Table 8 NARDL long run and short run estimates (daily number of new reported COVID-19 cases worldwide included)
Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\(\mathrm{ECT}\) | −1.090046*** (0.042107) | \(\mathrm{ECT}\) | −1.095174*** (0.042679) | \(\mathrm{ECT}\) | −1.132591*** (0.042498) | \(\mathrm{ECT}\) | −1.11978*** (0.042515) | \(\mathrm{ECT}\) | −1.094086*** (0.042804) | \(\mathrm{ECT}\) | −1.096896*** (0.042919) |
Long-run and short-run coefficients | |||||||||||
Const | 0.011766 (0.02905) | Const | 0.003942 (0.031316) | Const | −0.00041 (0.027761) | Const | 0.01041 (0.022178) | Const | 0.016295 (0.0315) | Const | −0.014911 (0.027113) |
\({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.090046*** (0.046904) | \({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.095174*** (0.047337) | \({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.132591*** (0.047067) | \({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.11978*** (0.046833) | \({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.094086*** (0.047676) | \({\mathrm{BTC}}_{\mathrm{t}-1}\) | −1.096896*** (0.047675) |
\({\mathrm{PI}}^{+}\) | 0.008929*** (0.002856) | \({\mathrm{HI}}^{+}\) | 0.000896* (0.000499) | \({\mathrm{FNI}}^{+}\) | 0.039701*** (0.010661) | \({\mathrm{SI}}_{\mathrm{t}-1}^{+}\) | −0.000149 (0.00018) | \({\mathrm{II}}^{+}\) | 0.001655* (0.000848) | \({\mathrm{MCI}}^{+}\) | 0.001342* (0.000722) |
\({\mathrm{PI}}^{-}\) | 0.00764*** (0.002485) | \({\mathrm{HI}}^{-}\) | 0.000766** (0.000329) | \({\mathrm{FNI}}_{\mathrm{t}-1}^{-}\) | 0.03784*** (0.010433) | \({\mathrm{SI}}^{-}\) | −0.00022* (0.00013) | \({\mathrm{II}}_{\mathrm{t}-1}^{-}\) | 0.001329* (0.000688) | \({\mathrm{MCI}}^{-}\) | 0.000859 (0.00057) |
\({\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.004168 (0.004575) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.005491 (0.007048) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.000792 (0.003991) | \({\mathrm{CNC}}^{+}\) | 0.003035 (0.004543) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.010901 (0.008179) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.006703 (0.006833) |
\({\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | −0.000471 (0.003542) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | −0.001544 (0.006103) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.004079 (0.00284) | \({\mathrm{CNC}}^{-}\) | 0.007222* (0.004311) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | −0.007015 (0.006038) | \({\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | −0.003014 (0.004615) |
\({\mathrm{VIX}}^{+}\) | −0.164421*** (0.02411) | \({\mathrm{VIX}}^{+}\) | −0.157511*** (0.024488) | \({\mathrm{VIX}}^{+}\) | −0.161608*** (0.023664) | \({\mathrm{VIX}}^{+}\) | −0.1567*** (0.023642) | \({\mathrm{VIX}}^{+}\) | −0.164333*** (0.024033) | \({\mathrm{VIX}}^{+}\) | −0.16386*** (0.024246) |
\({\mathrm{VIX}}^{-}\) | −0.163397*** (0.022702) | \({\mathrm{VIX}}^{-}\) | −0.162211*** (0.022835) | \({\mathrm{VIX}}^{-}\) | −0.163935*** (0.022708) | \({\mathrm{VIX}}^{-}\) | −0.158306*** (0.022925) | \({\mathrm{VIX}}^{-}\) | −0.164061*** (0.022973) | \({\mathrm{VIX}}^{-}\) | −0.163882*** (0.022868) |
\(\Delta {\mathrm{CNC}}^{+}\) | 0.028717** (0.014535) | \(\Delta {\mathrm{CNC}}^{+}\) | 0.032861** (0.014497) | \(\Delta {\mathrm{FNI}}^{+}\) | 0.025312** (0.012096) | \(\Delta {\mathrm{SI}}^{+}\) | 0.000807* (0.000483) | \(\Delta {\mathrm{II}}^{-}\) | −0.00105 (0.00129) | \(\Delta {\mathrm{CNC}}^{+}\) | 0.031113** (0.014683) |
\(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.023874* (0.013517) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.021712 (0.014058) | \(\Delta {\mathrm{FNI}}_{\mathrm{t}-1}^{+}\) | −0.037215** (0.016586) |  |  | \(\Delta {\mathrm{CNC}}^{+}\) | 0.029177** (0.014815) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.021358 (0.013731) |
\(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{+}\) | 0.025533** (0.011109) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{+}\) | 0.028266** (0.011359) | \(\Delta {\mathrm{FNI}}^{-}\) | −0.016338 (0.016756) |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.016774 (0.014142) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{+}\) | 0.027311** (0.011297) |
\(\Delta {\mathrm{CNC}}^{-}\) | −0.001122 (0.014702) | \(\Delta {\mathrm{CNC}}^{-}\) | −0.008519 (0.014833) | \(\Delta {\mathrm{CNC}}^{+}\) | 0.028241** (0.014226) |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{+}\) | 0.028706** (0.011464) | \(\Delta {\mathrm{CNC}}^{-}\) | −0.012482 (0.015553) |
\(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.039652** (0.018272) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.043047** (0.018396) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{+}\) | −0.019469 (0.013647) |  |  | \(\Delta {\mathrm{CNC}}^{-}\) | −0.002625 (0.016823) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.040951** (0.018305) |
\(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{-}\) | −0.040723** (0.017395) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{-}\) | −0.041628** (0.017463) | \(\Delta {\mathrm{CNC}}^{-}\) | −0.011874 (0.015298) |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.041516** (0.018362) | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{-}\) | −0.040451** (0.017309) |
|  |  |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-1}^{-}\) | 0.03323* (0.017541) |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{-}\) | −0.036842** (0.017236) |  |  |
|  |  |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-2}^{-}\) | −0.026595 (0.016372) |  |  |  |  |  |  |
|  |  |  |  | \(\Delta {\mathrm{CNC}}_{\mathrm{t}-3}^{-}\) | −0.032454** (0.013145) |  |  |  |  |  |  |
Long-run asymmetric effects | |||||||||||
\({\mathrm{L}}_{\mathrm{PI}}^{+}\) | 0.008191*** (0.002634) | \({\mathrm{L}}_{\mathrm{HI}}^{+}\) | 0.000818* (0.000455) | \({\mathrm{L}}_{\mathrm{FNI}}^{+}\) | 0.035054*** (0.00931) | \({\mathrm{L}}_{\mathrm{SI}}^{+}\) | −0.000133 (0.00016) | \({\mathrm{L}}_{\mathrm{II}}^{+}\) | 0.001512* (0.00077) | \({\mathrm{L}}_{\mathrm{MCI}}^{+}\) | 0.001223* (0.000654) |
\({\mathrm{L}}_{\mathrm{PI}}^{-}\) | 0.007009*** (0.00229) | \({\mathrm{L}}_{\mathrm{HI}}^{-}\) | 0.0007** (0.000299) | \({\mathrm{L}}_{\mathrm{FNI}}^{-}\) | 0.03341*** (0.009118) | \({\mathrm{L}}_{\mathrm{SI}}^{-}\) | −0.000196* (0.000116) | \({\mathrm{L}}_{\mathrm{II}}^{-}\) | 0.001215* (0.000625) | \({\mathrm{L}}_{\mathrm{MCI}}^{-}\) | 0.000783 (0.000516) |
\({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | −0.003823 (0.004201) | \({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | −0.005014 (0.006435) | \({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | −0.0007 (0.003524) | \({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | 0.002711 (0.004055) | \({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | −0.009964 (0.007447) | \({\mathrm{L}}_{\mathrm{CNC}}^{+}\) | −0.006111 (0.006208) |
\({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | −0.000432 (0.00325) | \({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | −0.00141 (0.005575) | \({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | 0.003602 (0.002496) | \({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | 0.006449* (0.00383) | \({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | −0.006411 (0.00551) | \({\mathrm{L}}_{\mathrm{CNC}}^{-}\) | −0.002748 (0.004203) |
\({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.150839*** (0.023894) | \({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.143823*** (0.024099) | \({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.142689*** (0.022549) | \({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.139938*** (0.022723) | \({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.150201*** (0.023827) | \({\mathrm{L}}_{\mathrm{VIX}}^{+}\) | −0.149385*** (0.023932) |
\({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.1499*** (0.022607) | \({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.148114*** (0.022629) | \({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.144743*** (0.02174) | \({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.141372*** (0.022083) | \({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.149953*** (0.022858) | \({\mathrm{L}}_{\mathrm{VIX}}^{-}\) | −0.149405*** (0.022651) |
Const | 0.010794 (0.026645) | Const | 0.003599 (0.028592) | Const | −0.000362 (0.024511) | Const | 0.009296 (0.019797) | Const | 0.014894 (0.028755) | Const | −0.013594 (0.024736) |
Long run asymmetry tests – Wald statistics | |||||||||||
\({\mathrm{W}}_{\mathrm{LR}}(\mathrm{PI})\) | 4.487301** | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{HI})\) | 0.3338 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{FNI})\) | 2.139061 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{SI})\) | 0.148092 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{II})\) | 4.581732** | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{MCI})\) | 1.265293 |
\({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 2.739795* | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 3.337275* | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 2.451346 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 1.772852 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 3.37373* | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{CNC})\) | 3.355494* |
\({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 0.001809 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 1.109015 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 0.316811 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 0.188459 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 0.113445 | \({\mathrm{W}}_{\mathrm{LR}}(\mathrm{VIX})\) | 0.4769 |
Statistics and diagnostics | |||||||||||
R-sq | 0.190674 | R−sq | 0.18174 | R−sq | 0.215594 | R−sq | 0.158729 | R−sq | 0.179996 | R−sq | 0.177612 |
Adj R-sq | 0.163765 | Adj R−sq | 0.154534 | Adj R−sq | 0.183163 | Adj R−sq | 0.14182 | Adj R−sq | 0.15056 | Adj R−sq | 0.150269 |
F-stat | 7.085999*** | F−stat | 6.680244*** | F−stat | 6.647919*** | F−stat | 9.386746*** | F−stat | 6.114826*** | F−stat | 6.495744*** |
D-W stat | 2.060461 | D−W stat | 2.058759 | D−W stat | 2.044533 | D−W stat | 2.03404 | D−W stat | 2.063541 | D−W stat | 2.070825 |
\({\upchi }_{\mathrm{SC}}^{2} (1)\) | 2.366963 [0.1247] | \({\upchi }_{\mathrm{SC}}^{2} (1)\) | 2.467295 [0.117] | \({\upchi }_{\mathrm{SC}}^{2} (1)\) | 1.263353 [0.2617] | \({\upchi }_{\mathrm{SC}}^{2} (1)\) | 1.098021 [0.2953] | \({\upchi }_{\mathrm{SC}}^{2} (1)\) | 2.856843 [0.0918] | \({\upchi }_{\mathrm{SC}}^{2} (1)\) | 3.44255 [0.0643] |
\({\upchi }_{\mathrm{SC}}^{2} (2)\) | 1.217663 [0.297] | \({\upchi }_{\mathrm{SC}}^{2} (2)\) | 1.238976 [0.2908] | \({\upchi }_{\mathrm{SC}}^{2} (2)\) | 0.816957 [0.4425] | \({\upchi }_{\mathrm{SC}}^{2} (2)\) | 0.552424 [0.576] | \({\upchi }_{\mathrm{SC}}^{2} (2)\) | 1.441961 [0.2377] | \({\upchi }_{\mathrm{SC}}^{2} (2)\) | 1.756983 [0.1739] |
\({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.118551 [0.7308] | \({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.050962 [0.8215] | \({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.090182 [0.7641] | \({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.003739 [0.9513] | \({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.016026 [0.8993] | \({\upchi }_{\mathrm{HET}}^{2} (1)\) | 0.047376 [0.8278] |
\({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.062791 [0.9391] | \({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.031419 [0.9691] | \({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.045698 [0.9553] | \({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.004194 [0.9958] | \({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.008891 [0.9911] | \({\upchi }_{\mathrm{HET}}^{2} (2)\) | 0.02622 [0.9741] |
\({\upchi }_{\mathrm{NORM}}^{2}\) | 1196.586 [0.0000] | \({\upchi }_{\mathrm{NORM}}^{2}\) | 1146.037 [0.0000] | \({\upchi }_{\mathrm{NORM}}^{2}\) | 1337.827 [0.0000] | \({\upchi }_{\mathrm{NORM}}^{2}\) | 1381.666 [0.0000] | \({\upchi }_{\mathrm{NORM}}^{2}\) | 1056.104 [0.0000] | \({\upchi }_{\mathrm{NORM}}^{2}\) | 1240.097 [0.0000] |
\({\upchi }_{\mathrm{RESET}}^{2}\) | 0.364455 [0.5464] | \({\upchi }_{\mathrm{RESET}}^{2}\) | 0.007184 [0.9325] | \({\upchi }_{\mathrm{RESET}}^{2}\) | 0.174737 [0.6762] | \({\upchi }_{\mathrm{RESET}}^{2}\) | 0.075537 [0.7836] | \({\upchi }_{\mathrm{RESET}}^{2}\) | 0.754172 [0.4512] | \({\upchi }_{\mathrm{RESET}}^{2}\) | 0.106922 [0.9149] |