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_July2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45012 -0.18349 -0.03008 0.15026 0.81916
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.92827 0.18236 5.090 6.46e-07 ***
## log_NatGasUSA 0.85873 0.04019 21.367 < 2e-16 ***
## Feb_July2022 0.17845 0.06145 2.904 0.00397 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2531 on 289 degrees of freedom
## Multiple R-squared: 0.7196, Adjusted R-squared: 0.7177
## F-statistic: 370.9 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_N ~ log_NatGasEU + Feb_July2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5722 -0.1348 -0.0135 0.1373 0.6071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.77950 0.06932 40.095 < 2e-16 ***
## log_NatGasEU 0.42780 0.01437 29.778 < 2e-16 ***
## Feb_July2022 0.29504 0.04581 6.441 4.94e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2015 on 289 degrees of freedom
## Multiple R-squared: 0.8222, Adjusted R-squared: 0.821
## F-statistic: 668.2 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_NPK ~ log_NatGasUSA + Feb_July2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43626 -0.20667 -0.00995 0.17207 0.58070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.50840 0.16478 9.154 < 2e-16 ***
## log_NatGasUSA 0.73675 0.03631 20.289 < 2e-16 ***
## Feb_July2022 0.17998 0.05553 3.241 0.00133 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2287 on 289 degrees of freedom
## Multiple R-squared: 0.704, Adjusted R-squared: 0.702
## F-statistic: 343.7 on 2 and 289 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log_NPK ~ log_NatGasEU + Feb_July2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30480 -0.09497 -0.01320 0.08913 0.31278
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.921939 0.043131 67.746 < 2e-16 ***
## log_NatGasEU 0.403838 0.008938 45.180 < 2e-16 ***
## Feb_July2022 0.229840 0.028500 8.064 1.97e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1254 on 289 degrees of freedom
## Multiple R-squared: 0.911, Adjusted R-squared: 0.9104
## F-statistic: 1479 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 July 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_July2022, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.82079 -0.01663 -0.00389 0.01892 0.72772
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.141253 0.082599 1.710 0.0883 .
## log_N_Lag1week 0.977693 0.025368 38.541 <2e-16 ***
## log_NatGasEU_Lag_4weeks -0.006928 0.012225 -0.567 0.5714
## Feb_July2022 0.029851 0.024976 1.195 0.2330
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1027 on 284 degrees of freedom
## (4 observations deleted due to missingness)
## Multiple R-squared: 0.9544, Adjusted R-squared: 0.9539
## F-statistic: 1980 on 3 and 284 DF, p-value: < 2.2e-16