Preparation Sheet for Final Report
You should run GRETL and fill in each of the following parts:
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#1. My original variable is xt =“Nominal Wage for Commerce in Taiwan”.
The original sample is from1978:1 to2003:1. A list of the data is as
follows:
YEAR 1ST 2ND 3RD 4TH
1978 48.360 49.360 48.800 54.310
1979 68.310 68.700 68.820 70.500
1980 76.210 79.380 94.680 111.880
1981 94.820 106.410 115.780 127.080
1982 107.140 111.530 113.290 118.270
1983 118.010 114.330 118.950 127.200
1984 135.080 136.570 140.920 137.110
1985 132.130 143.190 136.190 151.940
1986 144.540 145.400 145.960 164.450
1987 147.070 152.340 160.710 173.400
1988 162.230 163.500 174.770 191.890
1989 175.750 176.370 203.830 203.530
1990 206.720 209.350 216.970 237.450
1991 225.060 229.480 238.070 279.050
1992 242.490 243.690 254.360 279.140
1993 253.260 283.960 272.130 298.320
1994 276.820 285.620 292.170 338.870
1995 289.010 306.110 303.790 333.250
1996 303.670 312.800 315.590 340.140
1997 320.410 331.900 318.070 328.140
1998 329.330 325.880 331.140 342.580
1999 333.740 344.320 338.900 384.420
2000 332.220 360.950 353.000 381.280
2001 347.350 364.410 346.970 384.660
2002 346.940 349.450 347.810 384.070
2003 348.070
#2. My time series plot of xt is as follows:
My data appears to be non-stationary.
#3. I (did / did not ) take the log of xt to get zt. If not, let zt = xt.
#4. I took (n=1) number of regular differences to get wt = nzt.
#5. I took (m= 1) number of seasonal differences to get st = mwt
#6. My revised sample for st is now1979:2 to 2003:1.
#7. My data on st is as follows:
YEAR 1ST 2ND 3RD 4TH
1979 -61.000 68.000 -383.000
1980 -829.000 278.000 1518.000 1552.000
1981 -2277.000 842.000 -593.000 -590.000
1982 -288.000 -720.000 -761.000 -632.000
1983 1968.000 -807.000 286.000 327.000
1984 814.000 517.000 -27.000 -1206.000
1985 -1286.000 957.000 -1135.000 1956.000
1986 -242.000 -1020.000 756.000 274.000
1987 -998.000 441.000 781.000 -580.000
1988 621.000 -400.000 290.000 443.000
1989 -497.000 -65.000 1619.000 -1742.000
1990 1933.000 201.000 -1984.000 2078.000
1991 -1558.000 179.000 97.000 2050.000
1992 -2417.000 -322.000 208.000 -1620.000
1993 1068.000 2950.000 -2250.000 141.000
1994 438.000 -2190.000 1838.000 2051.000
1995 -2836.000 830.000 -887.000 -1724.000
1996 2028.000 -797.000 511.000 -491.000
1997 985.000 236.000 -1662.000 -1448.000
1998 2092.000 -1494.000 1909.000 137.000
1999 -1003.000 1403.000 -1068.000 3408.000
2000 -4336.000 1815.000 -253.000 -1724.000
2001 1827.000 -1167.000 -949.000 941.000
2002 -379.000 -1455.000 1580.000 -143.000
2003 172.000
#8. A time series plot of st is as follows:
#9. The summary statistics on st are as follows:
Mean -19.604
Standard deviation 1376.6
#9. The SACF (correlogram) and SPACF for st are as follows:
#10. I believe the best model given the SACF and SPACF is
an ARMA( 0 ,1) with a SAR(1) . My model is therefore written as:
#11. Using TRAMO, my estimation of this model gives the following results:
PARAMETER ESTIMATE STD ERROR T RATIO LAG
AR2 1 0.27518 0.10457 2.63 4
MA1 1 -.70746 0.79922E-01 -8.85 1
The estimate of the constant is as follows:
PARAMETER VALUE ST. ERROR T VALUE
MU -20.244 ( 25.72844) -0.79
#12. My model’s white noise residuals are as follows:
WHITE NOISE RESIDUALS
62.4300 -296.6959 -931.1977 -313.2464 1327.9207 2379.5555 -804.8032 377.3777
117.8598 -52.8152 -924.9167 -1115.5679 -1686.4169 -1960.5081 528.5910 -604.3865
-324.1972 -49.4808 1347.3245 1274.8923 980.4176 -395.6281 -1315.1118 195.6649
-977.2198 959.5813 109.7726 -652.2120 9.0481 845.4303 -439.7009 -123.9640
928.1188 178.7885 499.6451 101.6157 603.5864 737.1953 222.2041 8.9150
1731.8932 -368.0702 1562.6287 1315.3929 -581.1199 1214.3111 -140.2258 161.8917
-307.6320 2430.9639 -1099.1339 -1023.5493 -462.6408 -1356.4033 -529.9130 2513.2874
-387.9329 -552.4458 367.8408 -1091.2142 473.6515 2451.6736 -954.2317 -420.9286
-652.2309 -1594.2551 146.5181 -438.1634 -16.2779 -950.1338 897.6621 678.5283
-1014.5696 -2274.0915 781.0093 -849.7420 877.2863 385.9738 -127.4867 928.4811
140.9573 3572.2057 -2058.0307 771.8867 25.9749 -741.0395 136.3686 -544.2956
-1376.9005 -480.7171 -189.5557 -1883.4476 13.1834 152.0524 202.0643
#13. The Durbin-Watson statistic and SSE are as follows:
TEST-STATISTICS ON RESIDUALS
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SUM OF SQUARES= 0.1046142E+09
DURBIN-WATSON= 2.0773
STANDARD ERROR= 1060.606
OF RESID.
#14. The autocorrelations of the residuals are as follows:
AUTOCORRELATIONS of Residuals
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-0.0389 0.0434 0.0868 -0.0904 -0.0277 0.0933 -0.0915 -0.2813 0.1136 -0.0540 0.0135
SE 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026 0.1026
Q 0.15 0.33 1.09 1.92 2.00 2.90 3.77 12.15 13.54 13.85 13.87
PV -1.00 -1.00 0.30 0.38 0.57 0.58 0.58 0.06 0.06 0.09 0.13
#15. My estimated model is as follows:
Note that the estimated constant = -20.244 is statistically insignificant and can be omitted. I have included it in the above estimated equation be cause I wanted to show the use of .