Question

- Create a plot of the variable "fortw" (fortified wine sales).

- Create a plot of the ACF function for the same variable.

- create a naive and exponential smoothing forecast for the variable "fortw". makw sure to take into account the attricutes that yous aw fromthe above plots. make sure to produce plots with the actual data and forecasts overlaid (one graph per forecasting technique)

- Using the Mean Absolute Percentage Error (MAPE) measure of error, which of the forecasting techniques perform best?

- create a forecast for 1 period ahead (i.e. outside fo the sample).

- Compare the 1 period ahead forecasts for the 2 different basic forecasting techniques. Hint: the predict() functio will be helpful for the exponetial smoothing method.

Repeat the entirety of the above analysis but with the variable x.

Can someone aswer this Using R Script? What are the fuctions and steps to writing this script?

winet	fortw	dryw	sweetw	red	rose	spark
1	2585	1954	85	464	112	1686
2	3368	2302	89	675	118	1591
3	3210	3054	109	703	129	2304
4	3111	2414	95	887	99	1712
5	3756	2226	91	1139	116	1471
6	4216	2725	95	1077	168	1377
7	5225	2589	96	1318	118	1966
8	4426	3470	128	1260	129	2453
9	3932	2400	124	1120	205	1984
10	3816	3180	111	963	147	2596
11	3661	4009	178	996	150	4087
12	3795	3924	140	960	267	5179
13	2285	2072	150	530	126	1530
14	2934	2434	132	883	129	1523
15	2985	2956	155	894	124	1633
16	3646	2828	132	1045	97	1976
17	4198	2687	91	1199	102	1170
18	4935	2629	94	1287	127	1480
19	5618	3150	109	1565	222	1781
20	5454	4119	155	1577	214	2472
21	3624	3030	123	1076	118	1981
22	2898	3055	130	918	141	2273
23	3802	3821	150	1008	154	3857
24	2369	4001	163	1063	226	4551
25	2369	2529	101	544	89	1510
26	2511	2472	123	635	77	1329
27	3079	3134	127	804	82	1518
28	3728	2789	112	980	97	1790
29	4151	2758	108	1018	127	1537
30	4326	2993	116	1064	121	1449
31	5054	3282	153	1404	117	1954
32	5138	3437	163	1286	117	1897
33	3310	2804	128	1104	106	1706
34	3508	3076	142	999	112	2514
35	3790	3782	170	996	134	3593
36	3446	3889	214	1015	169	4524
37	2127	2271	134	615	75	1609
38	2523	2452	122	722	108	1638
39	3017	3084	142	832	115	2030
40	3265	2522	156	977	85	1375
41	3822	2769	145	1270	101	1320
42	4027	3438	169	1437	108	1245
43	4420	2839	134	1520	109	1600
44	5255	3746	165	1708	124	2298
45	4009	2632	156	1151	105	2191
46	3074	2851	111	934	95	2511
47	3465	3871	165	1159	135	3440
48	3718	3618	197	1209	164	4923
49	1954	2389	124	699	88	1609
50	2604	2344	124	830	85	1435
51	3626	2678	139	996	112	2061
52	2836	2492	137	1124	87	1789
53	4042	2858	127	1458	91	1567
54	3584	2246	134	1270	87	1404
55	4225	2800	136	1753	87	1597
56	4523	3869	171	2258	142	3159
57	2892	3007	112	1208	95	1759
58	2876	3023	110	1241	108	2504
59	3420	3907	147	1265	139	4273
60	3159	4209	196	1828	159	5274
61	2101	2353	112	809	61	1771
62	2181	2570	118	997	82	1682
63	2724	2903	125	1164	124	1846
64	2954	2910	122	1205	93	1589
65	4092	3782	120	1538	108	1896
66	3470	2759	118	1513	75	1379
67	3990	2931	281	1378	87	1645
68	4239	3641	344	2083	103	2512
69	2855	2794	366	1357	90	1771
70	2897	3070	362	1536	108	3727
71	3433	3576	580	1526	123	4388
72	3307	4106	523	1376	129	5434
73	1914	2452	348	779	57	1606
74	2214	2206	246	1005	65	1523
75	2320	2488	197	1193	67	1577
76	2714	2416	306	1522	71	1605
77	3633	2534	279	1539	76	1765
78	3295	2521	280	1546	67	1403
79	4377	3093	358	2116	110	2584
80	4442	3903	431	2326	118	3318
81	2774	2907	448	1596	99	1562
82	2840	3025	433	1356	85	2349
83	2828	3812	504	1553	107	3987
84	3758	4209	579	1613	141	5891
85	1610	2138	384	814	58	1389
86	1968	2419	335	1150	65	1442
87	2248	2622	320	1225	70	1548
88	3262	2912	496	1691	86	1935
89	3164	2708	448	1759	93	1518
90	2972	2798	377	1754	74	1250
91	4041	3254	523	2100	87	1847
92	3402	2895	468	2062	73	1930
93	2898	3263	428	2012	101	2638
94	2555	3736	520	1897	100	3114
95	3056	4077	493	1964	96	4405
96	3717	4097	662	2186	157	7242
97	1755	2175	304	966	63	1853
98	2193	3138	308	1549	115	1779
99	2198	2823	313	1538	70	2108
100	2777	2498	328	1612	66	2336
101	3076	2822	354	2078	67	1728
102	3389	2738	338	2137	83	1661
103	4231	4137	483	2907	79	2230
104	3118	3515	355	2249	77	1645
105	2524	3785	439	1883	102	2421
106	2280	3632	290	1739	116	3740
107	2862	4504	352	1828	100	4988
108	3502	4451	454	1868	135	6757
109	1558	2550	306	1138	71	1757
110	1940	2867	303	1430	60	1394
111	2226	3458	344	1809	89	1982
112	2676	2961	254	1763	74	1650
113	3145	3163	309	2200	73	1654
114	3224	2880	310	2067	91	1406
115	4117	3331	379	2503	86	1971
116	3446	3062	294	2141	74	1968
117	2482	3534	356	2103	87	2608
118	2349	3622	318	1972	87	3845
119	2986	4464	405	2181	109	4514
120	3163	5411	545	2344	137	6694
121	1651	2564	268	970	43	1720
122	1725	2820	243	1199	69	1321
123	2622	3508	273	1718	73	1859
124	2316	3088	273	1683	77	1628
125	2976	3299	236	2025	69	1615
126	3263	2939	222	2051	76	1457
127	3951	3320	302	2439	78	1899
128	2917	3418	285	2353	70	1605
129	2380	3604	309	2230	83	2424
130	2458	3495	322	1852	65	3116
131	2883	4163	362	2147	110	4286
132	2579	4882	471	2286	132	6047
133	1330	2211	198	1007	54	1902
134	1686	3260	253	1665	55	2049
135	2457	2992	173	1642	66	1874
136	2514	2425	186	1518	65	1279
137	2834	2707	185	1831	60	1432
138	2757	3244	105	2207	65	1540
139	3425	3965	228	2822	96	2214
140	3006	3315	214	2393	55	1857
141	2369	3333	189	2306	71	2408
142	2017	3583	270	1785	63	3252
143	2507	4021	277	2047	74	3627
144	3168	4904	378	2171	106	6153
145	1545	2252	185	1212	34	1577
146	1643	2952	182	1335	47	1667
147	2112	3573	258	2011	56	1993
148	2415	3048	179	1860	53	1997
149	2862	3059	197	1954	53	1783
150	2822	2731	168	2152	55	1625
151	3260	3563	250	2835	67	2076
152	2606	3092	211	2224	52	1773
153	2264	3478	260	2182	46	2377
154	2250	3478	234	1992	51	3088
155	2545	4308	305	2389	58	4096
156	2856	5029	347	2724	91	6119
157	1208	2075	203	891	33	1494
158	1412	3264	217	1247	40	1564
159	1964	3308	227	2017	46	1898
160	2018	3688	242	2257	45	2121
161	2329	3136	185	2255	41	1831
162	2660	2824	175	2255	55	1515
163	2923	3644	252	3057	57	2048
164	2626	4694	319	3330	54	2795
165	2132	2914	202	1896	46	1749
166	1772	3686	254	2096	52	3339
167	2526	4358	336	2374	48	4227
168	2755	5587	431	2535	77	6410
169	1154	2265	150	1041	30	1197
170	1568	3685	280	1728	35	1968
171	1965	3754	187	2201	42	1720
172	2659	3708	279	2455	48	1725
173	2354	3210	193	2204	44	1674
174	2592	3517	227	2660	45	1693
175	2714	3905	225	3670	46	2031
176	2294	3670	205	2665	44	1495
177	2416	4221	259	2639	46	2968
178	2016	4404	254	2226	51	3385
179	2799	5086	275	2586	63	3729
180	2467	5725	394	2684	84	5999
181	1153	2367	159	1185	30	1070
182	1482	3819	230	1749	39	1402
183	1818	4067	188	2459	45	1897
184	2262	4022	195	2618	52	1862
185	2612	3937	189	2585	28	1670
186	2967	4365	220	3310	40	1688
187	3179	4290	274	3923	62	2031

Answer 1

solving first 4

use library forecast using

library(forecast)

load the data in t1

convert to time series using

t<-ts(t1$fortw)

plot t using

plot(t)

we see a downward trend in the time series so we try to detrend usingfirst differece

t.d<-diff(t)

plotting we get

now acf

acf(t.d)

now we create the models

for nsive we use rwf

m1<-rwf(t.d)
plot(forecast(m1))

for smoothing we use
m2<-HoltWinters(t.d , beta = F, gamma=F)
plot(forecast(m2))

from summary we get the MAPE

for naive we have:

infinity

this is due to a zero record in the t.d (differenced variable)

so we remove this and calulate MAPE maually

t.d<-t.d[-24]
m2.fitted<-m2$fitted[,1][-24]
m1.fitted<-m1$fitted[-24]
mape_exp<-(100/185)*sum((abs(m2.fitted-t.d[2:185])/t.d[2:185]))
mape_naive<-(100/187)*sum((abs(m1.fitted[2:185]-t.d[2:185])/t.d[2:185]))

we have naive mape ~ 81

exponential mape: 16

so exponential is better as it is lower