Answer Happy

Next step was to run some ARIMA models and compare them. This led to the following ARIMA runs: Model 1 Model 1: ARMA, using observations 1948:02-2020:03 (T= 866) Dependent variable: d UNRATE Standard errors based on Hessian Coefficient Std. Error Z p-value 0.8460 const phi_1 0.00287270 0.0147910 0.1942 0.870665 0.0296668 29.35 -0.718031 0.0379465 -18.92 <0.0001 <0.0001 theta 1 Mean dependent var S.D. dependent var 0.001155 -0.000378 0.086522 162.6270 -298.1985 Mean of innovations R-squared Log-likelihood Schwarz criterion S.D. of innovations Adjusted R-squared Akaike criterion Hannan-Quinn Real Imaginary Modulus Frequency AR Root 1 1.1485 0.0000 1.1485 0.0000 ΜΑ Root 1 1.3927 0.0000 1.3927 0.0000 Test for autocorrelation up to order 12 Ljung-Box Q' = 75.3636, with p-value = P(Chi-square (10) > 75.3636) = 4.042e-012 *** 0.209924 0.200521 0.085465 -317.2540 -309.9612 Model 2 Model 2: ARMA, using observations 1948:02-2020:03 (T=866) Dependent variable: d UNRATE Standard errors based on Hessian Coefficient Std. Error z 0.00298555 0.0148977 0.555245 0.0625183 0.238727 0.0373804 -0.538385 0.0583563 p-value 0.8412 const phi_1 <0.0001 0.2004 8.881 6.386 -9.226 phi_2 <0.0001 <0.0001 theta_1 Mean dependent var Mean of innovations R-squared Log-likelihood Schwarz criterion 0.001155 S.D. dependent var -0.000420 S.D. of innovations 0.123133 Adjusted R-squared 180.2785 Akaike criterion -326.7375 Hannan-Quinn Imaginary Modulus AR Real 1.1911 -3.5169 0.0000 Root 1 Root 2 0.0000 ΜΑ Root 1 1.8574 0.0000 Test for autocorrelation up to order 12 Liung-Box Q' = 36.8101, with p-value = P(Chi-square (9) > 36.8101) = 2.845e-005 1.1911 3.5169 1.8574 *** 0.209924 0.196462 0.121101 -350.5570 -341.4410 Frequency 0.0000 0.5000 0.0000
Model 3 Model 3: ARMA, using observations 1948:02-2020:03 (T = 866) p-value 0.8228 const Dependent variable: d UNRATE Standard errors based on Hessian Coefficient Std. Error 0.00257941 0.0115202 1.65561 0.0374836 -0.782771 0.0433592 -1.64177 0.0383751 0.863215 0.0479172 phi_1 phi_2 theta_1 theta_2 Z 0.2239 44.17 -18.05 -42.78 18.01 <0.0001 <0.0001 <0.0001 <0.0001 Mean dependent var S.D. dependent var S.D. of innovations Mean of innovations R-squared Log-likelihood 0.001155 -0.000443 0.137289 187.0535 -333.5236 Adjusted R-squared Schwarz criterion Akaike criterion Hannan-Quinn Real Imaginary Modulus Frequency AR Root 1 1.0575 -0.3989 1.1303 -0.0574 Root 2 1.0575 0.3989 1.1303 0.0574 ΜΑ 0.9510 -0.5041 1.0763 -0.0776 Root 1 Root 2 0.9510 0.5041 1.0763 0.0776 Test for autocorrelation up to order 12 Ljung-Box Q' = 39.2977, with p-value = P(Chi-square(8) > 39.2977) = 4.328e-006 *** *** *** 0.209924 0.194870 0.134286 -362.1069 -351.1678 Model 4 Model 15: ARMA, using observations 1948:02-2020:03 (T=866) Z const phi_1 Dependent variable: d UNRATE Standard errors based on Hessian Coefficient Std. Error 0.00250730 0.0113898 0.2201 0.578072 0.0624914 9.250 0.117027 0.0739480 1.583 0.611279 0.108845 5.616 -0.695650 0.0557809 -12.47 phi 2 phi 3 phi 4 p-value 0.8258 <0.0001 0.1135 <0.0001 <0.0001 <0.0001 0.3932 <0.0001 <0.0001 0.6673 theta_1 -0.585967 -8.732 0.0671052 0.0631790 0.0740003 theta_2 theta_3 0.8538 -0.595233 0.107839 -5.520 0.766918 0.0693611 11.06 0.0305044 0.0709625 0.4299 theta_4 theta_5 Mean dependent var Mean of innovations R-squared Log-likelihood Schwarz criterion 0.001155 -0.000422 0.160680 198.7941 -323.1854 S.D. dependent var S.D. of innovations Adjusted R-squared Akaike criterion Hannan-Quinn Real Imaginary Modulus Frequency AR Root 1 1.0508 0.4052 1.1262 0.0586 Root 2 1.0508 -0.4052 1.1262 -0.0586 Root 3 -0.6114 -0.8715 1.0646 -0.3474 0.3474 Root 4 -0.6114 0.8715 1.0646 Root 1 0.9450 0.5028 1.0704 0.0778 Root 2 0.9450 -0.5028 1.0704 -0.0778 Root 3 -0.5661 -0.8856 1.0511 -0.3405 Root 4 -0.5661 0.8856 1.0511 0.3405 Root 5 -25.8989 0.0000 25.8989 0.5000 LM test for autocorrelation up to order 12 - Null hypothesis: no autocorrelation Test statistic: Chi-square(3) = 17.9674 Test for autocorrelation up to order 12 Ljung-Box Q¹ = 17.9674, with p-value = P(Chi-square(3) > 17.9674) = 0.0004467 MA *** *** *** *** *** 0.209924 0.192210 0.152845 -375.5881 -355.5330