Background
Methods
ARIMA model
BP-ANN model
Model validation and statistical comparisons
Information analysis based on computer software
Data sources
No. | training set | validation set | ||
---|---|---|---|---|
1 | P1(2004–01) | P13(2005–01) | P25(2006–01) | P37(2007–01) |
2 | P2(2004–02) | P14(2005–02) | P26(2006–02) | P38(2007–02) |
3 | P3(2004–03) | P15(2005–03) | P27(2006–03) | P39(2007–03) |
i | P(i) | P(i + 12) | P(i + 24) | P(i + 36) |
82 | P82(2010–10) | P94(2011–10) | P106(2012–10) | P118(2013–10) |
83 | P83(2010–11) | P95(2011–11) | P107(2012–11) | P119(2013–11) |
84 | P84(2010–12) | P96(2011–12) | P108(2012–12) | P120(2013–12) |
85 | P85(2011–01) | P97(2012–01) | P109(2013–01) | P121(2014–01) |
109 | P109(2013–01) | P121(2014–01) | P133(2015–01) | P145(2016–01) |
119 | P119(2013–11) | P131(2014–11) | P143(2015–11) | P155(2016–11) |
120 | P120(2013–12) | P132(2014–12) | P144(2015–12) | P156(2016–12) |
121 | P121(2014–01) | P133(2015–01) | P145(2016–01) | P157(2017–01) |
131 | P131(2014–11) | P143(2015–11) | P155(2016–11) | P167(2017–11) |
132 | P132(2014–12) | P144(2015–12) | P156(2016–12) |
Results
Features of time series analysis in the report rate of AIDS
year | Incidence (per 100,000 people) | chain growth rate(%) | growth rate(%) |
---|---|---|---|
2004 | 0.2648 | – | – |
2005 | 0.5076 | 91.6994 | 91.6994 |
2006 | 0.5320 | 4.7930 | 100.8875 |
2007 | 0.5921 | 11.3056 | 123.5989 |
2008 | 0.9368 | 58.2124 | 253.7613 |
2009 | 1.4507 | 54.8668 | 447.8588 |
2010 | 2.7356 | 88.5664 | 933.0778 |
2011 | 3.1107 | 13.7129 | 1074.7432 |
2012 | 3.6908 | 18.6491 | 1293.8218 |
2013 | 3.2777 | −11.1931 | 1137.8097 |
2014 | 3.4608 | 5.5865 | 1206.9600 |
2015 | 3.7506 | 8.3738 | 1316.3897 |
2016 | 4.0211 | 7.2122 | 1418.5423 |
ARIMA model
Model identification
Models | Fitted Model Statistics | Ljung-Box Q(18) | |||||
---|---|---|---|---|---|---|---|
Stationary R2 | RMSE | MAPE | MAE | BIC | Statistics | Sig. | |
ARIMA(0,1,0) × (0,1,0)12 | 0.000 | 0.087 | 30.213 | 0.047 | −4.848 | 78.375 | 0.000 |
ARIMA(0,1,0) × (0,1,1)12 | 0.205 | 0.057 | 26.869 | 0.037 | −5.668 | 48.93 | 0.000 |
ARIMA(0,1,0) × (1,1,0)12 | 0.115 | 0.066 | 28.243 | 0.041 | −5.361 | 53.683 | 0.000 |
ARIMA(0,1,0) × (1,1,1)12 | 0.210 | 0.057 | 26.806 | 0.037 | −5.609 | 46.879 | 0.000 |
ARIMA(0,1,1) × (0,1,0)12 | 0.274 | 0.061 | 24.461 | 0.036 | −5.522 | 30.871 | 0.021 |
ARIMA(0,1,1) × (0,1,1)12 | 0.419 | 0.045 | 22.464 | 0.030 | −6.091 | 13.909 | 0.605 |
ARIMA(0,1,1) × (1,1,0)12 | 0.365 | 0.051 | 23.118 | 0.033 | −5.834 | 13.873 | 0.608 |
ARIMA(0,1,1) × (1,1,1)12 | 0.428 | 0.046 | 22.079 | 0.030 | −6.032 | 10.764 | 0.769 |
ARIMA(1,1,0) × (0,1,0)12 | 0.197 | 0.068 | 26.551 | 0.040 | −5.307 | 53.543 | 0.000 |
ARIMA(1,1,0) × (0,1,1)12 | 0.369 | 0.049 | 23.588 | 0.033 | −5.927 | 16.727 | 0.403 |
ARIMA(1,1,0) × (1,1,0)12 | 0.305 | 0.056 | 24.379 | 0.036 | −5.665 | 19.492 | 0.244 |
ARIMA(1,1,0) × (1,1,1)12 | 0.374 | 0.049 | 23.353 | 0.033 | −5.874 | 16.066 | 0.378 |
ARIMA (1,1,1)×(0,1,0)12 | 0.274 | 0.061 | 24.485 | 0.036 | −5.479 | 30.781 | 0.014 |
ARIMA (1,1,1)×(0,1,1)12 | 0.420 | 0.045 | 22.494 | 0.030 | −6.049 | 13.949 | 0.529 |
ARIMA (1,1,1)×(1,1,0)12 | 0.365 | 0.052 | 23.095 | 0.033 | −5.790 | 13.923 | 0.531 |
ARIMA (1,1,1)×(1,1,1)12 | 0.428 | 0.046 | 22.081 | 0.030 | −5.990 | 10.758 | 0.705 |
Forecast analysis with ARIMA
Month | Actual value | Predictive value | UCL | LCL |
---|---|---|---|---|
201,701 | 0.1810 | 0.2164 | 0.3437 | 0.1280 |
201,702 | 0.2405 | 0.2162 | 0.3502 | 0.1246 |
201,703 | 0.3746 | 0.3496 | 0.5772 | 0.1966 |
201,704 | 0.2994 | 0.3645 | 0.6128 | 0.2002 |
201,705 | 0.3634 | 0.3672 | 0.6281 | 0.1970 |
201,706 | 0.4279 | 0.4065 | 0.7069 | 0.2132 |
201,707 | 0.358 | 0.4077 | 0.7204 | 0.2092 |
201,708 | 0.3905 | 0.3756 | 0.6740 | 0.1887 |
201,709 | 0.3821 | 0.4073 | 0.7418 | 0.200 |
201,710 | 0.3244 | 0.3241 | 0.5988 | 0.1563 |
201,711 | 0.4438 | 0.3752 | 0.7031 | 0.1773 |
201,712 | 0.4789 | 0.4284 | 0.8137 | 0.1986 |
BP-ANN model
Network architecture
Algorithm | Number of neurons in the hidden layer | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
Traingd | 0.597710 | 0.633182 | 0.566311 | 0.888439 | 0.778596 | 0.895304 | 1.025611 | 1.057920 | 0.425543 | 0.382488 |
Traingdm | 0.003257 | 0.002775 | 0.003120 | 0.003124 | 0.003389 | 0.003088 | 0.003015 | 0.003237 | 0.003293 | 0.003116 |
Traingda | 0.002978 | 0.002820 | 0.003169 | 0.002910 | 0.002736 | 0.003304 | 0.002894 | 0.003054 | 0.003250 | 0.002987 |
Traingdx | 0.004025 | 0.003410 | 0.003930 | 0.003967 | 0.003496 | 0.002735 | 0.003296 | 0.003464 | 0.003186 | 0.003055 |
Trainrp | 0.004357 | 0.004044 | 0.004410 | 0.004013 | 0.004315 | 0.004017 | 0.004347 | 0.004304 | 0.004002 | 0.003873 |
Traincgf | 0.004123 | 0.004409 | 0.003290 | 0.003908 | 0.003490 | 0.004200 | 0.004084 | 0.003001 | 0.004252 | 0.004482 |
Traincgp | 0.003626 | 0.004292 | 0.003758 | 0.002979 | 0.003060 | 0.003433 | 0.004048 | 0.004186 | 0.004122 | 0.003273 |
Traincgb | 0.003661 | 0.002862 | 0.002901 | 0.002945 | 0.003922 | 0.003591 | 0.003041 | 0.003591 | 0.002966 | 0.002799 |
Trainscg | 0.004381 | 0.004148 | 0.004444 | 0.004257 | 0.004166 | 0.004352 | 0.004403 | 0.004491 | 0.003700 | 0.004392 |
Trainoss | 0.003074 | 0.003489 | 0.002980 | 0.002927 | 0.003281 | 0.002651 | 0.002948 | 0.003391 | 0.003032 | 0.003330 |
Trainlm | 0.002369 | 0.002293 | 0.002123 | 0.001863 | 0.002042 | 0.002313 | 0.002330 | 0.002365 | 0.002445 | 0.002491 |
Forecast analysis with BP-ANN
Month | Actual value | Predictive value |
---|---|---|
201701 | 0.1810 | 0.193743 |
201702 | 0.2405 | 0.187785 |
201703 | 0.3746 | 0.356085 |
201704 | 0.2994 | 0.332513 |
201705 | 0.3634 | 0.352712 |
201706 | 0.4279 | 0.400424 |
201707 | 0.3580 | 0.360190 |
201708 | 0.3905 | 0.349451 |
201709 | 0.3821 | 0.376242 |
201710 | 0.3244 | 0.342154 |
201711 | 0.4438 | 0.445962 |
201712 | 0.4789 | 0.477938 |
Comparative analysis
Prediction error | ARIMA | BP-ANN |
---|---|---|
MSE | 0.0020 | 0.0019 |
MAE | 0.0301 | 0.0129 |
MAPE | 22.4638 | 1.2139 |