目录
原文博客地址:https://blog.csdn.net/s1164548515/article/details/101021959背景
加载包
数据加载
数据预览
数据预处理
混频回归
基于季度GDP和月度非农就业总额预测下一季度GDP增长率
library(midasr)
-
data(
"USqgdp")
-
data(
"USpayems")
USqgdp
1947至2013年季度GDP
-
Qtr1
Qtr2
Qtr3
Qtr4
-
1947 243
.1 246
.3 250
.1 260
.3
-
1948 266
.2 272
.9 279
.5 280
.7
-
1949 275
.4 271
.7 273
.3 271
.0
-
1950 281
.2 290
.7 308
.5 320
.3
-
1951 336
.4 344
.5 351
.8 356
.6
-
1952 360
.2 361
.4 368
.1 381
.2
-
1953 388
.5 392
.3 391
.7 386
.5
-
1954 385
.9 386
.7 391
.6 400
.3
-
1955 413
.8 422
.2 430
.9 437
.8
-
1956 440
.5 446
.8 452
.0 461
.3
-
1957 470
.6 472
.8 480
.3 475
.7
-
1958 468
.4 472
.8 486
.7 500
.4
-
1959 511
.1 524
.2 525
.2 529
.3
-
1960 543
.3 542
.7 546
.0 541
.1
-
1961 545
.9 557
.4 568
.2 581
.6
-
1962 595
.2 602
.6 609
.6 613
.1
-
1963 622
.7 631
.8 645
.0 654
.8
-
1964 671
.2 680
.8 692
.8 698
.4
-
1965 719
.2 732
.4 750
.2 773
.1
-
1966 797
.3 807
.2 820
.8 834
.9
-
1967 846
.0 851
.1 866
.6 883
.2
-
1968 911
.1 936
.3 952
.3 970
.1
-
1969 995
.4 1011
.4 1032
.0 1040
.7
-
1970 1053
.5 1070
.1 1088
.5 1091
.5
-
1971 1137
.8 1159
.4 1180
.3 1193
.6
-
1972 1233
.8 1270
.1 1293
.8 1332
.0
-
1973 1380
.7 1417
.6 1436
.8 1479
.1
-
1974 1494
.7 1534
.2 1563
.4 1603
.0
-
1975 1619
.6 1656
.4 1713
.8 1765
.9
-
1976 1824
.5 1856
.9 1890
.5 1938
.4
-
1977 1992
.5 2060
.2 2122
.4 2168
.7
-
1978 2208
.7 2336
.6 2398
.9 2482
.2
-
1979 2531
.6 2595
.9 2670
.4 2730
.7
-
1980 2796
.5 2799
.9 2860
.0 2993
.5
-
1981 3131
.8 3167
.2 3261
.2 3283
.5
-
1982 3273
.8 3331
.3 3367
.1 3407
.8
-
1983 3480
.3 3583
.8 3692
.3 3796
.1
-
1984 3912
.8 4015
.0 4087
.4 4147
.6
-
1985 4237
.0 4302
.3 4394
.6 4453
.1
-
1986 4516
.3 4555
.2 4619
.6 4669
.4
-
1987 4736
.2 4821
.4 4900
.5 5022
.7
-
1988 5090
.6 5207
.7 5299
.5 5412
.7
-
1989 5527
.3 5628
.4 5711
.5 5763
.4
-
1990 5890
.8 5974
.6 6029
.5 6023
.3
-
1991 6054
.8 6143
.6 6218
.4 6279
.3
-
1992 6380
.8 6492
.3 6586
.5 6697
.5
-
1993 6748
.2 6829
.6 6904
.2 7032
.8
-
1994 7136
.2 7269
.8 7352
.2 7476
.6
-
1995 7545
.3 7604
.9 7706
.5 7799
.5
-
1996 7893
.1 8061
.5 8159
.0 8287
.0
-
1997 8402
.0 8551
.9 8691
.7 8788
.3
-
1998 8889
.7 8994
.7 9146
.5 9325
.6
-
1999 9450
.3 9561
.5 9718
.7 9932
.3
-
2000 10036
.1 10283
.7 10363
.8 10475
.3
-
2001 10512
.5 10641
.6 10644
.3 10702
.7
-
2002 10837
.3 10938
.0 11039
.8 11105
.7
-
2003 11230
.8 11371
.4 11628
.4 11818
.5
-
2004 11991
.4 12183
.5 12369
.4 12563
.8
-
2005 12816
.2 12975
.7 13206
.5 13383
.3
-
2006 13649
.8 13802
.9 13910
.5 14068
.4
-
2007 14235
.0 14424
.5 14571
.9 14690
.0
-
2008 14672
.9 14817
.1 14844
.3 14546
.7
-
2009 14381
.2 14342
.1 14384
.4 14564
.1
-
2010 14672
.5 14879
.2 15049
.8 15231
.7
-
2011 15242
.9 15461
.9 15611
.8 15818
.7
-
2012 16041
.6 16160
.4 16356
.0 16420
.3
-
2013 16535
.3 16661
.0 16912
.9 17089
.6
USpayems
1939至2014年3月,月度非农就业总额
-
Jan Feb Mar Apr May Jun Jul Aug Sep
Oct Nov Dec
-
1939
29923
30101
30280
30094
30300
30502
30419
30663
31032
31408
31469
31539
-
1940
31603
31715
31826
31700
31880
31978
31942
32352
32810
33265
33668
34172
-
1941
34480
34844
35094
35469
36182
36651
37137
37544
37835
37948
38024
38104
-
1942
38347
38513
38936
39352
39772
40028
40471
40988
41255
41515
41673
41915
-
1943
42172
42395
42553
42647
42596
42781
42701
42546
42485
42675
42820
42746
-
1944
42655
42544
42292
42063
41985
41947
41905
41850
41672
41709
41712
41861
-
1945
41897
41904
41796
41443
41304
41149
40873
40467
38500
38599
38997
39112
-
1946
39832
39251
40193
40909
41349
41733
42153
42643
42909
43094
43397
43379
-
1947
43539
43563
43606
43492
43638
43808
43743
43959
44201
44415
44487
44579
-
1948
44682
44537
44681
44370
44795
45033
45160
45176
45295
45251
45194
45029
-
1949
44671
44500
44238
44230
43982
43739
43529
43622
43784
42950
43245
43517
-
1950
43528
43298
43952
44376
44718
45084
45454
46188
46442
46712
46778
46855
-
1951
47288
47577
47871
47856
47953
48068
48062
48009
47955
48009
48148
48309
-
1952
48298
48522
48504
48616
48645
48286
48144
48923
49319
49598
49816
50164
-
1953
50145
50339
50475
50432
50491
50522
50536
50487
50365
50242
49907
49702
-
1954
49468
49382
49158
49178
48965
48896
48835
48825
48882
48944
49178
49331
-
1955
49497
49644
49963
50247
50512
50790
50985
51111
51262
51431
51592
51805
-
1956
51975
52167
52295
52375
52506
52584
51954
52630
52601
52781
52822
52930
-
1957
52888
53097
53157
53238
53149
53066
53123
53126
52932
52765
52559
52385
-
1958
52077
51576
51300
51027
50913
50912
51037
51231
51506
51486
51944
52088
-
1959
52480
52687
53016
53320
53549
53679
53803
53334
53429
53359
53635
54175
-
1960
54274
54513
54458
54812
54473
54347
54304
54271
54228
54144
53962
53744
-
1961
53683
53556
53662
53626
53785
53977
54123
54298
54388
54522
54743
54871
-
1962
54891
55187
55276
55602
55627
55644
55746
55838
55977
56041
56056
56028
-
1963
56116
56230
56322
56580
56616
56658
56794
56910
57077
57284
57255
57360
-
1964
57487
57751
57898
57922
58089
58221
58413
58619
58903
58794
59217
59421
-
1965
59583
59800
60003
60259
60492
60690
60963
61228
61490
61718
61997
62321
-
1966
62528
62796
63192
63436
63711
64110
64301
64507
64644
64854
65019
65200
-
1967
65407
65428
65530
65467
65619
65750
65887
66142
66164
66225
66703
66900
-
1968
66805
67215
67295
67555
67653
67904
68125
68328
68487
68720
68985
69246
-
1969
69438
69700
69905
70072
70328
70636
70729
71006
70917
71120
71087
71240
-
1970
71176
71304
71452
71348
71123
71029
71053
70933
70948
70519
70409
70790
-
1971
70866
70806
70859
71037
71247
71253
71315
71370
71617
71642
71846
72108
-
1972
72445
72652
72945
73163
73467
73760
73708
74138
74263
74673
74967
75270
-
1973
75621
76017
76285
76455
76646
76887
76911
77166
77276
77606
77912
78035
-
1974
78104
78254
78296
78382
78547
78602
78635
78619
78611
78629
78261
77657
-
1975
77297
76919
76649
76461
76623
76520
76769
77155
77230
77535
77680
78018
-
1976
78506
78817
79049
79292
79311
79376
79547
79704
79892
79905
80237
80448
-
1977
80692
80988
81391
81729
82089
82488
82836
83074
83532
83794
84173
84408
-
1978
84595
84948
85461
86163
86509
86951
87205
87481
87618
87954
88391
88673
-
1979
88810
89054
89480
89418
89791
90109
90215
90297
90325
90482
90576
90673
-
1980
90802
90882
90994
90850
90419
90099
89837
90097
90210
90491
90748
90943
-
1981
91037
91105
91210
91283
91293
91490
91602
91566
91479
91380
91171
90893
-
1982
90567
90562
90432
90152
90107
89864
89522
89364
89183
88906
88783
88769
-
1983
88993
88918
89090
89366
89643
90022
90440
90132
91247
91518
91871
92227
-
1984
92673
93154
93429
93792
94100
94479
94792
95034
95344
95630
95979
96107
-
1985
96373
96497
96843
97039
97313
97459
97649
97842
98045
98233
98442
98609
-
1986
98734
98841
98935
99122
99249
99155
99473
99587
99934
100120
100306
100511
-
1987
100683
100915
101164
101502
101728
101900
102247
102418
102646
103138
103370
103664
-
1988
103758
104211
104487
104732
104961
105324
105546
105670
106009
106277
106616
106906
-
1989
107168
107426
107619
107792
107910
108026
108066
108115
108365
108476
108753
108849
-
1990
109183
109432
109647
109688
109838
109863
109833
109613
109525
109366
109216
109160
-
1991
109039
108735
108577
108367
108240
108338
108302
108308
108340
108356
108299
108324
-
1992
108378
108313
108368
108527
108654
108721
108790
108930
108966
109145
109284
109494
-
1993
109805
110047
109998
110306
110573
110754
111053
111212
111451
111737
111999
112311
-
1994
112583
112783
113248
113597
113931
114247
114624
114902
115253
115468
115887
116162
-
1995
116487
116691
116913
117075
117059
117294
117395
117644
117885
118041
118189
118321
-
1996
118303
118735
119001
119165
119485
119774
120029
120202
120427
120677
120976
121146
-
1997
121382
121684
122000
122293
122551
122818
123131
123092
123604
123945
124251
124554
-
1998
124830
125026
125177
125456
125862
126080
126204
126551
126775
126971
127254
127601
-
1999
127726
128137
128244
128619
128831
129092
129411
129578
129791
130192
130483
130778
-
2000
131008
131138
131606
131893
132119
132074
132251
132237
132371
132357
132582
132724
-
2001
132694
132766
132741
132460
132422
132293
132178
132020
131778
131454
131160
130989
-
2002
130847
130714
130695
130615
130607
130664
130579
130564
130504
130629
130639
130481
-
2003
130575
130422
130212
130167
130156
130166
130189
130148
130250
130446
130462
130586
-
2004
130747
130791
131123
131372
131679
131753
131785
131917
132079
132425
132490
132619
-
2005
132753
132992
133126
133489
133664
133909
134282
134478
134545
134629
134966
135125
-
2006
135402
135717
135997
136179
136202
136279
136486
136670
136827
136829
137039
137210
-
2007
137448
137536
137724
137802
137946
138017
137984
137968
138053
138135
138253
138350
-
2008
138365
138279
138199
137985
137803
137631
137421
137162
136710
136236
135471
134774
-
2009
133976
133275
132449
131765
131411
130944
130617
130401
130174
129976
129970
129687
-
2010
129705
129655
129811
130062
130578
130456
130395
130353
130296
130537
130674
130745
-
2011
130815
130983
131195
131517
131619
131836
131942
132064
132285
132468
132632
132828
-
2012
133188
133414
133657
133753
133863
133951
134111
134261
134422
134647
134850
135064
-
2013
135261
135541
135682
135885
136084
136285
136434
136636
136800
137037
137311
137395
-
2014
137539
137736
137928
1.分割训练集数据:
y:GDP--1947年1季度至2011年2季度
x:非农就业总额--1919年1月至2011年7月
-
y <- window(USqgdp,
end = c(
2011,
2))
-
x <- window(USpayems,
end = c(
2011,
7))
2.计算对数差
-
yg <- diff(
log(y))*
100
-
xg <- diff(
log(x))*
100
3.数据对齐
一是计算对数差会损失一个数值,二是初始数据起止日期不一致需要补齐
-
nx <- ts(c(NA, xg, NA, NA), start = start(x), frequency =
12)
#月度数据
-
ny <- ts(c(rep(NA,
33), yg, NA), start = start(x), frequency =
4)
#季度数据
4.补齐后数据的可视化
-
plot.ts(nx, xlab =
"Time", ylab =
"Percentages", col =
4, ylim = c(
-5,
6))
-
lines(ny, col =
2)
1.样本数据选取:1985年1月至2009年3月非农就业总额数据,1985年1季度至2009年1季度GDP数据
-
xx <- window(nx, start = c(
1985,
1), end = c(
2009,
3))
-
yy <- window(ny, start = c(
1985,
1), end = c(
2009,
1))
2.模型拟合
mod_1:
-
mod_1 <- midas_r(yy ~ mls(yy,
1,
1) + mls(xx,
3:
11,
3, nbeta), start = list(xx = c(
1.7,
1,
5)))
# nbeta
-
-
coef(mod_1)
系数:
-
(
Intercept)
yy
xx1
xx2
xx3
-
0
.8311331 0
.1056152 2
.5924606 1
.0149478 12
.4761333
mod_2:
-
mod_2 <- midas_r(yy ~ mls(yy,
1,
1) + mls(xx,
3:
11,
3, nbetaMT), start = list(xx = c(
2,
1,
5,
0)))
#nbetaMT
-
-
coef(mod_2)
系数:
-
(
Intercept)
yy
xx1
xx2
xx3
xx4
-
0
.93868569 0
.06618413 2
.27682100 0
.98674913 1
.50874150
-0
.09164647
mod_3:
-
mod_3 <- midas_r(yy ~ mls(yy,
1,
1) + mls(xx,
3:
11,
3), start = NULL)
#无约束
-
-
coef(mod_3)
系数:
-
Intercept)
yy
xx1
xx2
xx3
xx4
xx5
xx6
xx7
xx8
xx9
-
0
.92989757 0
.08358393 2
.00047205 0
.88134597 0
.42964662
-0
.17596814 0
.28351010 1
.16285271
-0
.53081967
-0
.73391876
-1
.18732001
3.分割训练集、测试集
-
fulldata <- list(xx = window(nx, start = c(
1985,
1), end = c(
2011,
6)), yy = window(ny, start = c(
1985,
1), end = c(
2011,
2)))
#
-
insample <-
1:length(yy)
#训练集
-
outsample <- (
1:length(fulldata$yy))[-insample]
#测试集
4.mod_1~mod_3 模型平均
-
avgf <- average_forecast(
list(mod_1, mod_2, mod_3), data = fulldata, insample = insample, outsample = outsample)
-
sqrt(avgf$accuracy$individual$MSE.out.of.sample)
三模型样本外预测的MSE,mod_3好一点
[1] 0.5383774 0.4770977 0.4457144