Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Table 1

The estimation results of parameters in model (12) with ℎ=0.65.

𝐴1	𝐷^𝑞1𝑡𝑥1(𝑡)		𝐴2	𝐷^𝑞2𝑡𝑥2(𝑡)		𝐴3	𝐷^𝑞3𝑡𝑥3(𝑡)
	L	NL		L	NL		L	NL
𝑐1	−0.0050	−0.0753	𝑐2	0.0016	−0.0407	𝑐3	0.0215	0.0754
𝑎11	−0.6284	1.0035	𝑎21	0.1551	1.2353	𝑎31	−0.2587	−1.4196
𝑎12	−0.2203	−0.6022	𝑎22	−0.4282	0.5073	𝑎32	0.1220	−0.1173
𝑎13	0.4818	2.1463	𝑎23	0.1034	0.4666	𝑎33	−0.2939	−1.3398
𝑎14		−16.778	𝑎24		−2.7541	𝑎34		7.3886
𝑎15		4.7152	𝑎25		−18.606	𝑎35		4.4934
𝑎16		−16.371	𝑎26		−9.1467	𝑎36		10.295
𝑎17		4.7435	𝑎27		−4.9194	𝑎37		2.8206
𝑎18		1.2345	𝑎28		3.6713	𝑎38		−1.0608
𝑎19		−10.108	𝑎29		3.6943	𝑎39		4.0766
SSR	9.3𝑒−3	5.9𝑒−3	SSR	3.2𝑒−3	1.9𝑒−3	SSR	1.6𝑒−3	9.3𝑒−4
𝑅^2	0.4955	0.6803	𝑅^2	0.5615	0.7399	𝑅^2	0.4705	0.6918

Note: SSR is the sum squared residuals. L stands for the linear economic model (1). NL stands for the nonlinear economic model (14). 𝑅 stands for the 𝑅-squared value.