231	0.112
14.74363012	0.313
9.490281587	0.331
7.05849123	0.448
8.632956645	0.418714
13.41790718	0.344629
18.56569006	0.348486
23.2153055	0.380029
28.21667309	0.375571
32.47388956	0.219886
32.6643695	0.057
30.16327486	0.052857
25.35620228	0.059371
16.65636348	0.2806
11.32928263	0.348771
8.50288941	0.434429
25.94225016	0.928086
17.45086152	0.895114
22.12416768	0.719886
32.21268096	0.514714
37.21255752	0.309429
38.30698704	0.062286
41.61874584	0.026571
39.24510936	0.028629
30.63844416	0.072886
27.15781776	0.406343
18.64493688	0.712857
15.44398872	0.958457
7.747118094	0.790057
12.32295504	0.753229
18.71687488	0.629
22.59262814	0.441114
25.73579047	0.243771
31.82067334	0.068257
31.50269454	0.013029
28.35465379	0.014971
23.30726541	0.052343
16.76689072	0.358571
11.49504815	0.622029
7.693238834	0.827314
6.421103265	1.23834
8.353799925	1.10071
13.23729701	0.89746
17.2247185	0.66031
21.26798104	0.37446
23.72912319	0.07817
24.18157671	0.01103
21.429438	0.00846
18.03344699	0.05109
12.65871227	0.44391
8.4674541	0.78563
6.43507671	1.3342
14.12146234	0.865
17.82136541	0.712
30.14951896	0.643
38.10075723	0.48
47.34708573	0.283
49.8714171	0.034
53.00670228	0.007
44.50507924	0.009
35.69163264	0.029
28.46541521	0.274
18.48081432	0.466
14.01986266	0.788
5.785138812	0.640235
7.456721813	0.727382
11.96913503	0.695
15.46037306	0.628265
19.99155132	0.401059
22.85398274	0.085941
23.27891813	0.004382
19.91074608	0.003471
16.69933092	0.041941
12.31998464	0.336353
8.10931988	0.540941
6.499640655	0.720588
8.170253697	0.8314
12.24594205	1.0768
15.88975743	1.10157
19.17199604	1.18706
23.53022591	0.63683
28.79977811	0.15082
28.69091623	0.04506
25.55061562	0.02374
21.64898526	0.05871
14.39256593	0.57541
10.26346299	0.88662
7.455941424	0.94738
4.65916408	2.17154
6.606690651	1.34306
9.333371565	1.02269
8.985750034	0.62697
15.13942893	0.3192
16.35537755	0.07617
17.51343674	0.02703
13.80228241	0.01926
11.98460335	0.12369
8.854551672	0.8298
5.505949032	1.75666
4.875301815	2.72129
6.98883916	1.96477
9.06577108	1.40363
14.41075626	0.90343
16.69667928	0.52514
20.85664887	0.217
22.45684383	0.04311
22.44129452	0.00246
20.417628	0.0108
16.00971844	0.09746
12.82677352	0.69371
8.41309548	1.46297
5.2010523	2.00397
8.255584575	1.098
10.19314341	0.835
16.38441378	0.553
19.33026022	0.36
23.4227037	0.225
24.58900662	0.085
24.68099992	0.079
22.08840931	0.04
18.36052756	0.072
14.33903017	0.394
9.778348933	0.802
7.5739212	1.404
5.28115974	1.81706
6.47986384	1.65246
11.93949756	1.44114
15.56847624	1.03991
18.54459324	0.91786
19.82254416	0.13934
20.28067312	0.12054
17.95057936	0.02511
14.08732596	0.40706
10.20383636	0.77597
6.81462176	1.18466
4.77993	1.72146
7.341332789	0.724086
9.802918412	0.578657
15.23896513	0.559457
20.33103595	0.606486
26.64957783	0.414943
24.24234981	0.254114
29.1933482	0.092314
27.54532655	0.105886
18.45321287	0.1122974
10.9467614	0.441514
10.35625125	0.6978
6.693188322	0.803543
8.276219961	0.159829
12.70249823	0.222257
17.2507797	0.290114
18.15558524	0.401629
23.18990506	0.560029
27.52934295	0.4254
27.96756048	0.214457
25.04415692	0.127143
20.68342645	0.153886
13.98594027	0.3334
8.888159361	0.247143
6.929822386	0.185371
7.803637397	0.83149
10.32716075	0.74289
16.5322018	0.58774
21.73007554	0.49854
26.44749436	0.3548
31.15603303	0.16443
31.14351281	0.05826
27.74203216	0.05211
22.29732973	0.18403
15.45572997	0.4348
9.680586309	1.06603
6.801510181	1.07897
7.532919413	0.346914
10.93140446	0.346686
16.29529828	0.464886
19.6956767	0.560143
22.80535623	0.573771
30.15349358	0.254971
29.93791266	0.0798
27.31757097	0.039629
21.61039626	0.123143
13.79415165	0.374229
9.537539852	0.364629
6.208413325	0.3812
7.876618651	0.397457
12.79680818	0.385371
17.72527118	0.452257
21.80381458	0.549171
25.76283093	0.485829
30.30400228	0.203829
31.69612286	0.052714
28.97048437	0.035114
23.91400917	0.088429
15.39247944	0.285171
10.03582075	0.3614
7.745298061	0.423571
7.244759463	1.12954
11.00972914	1.20386
17.48017142	1.0514
21.498356	0.86917
25.58965462	0.52854
30.58064314	0.12886
30.6540633	0.00674
27.89677259	0.01337
22.64831076	0.05737
15.29452676	0.53383
9.764016076	0.90854
6.823601671	1.24657
8.468376595	0.846714
12.48892345	0.721971
17.72412116	0.750914
19.94927272	0.699143
24.22892291	0.601314
26.01673363	0.168943
31.4108063	0.064686
27.99788933	0.049257
22.62585537	0.1288
14.58299553	0.478171
9.032951851	0.744886
7.454832516	0.877629
9.363384193	0.769943
13.2887833	0.570057
19.69167996	0.5174
24.27259366	0.3594
26.4282707	0.289657
30.2743201	0.252257
31.0964509	0.105857
28.17371513	0.084886
23.90611237	0.067229
16.09042643	0.345029
11.71584927	0.590371
8.098714689	0.816
5.481189019	0.848
6.70059961	1.004
10.23565859	1.017
12.94545991	1.069
16.29575971	0.671
17.87237139	0.263
18.57445627	0.062
16.77613358	0.038
13.05631542	0.132
9.521256431	0.625
6.441936757	0.909
4.963863314	0.89
5.684825661	0.642
6.949539684	0.827
10.61593286	0.801
13.42640847	0.8
16.90117831	0.412
18.53636412	0.043
19.2645328	0.029
17.39939899	0.001
13.54138247	0.027
9.874989294	0.307
6.681267013	0.58
5.148280318	0.785

.

Yourtaskistogivebest 2yearsaheadforecastsintermsofMASEforthesolarradiationseriesbyusingoneofthetimeseriesregressionmethods (dLagMpackage),dynamiclinearmodels (dynlmpackage),andexponentialsmoothingandcorrespondingstate-spacemodelscoveredintheModules 3 - 7ofourcoursethissemester.Hint:UseMASE()functionfromthedLagMpackagetocomputeMASEfortimeseriesregressionmethodsformodelcomparisons.

Forthesolarradiationforecasts,therequiredprecipitationmeasurements (predictorseries)forthemonthsfromJanuary 2015toDecember 2016attheexactsamelocationsaregivenindata.x.csvfile.Youwillusethisdataforthecalculationof 2yearsaheadforecasts.

x

0.189009998

0.697262522

0.595213491

0.487388526

0.261677017

0.808606651

0.94186202

0.905636325

1.059964682

0.341438784

0.525805322

0.602471062

0.109860632

0.781464707

0.69685501

0.502413906

0.649385609

0.745960773

0.663047123

0.533770112

0.61542621

0.54606508

0.142673325

0.013650407

Task 2

Inthesecondtask,youwillanalysethecorrelationbetweenquarterlyResidentialPropertyPriceIndex (PPI)inMelbourneandquarterlypopulationchangeoverthepreviousquarterinVictoriabetweenSeptember 2003andDecember 2016.ThequarterlyPPIandpopulationchangeseriesareavailableindata2.csv

Quarter	price	change
Sep-03	60.7	14017
Dec-03	62.1	12350
Mar-04	60.8	17894
Jun-04	60.9	9079
Sep-04	60.9	16210
Dec-04	62.4	13788
Mar-05	62.5	21195
Jun-05	63.2	10904
Sep-05	63.1	16995
Dec-05	64	16962
Mar-06	65.4	25004
Jun-06	67.2	13059
Sep-06	68.1	22327
Dec-06	69.5	20372
Mar-07	71	30109
Jun-07	76	19448
Sep-07	79.5	24993
Dec-07	84.7	20988
Mar-08	85.7	33497
Jun-08	85.5	23375
Sep-08	83	30174
Dec-08	82.3	26736
Mar-09	82.5	34387
Jun-09	86.9	24262
Sep-09	92.5	26940
Dec-09	98.6	20375
Mar-10	103.3	25923
Jun-10	106.2	15929
Sep-10	104.3	17609
Dec-10	105.7	17001
Mar-11	104.7	24667
Jun-11	103.5	17439
Sep-11	101.3	27892
Dec-11	100	27378
Mar-12	99.4	34569
Jun-12	99.3	25773
Sep-12	98.6	29453
Dec-12	100.4	29174
Mar-13	100.8	35704
Jun-13	102.7	28048
Sep-13	105.9	32942
Dec-13	109.7	29061
Mar-14	110.7	37877
Jun-14	112.1	26282
Sep-14	113.1	33154
Dec-14	115.2	31115
Mar-15	115.9	38857
Jun-15	120.8	27872
Sep-15	124.3	32948
Dec-15	126.3	31683
Mar-16	127.3	43701
Jun-16	130.7	37949
Sep-16	132.9	32275
Dec-16	140	32703

Inthistask,themaingoalofyouranalysisistodemonstratewhetherthecorrelationbetweenthesetwoseriesisspuriousornot.

Summary

Inbothtasks,itisexpectedthatyouaskyourselfwhataretheelementsof asuitableandsuccessfuldataanalysis,andhowyoumightgoaboutpresentingyourresultsin awrittenreportformat.Pleasereviewthecontentsoftherelevantmodulesandapplysuitableapproacheshere.Therubricgivenbelowwillguideyouthroughmyexpectationsintermsofreporting, Rcodes,descriptiveanalysis,modeling,anddiagnosticchecking.