First the simple models trying out both EU Price and US nat gas price - the third model includes a dummy for the period of spiking
##
## Call:
## lm(formula = log_N ~ log_NatGasEU, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.60523 -0.14196 -0.02772 0.15044 0.55465
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.61315 0.06868 38.05 <2e-16 ***
## log_NatGasEU 0.46735 0.01386 33.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2151 on 290 degrees of freedom
## Multiple R-squared: 0.7967, Adjusted R-squared: 0.796
## F-statistic: 1136 on 1 and 290 DF, p-value: < 2.2e-16| Term | Estimate | Std. Error | t Value | P-Value |
|---|---|---|---|---|
| (Intercept) | 2.613149 | 0.0686756 | 38.05060 | 0 |
| log_NatGasEU | 0.467354 | 0.0138642 | 33.70935 | 0 |
##
## Call:
## lm(formula = log_N ~ log_NatGasUSA, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43645 -0.18220 -0.02592 0.15731 0.81541
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.65849 0.15892 4.143 4.49e-05 ***
## log_NatGasUSA 0.92091 0.03444 26.739 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2563 on 290 degrees of freedom
## Multiple R-squared: 0.7114, Adjusted R-squared: 0.7104
## F-statistic: 715 on 1 and 290 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_NatGasUSA + Feb_Sept2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43189 -0.18039 -0.02722 0.16226 0.81670
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.80357 0.21304 3.772 0.000197 ***
## log_NatGasUSA 0.88764 0.04739 18.732 < 2e-16 ***
## Feb_Sept2022 0.06496 0.06354 1.022 0.307432
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2563 on 289 degrees of freedom
## Multiple R-squared: 0.7125, Adjusted R-squared: 0.7105
## F-statistic: 358.1 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_NatGasEU + Feb_Sept2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57330 -0.14544 -0.01741 0.14001 0.60725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.79300 0.07740 36.086 < 2e-16 ***
## log_NatGasEU 0.42533 0.01631 26.083 < 2e-16 ***
## Feb_Sept2022 0.20679 0.04559 4.536 8.42e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2082 on 289 degrees of freedom
## Multiple R-squared: 0.8102, Adjusted R-squared: 0.8089
## F-statistic: 616.8 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_NPK ~ log_NatGasUSA + Feb_Sept2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43988 -0.20831 -0.01761 0.17176 0.57903
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.47389 0.19238 7.661 2.79e-13 ***
## log_NatGasUSA 0.74498 0.04279 17.411 < 2e-16 ***
## Feb_Sept2022 0.10637 0.05737 1.854 0.0647 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2314 on 289 degrees of freedom
## Multiple R-squared: 0.6969, Adjusted R-squared: 0.6948
## F-statistic: 332.2 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_NPK ~ log_NatGasEU + Feb_Sept2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38350 -0.10519 -0.01552 0.10001 0.31751
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.92337 0.04934 59.247 < 2e-16 ***
## log_NatGasEU 0.40404 0.01040 38.866 < 2e-16 ***
## Feb_Sept2022 0.15065 0.02907 5.183 4.11e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1328 on 289 degrees of freedom
## Multiple R-squared: 0.9003, Adjusted R-squared: 0.8996
## F-statistic: 1304 on 2 and 289 DF, p-value: < 2.2e-16Now we move on to trying out the ARDL models with various lags of the nat gas EU variable
##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_1weeks,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.83167 -0.01597 -0.00155 0.01627 0.73642
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.17158 0.07988 2.148 0.0326 *
## log_N_Lag1week 0.94944 0.02791 34.015 <2e-16 ***
## log_NatGasEU_Lag_1weeks 0.01573 0.01462 1.076 0.2829
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1022 on 288 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9544, Adjusted R-squared: 0.9541
## F-statistic: 3015 on 2 and 288 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_4weeks,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.82932 -0.01685 -0.00250 0.01676 0.72391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.092726 0.071985 1.288 0.199
## log_N_Lag1week 0.989965 0.023214 42.645 <2e-16 ***
## log_NatGasEU_Lag_4weeks -0.008739 0.012140 -0.720 0.472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1028 on 285 degrees of freedom
## (4 observations deleted due to missingness)
## Multiple R-squared: 0.9542, Adjusted R-squared: 0.9538
## F-statistic: 2965 on 2 and 285 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_8weeks,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81646 -0.01941 -0.00254 0.01864 0.72019
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.085037 0.065356 1.301 0.1943
## log_N_Lag1week 1.001154 0.018491 54.142 <2e-16 ***
## log_NatGasEU_Lag_8weeks -0.018389 0.009646 -1.906 0.0576 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1028 on 281 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.9544, Adjusted R-squared: 0.9541
## F-statistic: 2943 on 2 and 281 DF, p-value: < 2.2e-16model <- lm(log_N ~ log_N_Lag1week + log_NatGasEU_Lag_24weeks, data = data)
summary(model)##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_24weeks,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81971 -0.02089 -0.00261 0.01831 0.70946
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.185305 0.070517 2.628 0.00909 **
## log_N_Lag1week 0.977663 0.013547 72.167 < 2e-16 ***
## log_NatGasEU_Lag_24weeks -0.015169 0.006876 -2.206 0.02824 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1054 on 265 degrees of freedom
## (24 observations deleted due to missingness)
## Multiple R-squared: 0.9522, Adjusted R-squared: 0.9518
## F-statistic: 2637 on 2 and 265 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_48weeks,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81071 -0.02550 -0.00257 0.02516 0.71463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.371992 0.120007 3.100 0.00217 **
## log_N_Lag1week 0.946535 0.018052 52.434 < 2e-16 ***
## log_NatGasEU_Lag_48weeks -0.021887 0.008807 -2.485 0.01363 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1099 on 241 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.9487, Adjusted R-squared: 0.9482
## F-statistic: 2227 on 2 and 241 DF, p-value: < 2.2e-16We see that the coefficient for natural gas doesn’t make sense. We would expect that to be a positive coefficient. Anyway, we try out the dummy variable for Feb to September 2022 - the period where the price spikes were the highest. Here’s that with the 4 week lag.
##
## Call:
## lm(formula = log_N ~ log_N_Lag1week + log_NatGasEU_Lag_4weeks +
## Feb_Sept2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81132 -0.01938 -0.00398 0.02104 0.72866
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.169118 0.082780 2.043 0.0420 *
## log_N_Lag1week 0.974433 0.024602 39.608 <2e-16 ***
## log_NatGasEU_Lag_4weeks -0.009886 0.012105 -0.817 0.4148
## Feb_Sept2022 0.042524 0.023046 1.845 0.0661 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1023 on 284 degrees of freedom
## (4 observations deleted due to missingness)
## Multiple R-squared: 0.9547, Adjusted R-squared: 0.9542
## F-statistic: 1995 on 3 and 284 DF, p-value: < 2.2e-16