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Bai tâp Dư bao kinh têLơp Vât Gia 1Nhom thưc hiên: Nguyên Hoang Viêt Lê Thanh Tâm Huynh Tiên Dung Huynh Thanh Nhân
Chuỗi số liệu miêu tả Ty gia thi trương (Exchange Rate Index) cua SingaporeĐăt biên X la ty gia thi trương cua SingaporeĐồ thi biên X như sau:
85
90
95
100
105
110
115
120
125
90 92 94 96 98 00 02 04 06 08
X
Kiêm đinh tinh dưng.Giản đồ tư tương quan cua biên X:
X la chuỗi không dưng( cac hệ số tư tương quan la rất cao giảm dần nhưng vẫn còn cao ở những độ trễ tiêp theo)
Kiêm đinh tinh dưng cua sai phân bậc 1 cua X( dX)
Ta đươc Y=d(x) la chuỗi dưng
Ươc lượng mô hình 1: LS Y C AR(2) AR(4) AR(5) AR(7) MA(4) MA(5) MA(6)
-6
-4
-2
0
2
4
6-8
-4
0
4
8
92 94 96 98 00 02 04 06 08
Residual Actual Fitted
-6
-4
-2
0
2
4
6
92 94 96 98 00 02 04 06 08
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1990M09 2009M03Included observations: 223
Root Mean Squared Error 1.372465Mean Absolute Error 1.001483Mean Abs. Percent Error 156.4858Theil Inequality Coefficient 0.787882 Bias Proportion 0.000005 Variance Proportion 0.611801 Covariance Proportion 0.388194
Mô hinh 1 co: RMSE = 1.372465 AIC = 3.542843
Ươc lượng mô hình 2 : LS Y C AR(2) AR(4) AR(5) AR(7) AR(8) MA(4) MA(5) MA(6) MA(8)
-6
-4
-2
0
2
4
6
-8
-4
0
4
8
92 94 96 98 00 02 04 06 08
Residual Actual Fitted
-4
-3
-2
-1
0
1
2
3
4
92 94 96 98 00 02 04 06 08
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1990M10 2009M03Included observations: 222
Root Mean Squared Error 1.354686Mean Absolute Error 1.015107Mean Abs. Percent Error 149.1005Theil Inequality Coefficient 0.768934 Bias Proportion 0.000006 Variance Proportion 0.602821 Covariance Proportion 0.397173
Mô hinh 2 co: RMSE = 1.354686 AIC = 3.535106
Ươc lượng mô hình 3 : LS Y C AR(5) AR(8) AR(34) AR(35) AR(36) MA(5) MA(6) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4
6
-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.266083Mean Absolute Error 0.938321Mean Abs. Percent Error 280.5090Theil Inequality Coefficient 0.613345 Bias Proportion 0.000042 Variance Proportion 0.419822 Covariance Proportion 0.580135
Mô hinh 3 co: RMSE = 1.266083 AIC = 3.423135
Ươc lượng mô hình 4 : LS Y C AR(2) AR(4) AR(5) AR(8) AR(29) AR(30) AR(34) AR(35) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4
6
-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M01 2009M03Included observations: 195
Root Mean Squared Error 1.255021Mean Absolute Error 0.950393Mean Abs. Percent Error 223.0442Theil Inequality Coefficient 0.571673 Bias Proportion 0.001129 Variance Proportion 0.300331 Covariance Proportion 0.698539
Mô hinh 4 co : RMSE = 1.255021 AIC = 3.415259
Ươc lượng mô hình 5: LS Y C AR(4) AR(5) AR(8) AR(29) AR(30) AR(34) AR(35) MA(5) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4
-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M01 2009M03Included observations: 195
Root Mean Squared Error 1.189646Mean Absolute Error 0.926291Mean Abs. Percent Error 298.9424Theil Inequality Coefficient 0.504449 Bias Proportion 0.003096 Variance Proportion 0.195851 Covariance Proportion 0.801053
Mô hinh 5 : RMSE = 1.189646 AIC = 3.308266
Ươc lượng mô hình 6 : LS Y C AR(4) AR(5) AR(8) AR(30) AR(34) AR(35) AR(36) MA(5) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.169731Mean Absolute Error 0.920834Mean Abs. Percent Error 308.6569Theil Inequality Coefficient 0.496086 Bias Proportion 0.002608 Variance Proportion 0.206365 Covariance Proportion 0.791027
Mô hinh 6 : RMSE = 1.169731 AIC = 3.275136
Ươc lượng mô hình 7 : LS Y C AR(2) AR(5) AR(8) AR(30) AR(34) AR(35) AR(36) MA(5) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4
-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.168444Mean Absolute Error 0.919405Mean Abs. Percent Error 313.8992Theil Inequality Coefficient 0.495283 Bias Proportion 0.002752 Variance Proportion 0.205997 Covariance Proportion 0.791252
Mô hinh 7 : RMSE = 1.168444 AIC = 3.272935
Ươc lượng mô hình 8 : LS Y C AR(2) AR(5) AR(29) AR(30) AR(34) AR(35) AR(36) MA(5) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.184735Mean Absolute Error 0.913579Mean Abs. Percent Error 280.4636Theil Inequality Coefficient 0.510451 Bias Proportion 0.002408 Variance Proportion 0.230173 Covariance Proportion 0.767419
Mô hinh 8 : RMSE = 1.184735 AIC = 3.300627
Ươc lượng mô hình 9 : LS Y C AR(2) AR(5) AR(35) AR(36) MA(5) MA(8) MA(30) MA(35)
-6
-4
-2
0
2
4-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.186497Mean Absolute Error 0.910794Mean Abs. Percent Error 298.7281Theil Inequality Coefficient 0.517789 Bias Proportion 0.001576 Variance Proportion 0.253044 Covariance Proportion 0.745380
Mô hinh 9 : RMSE = 1.186497 AIC = 3.272672
Ươc lượng mô hình 10 : LS Y C AR(2) AR(5) AR(35) AR(36) MA(7) MA(8) MA(30) MA(35)
-4
-2
0
2
4
-8
-4
0
4
8
1994 1996 1998 2000 2002 2004 2006 2008
Residual Actual Fitted
-6
-4
-2
0
2
4
6
8
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M03Adjusted sample: 1993M02 2009M03Included observations: 194
Root Mean Squared Error 1.201086Mean Absolute Error 0.910570Mean Abs. Percent Error 265.4932Theil Inequality Coefficient 0.522489 Bias Proportion 0.001499 Variance Proportion 0.240840 Covariance Proportion 0.757661
Mô hinh 10 : RMSE = 1.201086 AIC = 3.297112
Quan sat 10 mô hình ta thâ mô hình 7 co RMSE va AIC nho nhât nên mô hình 7 la tôt nhât.
Dư bao ty gia thi trương cua Singapore thang 4/2009:Thay đôi range ta đươc biên X mơiKiêm đinh tinh dưng.Giản đồ tư tương quan cua biên X
X la chuỗi không dưng( cac hệ số tư tương quan la rất cao giảm dần nhưng vẫn còn cao ở những độ trễ tiêp theo)Kiêm đinh tinh dưng cua sai phân bậc 1 cua X( dX)
Ta đươc Y=d(x) la chuỗi dưng
Theo cac mô hinh kiêm đinh ở trên thi mô hinh 7 la tốt nhất (RMSE = 1.168444, AIC = 3.272935) nên ta sư dung mô hinh 7 đê dư bao Exchange Rate thang 4/2009
-6
-4
-2
0
2
4
6
1994 1996 1998 2000 2002 2004 2006 2008
YF ± 2 S.E.
Forecast: YFActual: YForecast sample: 1990M01 2009M04Adjusted sample: 1993M02 2009M04Included observations: 194
Root Mean Squared Error 1.168444Mean Absolute Error 0.919405Mean Abs. Percent Error 313.8992Theil Inequality Coefficient 0.495283 Bias Proportion 0.002752 Variance Proportion 0.205997 Covariance Proportion 0.791252
Ta co gia tri dư bao Exchange Rate thang 4/2009= 108.74 + (-0.539288) =108.200712
