Estimates at each iteration
Iteration SSE Parameters
0 11.6497 0.100 0.100 0.080
1 8.8027 0.236 -0.036 0.019
2 8.6293 0.111 -0.186 0.012
3 8.4985 -0.010 -0.336 0.004
4 8.4433 -0.107 -0.476 -0.011
5 8.4402 -0.057 -0.429 -0.012
6 8.4400 -0.067 -0.439 -0.012
7 8.4400 -0.065 -0.437 -0.012
8 8.4400 -0.066 -0.437 -0.012
9 8.4400 -0.066 -0.437 -0.012
Relative change in each estimate less than 0.0010
Final Estimates of Parameters
Type Coef SE Coef T P
AR 1 -0.0656 0.1841 -0.36 0.722
MA 1 -0.4374 0.1659 -2.64 0.009
Constant -0.01183 0.02062 -0.57 0.567
Differencing: 1 regular difference
Number of observations: Original series 205, after differencing 204
Residuals: SS = 8.43828 (backforecasts excluded)
MS = 0.04198 DF = 201
Modified Box-Pierce (Ljung-Box) Chi-Square statistic
Lag 12 24 36 48
Chi-Square 5.0 12.6 28.8 42.1
DF 9 21 33 45
P-Value 0.833 0.921 0.675 0.595
Forecasts from period 205
95% Limits
Period Forecast Lower Upper Actual
206 8.27651 7.87483 8.67818Estimates at each iteration
Iteration SSE Parameters
0 11.4040 0.100 0.100 0.100 0.071
1 10.5229 0.250 0.050 0.190 0.052
2 10.1334 0.400 0.015 0.310 0.040
3 9.8926 0.550 -0.018 0.439 0.029
4 9.6985 0.700 -0.053 0.572 0.021
5 9.4953 0.850 -0.092 0.702 0.013
6 9.2428 1.000 -0.142 0.824 0.006
7 9.1464 1.150 -0.179 0.963 0.001
8 8.6521 1.227 -0.280 0.941 -0.001
9 8.6227 1.295 -0.320 0.981 -0.000
10 8.6181 1.294 -0.322 0.981 -0.000
11 8.6170 1.294 -0.323 0.982 -0.000
12 8.6166 1.296 -0.325 0.982 -0.000
13 8.6165 1.296 -0.325 0.982 -0.000
14 8.6152 1.298 -0.327 0.983 -0.000
15 8.6152 1.303 -0.332 0.983 -0.000
16 8.6150 1.304 -0.332 0.983 -0.000
17 8.6148 1.304 -0.333 0.983 -0.000
18 8.6146 1.305 -0.333 0.983 -0.000
19 8.6145 1.305 -0.333 0.983 -0.000
20 8.6144 1.306 -0.334 0.983 -0.000
21 8.6143 1.306 -0.334 0.983 -0.000
22 8.6142 1.306 -0.334 0.983 -0.000
23 8.6141 1.306 -0.334 0.983 -0.000
24 8.6140 1.307 -0.335 0.983 -0.000
25 8.6139 1.307 -0.335 0.983 -0.000
** Convergence criterion not met after 25 iterations **
Final Estimates of Parameters
Type Coef SE Coef T P
AR 1 1.3067 0.0670 19.49 0.000
AR 2 -0.3348 0.0670 -4.99 0.000
MA 1 0.9833 0.0002 4337.66 0.000
Constant -0.0001720 0.0003220 -0.53 0.594
Differencing: 1 regular difference
Number of observations: Original series 205, after differencing 204
Residuals: SS = 8.60330 (backforecasts excluded)
MS = 0.04302 DF = 200
Modified Box-Pierce (Ljung-Box) Chi-Square statistic
Lag 12 24 36 48
Chi-Square 8.7 16.6 32.4 46.1
DF 8 20 32 44
P-Value 0.367 0.678 0.449 0.384
Forecasts from period 205
95% Limits
Period Forecast Lower Upper Actual
206 8.32003 7.91343 8.72662