# Macroeconomic News Sentiment: Enhanced Risk Assessment for Sovereign Bonds

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Bond Data

#### 2.2. Macroeconomic News Sentiment

- a mean news-sentiment value time series,
- a volume of news time series,
- a news-impact time series,

- all news,
- positive news,
- negative news.

#### 2.3. Correlation and ARIMAX Models

## 3. Results and Discussion

#### 3.1. Correlation and Market Regimes

#### 3.2. Sovereign Bonds Spreads in Spain and Germany

#### 3.3. Market Regime Detection

**Definition**

**1**

**Definition**

**2**

#### 3.4. Analysis of Mean Bond Spreads

#### Linear Regression for Spread Volatility

## 4. Prediction of Sovereign Bond Spreads through News Sentiment

ARIMAX Model | External Variables |

ARIMAX 1 | No external variable |

ARIMAX 2 | Positive Impact; Negative Impact |

ARIMAX 3 | Volume of All News; All Impact |

ARIMAX 4 | Volume of Positive News |

ARIMAX 5 | Volume of All News |

#### Countries’ Mean Bond Spreads

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Estimation of market states through changing correlations between volume of news and mean long-term bond spread in Spain.

**Figure 5.**News volume and its rolling correlation with a mean spread of long-term German sovereign bonds.

**Figure 7.**Rolling correlations between mean spread change in Spain and (

**a**) the impact of news and (

**b**) the volume of news.

**Figure 9.**Mean volatility of daily spread change and its correlation with daily news impact series for five European countries.

**Table 1.**Percentage of significant correlations between spread and sentiment time series for long-term bonds issued by Spain.

Spain: News Time Series | ${\mathit{S}}_{\mathit{t}}$ | ${\mathit{D}}_{\mathit{t}}$ | ${\mathit{V}}_{\mathit{t}}$ |
---|---|---|---|

All Sentiment | 66% | 75% | 47% |

Volume All News | 97% | 31% | 88% |

All impact | 50% | 78% | 28% |

Positive Sentiment | 78% | 0% | 56% |

Volume Positive News | 88% | 37% | 91% |

Positive Impact | 78% | 0% | 59% |

Negative Sentiment | 91% | 3% | 78% |

Volume Negative News | 97% | 59% | 84% |

Negative Impact | 91% | 3% | 78% |

**Table 2.**Percentage of significant correlations between spread and sentiment time series for short-term bonds issued by Spain.

Spain: News Time Series | ${\mathit{S}}_{\mathit{t}}$ | ${\mathit{D}}_{\mathit{t}}$ | ${\mathit{V}}_{\mathit{t}}$ |
---|---|---|---|

All Sentiment | 55% | 30% | 30% |

Volume All News | 70% | 15% | 50% |

All impact | 55% | 25% | 25% |

Positive Sentiment | 35% | 0% | 30% |

Volume Positive News | 60% | 30% | 60% |

Positive Impact | 40% | 5% | 25% |

Negative Sentiment | 60% | 0% | 30% |

Volume Negative News | 75% | 30% | 35% |

Negative Impact | 60% | 5% | 35% |

**Table 3.**Regression analysis for volatility of German mean bond spread difference. Residual standard error: 0.02701 on 2582 degrees of freedom Multiple R-squared: 0.01342, Adjusted R-squared: 0.01227 F-statistic: 11.71 on 3 and 2582 DF, p-value: 1.288 × 10${}^{-7}$. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Coefficients: | Estimate | Std. Error | t Value | Pr (>|t|) | |
---|---|---|---|---|---|

(Intercept) | 2.488 × 10${}^{-2}$ | 2.804 × 10${}^{-3}$ | 8.871 | <2 × 10${}^{-16}$ | *** |

NrOfAllNews | −4.802 × 10${}^{-6}$ | 9.024 × 10${}^{-6}$ | −0.532 | 0.594649 | |

PosImpact | −2.385 × 10${}^{-2}$ | 4.842 × 10${}^{-3}$ | −4.927 | 8.9 × 10${}^{-7}$ | *** |

NegImpact | −1.265 × 10${}^{-2}$ | 3.583 × 10${}^{-3}$ | −3.531 | 0.000421 | *** |

**Table 4.**Regression analysis for volatility of the mean bond spread difference from Spain. Residual standard error: 0.05141 on 2505 degrees of freedom Multiple R-squared: 0.06588, Adjusted R-squared: 0.06476 F-statistic: 58.89 on 3 and 2505 DF, p-value: <2.2 × 10${}^{-16}$. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Coefficients: | Estimate | Std. Error | t Value | Pr (>|t|) | |
---|---|---|---|---|---|

(Intercept) | 2.476 × 10${}^{-2}$ | 3.372 × 10${}^{-3}$ | 7.343 | 2.81 × 10${}^{-13}$ | *** |

NrOfAllNews | 2.082 × 10${}^{-4}$ | 1.901 × 10${}^{-5}$ | 10.956 | <2 × 10${}^{-16}$ | *** |

PosImpact | 2.710 × 10${}^{-3}$ | 5.657 × 10${}^{-3}$ | 0.479 | 0.632 | |

NegImpact | −2.365 × 10${}^{-2}$ | 4.876 × 10${}^{-3}$ | −4.850 | 1.31 × 10${}^{-6}$ | *** |

**Table 5.**Regression analysis for volatility of mean bond spread difference from the UK. Residual standard error: 0.04189 on 2602 degrees of freedom Multiple R-squared: 0.005889, Adjusted R-squared: 0.004742 F-statistic: 5.138 on 3 and 2602 DF, p-value: 0.001526. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Coefficients: | Estimate | Std. Error | t Value | Pr (>|t|) | |
---|---|---|---|---|---|

(Intercept) | 3.145 × 10${}^{-2}$ | 9.323 × 10${}^{-3}$ | 3.373 | 0.000753 | *** |

NrOfAllNews | −7.625 × 10${}^{-6}$ | 4.947 × 10${}^{-6}$ | −1.541 | 0.123393 | |

PosImpact | −3.579 × 10${}^{-2}$ | 1.457 × 10${}^{-2}$ | −2.456 | 0.014109 | * |

NegImpact | −3.485 × 10${}^{-2}$ | 1.189 × 10${}^{-2}$ | −2.931 | 0.003413 | ** |

**Table 6.**Regression analysis for volatility of the mean bond spread difference from Italy. Residual standard error: 0.08624 on 2415 degrees of freedom Multiple R-squared: 0.1526, Adjusted R-squared: 0.1516 F-statistic: 145 on 3 and 2415 DF, p-value: <2.2 × 10${}^{-16}$. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Coefficients: | Estimate | Std. Error | t Value | Pr (>|t|) | |
---|---|---|---|---|---|

(Intercept) | 3.166 × 10${}^{-2}$ | 5.526 × 10${}^{-3}$ | 5.730 | 1.13 × 10${}^{-8}$ | *** |

NrOfAllNews | 4.022 × 10${}^{-4}$ | 1.997 × 10${}^{-5}$ | 20.145 | <2 × 10${}^{-16}$ | *** |

PosImpact | 9.936 × 10${}^{-3}$ | 9.451 × 10${}^{-3}$ | 1.051 | 0.293 | |

NegImpact | −1.279 × 10${}^{-2}$ | 8.609 × 10${}^{-3}$ | −1.486 | 0.137 |

**Table 7.**Regression analysis for volatility of the mean bond spread difference for France. Residual standard error: 0.02362 on 1793 degrees of freedom Multiple R-squared: 0.00222, Adjusted R-squared: 0.0005506 F-statistic: 1.33 on 3 and 1793 DF, p-value: 0.263. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Coefficients: | Estimate | Std. Error | t Value | Pr (>|t|) | |
---|---|---|---|---|---|

(Intercept) | 1.755 × 10${}^{-2}$ | 2.087 × 10${}^{-3}$ | 8.411 | <2 × 10${}^{-16}$ | *** |

NrOfAllNews | −4.636× 10${}^{-6}$ | 9.721 × 10${}^{-6}$ | −0.477 | 0.6335 | |

PosImpact | 3.435 × 10${}^{-3}$ | 3.681 × 10${}^{-3}$ | 0.933 | 0.3508 | |

NegImpact | 4.680 × 10${}^{-3}$ | 2.783 × 10${}^{-3}$ | 1.681 | 0.0929 | . |

**Table 8.**Error distribution of ARIMAX models for in-sample and out-of-sample window of analysis of sovereign bonds issued by Germany. The highlighted data show the lowest Median RMSE over all models.

ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 | |
---|---|---|---|---|---|

In-Sample | |||||

Min. | 0.01424 | 0.01400 | 0.01418 | 0.01421 | 0.01424 |

1st Quartile | 0.02337 | 0.02328 | 0.02326 | 0.02334 | 0.02327 |

Median | 0.02930 | 0.02895 | 0.02924 | 0.02926 | 0.02925 |

Mean | 0.04532 | 0.04492 | 0.04478 | 0.04513 | 0.04496 |

3rd Quartile | 0.04043 | 0.04015 | 0.04036 | 0.04042 | 0.04037 |

Max. | 0.41261 | 0.41258 | 0.41236 | 0.41233 | 0.41244 |

Out-of-Sample | |||||

Min. | 0.01430 | 0.01431 | 0.01430 | 0.01432 | 0.01430 |

1st Quartile | 0.02147 | 0.02251 | 0.02233 | 0.02256 | 0.02152 |

Median | 0.03570 | 0.03537 | 0.03513 | 0.03547 | 0.03513 |

Mean | 0.05260 | 0.05307 | 0.05300 | 0.05291 | 0.05280 |

3rd Quartile | 0.06758 | 0.06843 | 0.06808 | 0.06795 | 0.06776 |

Max. | 0.33667 | 0.32860 | 0.33296 | 0.33527 | 0.33662 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

Spain | −4955.11 | −4951.16 | −4960.94 | −4961.23 | −4961.48 |

Germany | −7908.22 | −7905.09 | −7904.37 | −7906.39 | −7906.37 |

UK | −6141.76 | −6143.39 | −6142.24 | −6139.86 | −6143.06 |

Italy | −2828.18 | −2824.33 | −2856.49 | −2869.29 | −2841.23 |

France | −6151.18 | −6150.12 | −6148.75 | −6149.49 | −6150.58 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

Spain | −6383.28 | −6379.91 | −6381.87 | −6392.53 | −6383.87 |

Germany | −8709.1 | −8720.27 | −8718.92 | −8707.35 | −8707.16 |

UK | −7161.99 | −7159.02 | −7152.87 | −7161.13 | −7145.24 |

Italy | −4029.1 | −4025.82 | −4226.42 | −4089 | −4224.94 |

France | −6768.78 | −6766.79 | −6768.88 | −6767.23 | −6770.87 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

Spain | 0.070017 | 0.070016 | 0.069845 | 0.069875 | 0.069871 |

Germany | 0.035505 | 0.035497 | 0.035504 | 0.035503 | 0.035504 |

UK | 0.055108 | 0.055034 | 0.055049 | 0.055107 | 0.055065 |

Italy | 0.115992 | 0.115988 | 0.115026 | 0.114704 | 0.115541 |

France | 0.028150 | 0.028121 | 0.028135 | 0.028147 | 0.028136 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

Spain | 0.033116 | 0.033145 | 0.033686 | 0.033288 | 0.033648 |

Germany | 0.015860 | 0.015853 | 0.015883 | 0.015878 | 0.015882 |

UK | 0.024518 | 0.024727 | 0.025383 | 0.024847 | 0.024373 |

Italy | 0.035764 | 0.035781 | 0.040910 | 0.044636 | 0.037804 |

France | 0.030514 | 0.030528 | 0.030511 | 0.030509 | 0.030512 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

France | 0.035559 | 0.035486 | 0.035510 | 0.035481 | 0.035514 |

Germany | 0.028480 | 0.028455 | 0.028443 | 0.028478 | 0.028480 |

Italy | 0.084966 | 0.084950 | 0.080648 | 0.083615 | 0.080722 |

Spain | 0.049003 | 0.048996 | 0.048972 | 0.048867 | 0.048972 |

UK | 0.054074 | 0.053979 | 0.053868 | 0.054074 | 0.054054 |

Country | ARIMAX 1 | ARIMAX 2 | ARIMAX 3 | ARIMAX 4 | ARIMAX 5 |
---|---|---|---|---|---|

France | 0.047645 | 0.048033 | 0.047683 | 0.047741 | 0.047616 |

Germany | 0.012011 | 0.012087 | 0.012076 | 0.012003 | 0.012009 |

Italy | 0.027662 | 0.027744 | 0.047507 | 0.028939 | 0.047335 |

Spain | 0.021855 | 0.021876 | 0.021889 | 0.022415 | 0.021893 |

UK | 0.018621 | 0.019222 | 0.020254 | 0.018591 | 0.019527 |

**Table 15.**z-test of coefficients for ARIMAX models in France for first difference of mean country spread. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

France | |||||
---|---|---|---|---|---|

ARIMAX 1 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ma1 | 0.1570987 | 0.0269996 | 5.8186 | 5.936 × 10${}^{-9}$ | *** |

ma2 | 0.1419447 | 0.0243265 | 5.8350 | 5.380 × 10${}^{-9}$ | *** |

intercept | 0.0162441 | 0.0007797 | 20.8338 | <2.2 × 10${}^{-16}$ | *** |

ARIMAX 2 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ma1 | 0.1589004 | 0.0270083 | 5.8834 | 4.019 × 10${}^{-9}$ | *** |

ma2 | 0.1417316 | 0.0242918 | 5.8345 | 5.394 × 10${}^{-9}$ | *** |

intercept | 0.0158352 | 0.0023098 | 6.8556 | 7.103 × 10${}^{-12}$ | *** |

Pos Impact | 0.0040005 | 0.0038430 | 1.0410 | 0.2979 | |

Neg Impact | 0.0031073 | 0.0030199 | 1.0290 | 0.3035 | |

ARIMAX 3 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ma1 | 1.5698 × 10${}^{-1}$ | 2.7021 × 10${}^{-2}$ | 5.8097 | 6.260 × 10${}^{-9}$ | *** |

ma2 | 1.4238 × 10${}^{-1}$ | 2.4296 × 10${}^{-2}$ | 5.8602 | 4.624 × 10${}^{-9}$ | *** |

intercept | 1.6286 × 10${}^{-2}$ | 8.6834 × 10${}^{-4}$ | 18.7556 | <2.2 × 10${}^{-16}$ | *** |

All Impact | 4.0236 × 10${}^{-3}$ | 2.0067 × 10${}^{-3}$ | 2.0051 | 0.04495 | * |

Vol of All News | −1.2558 × 10${}^{-6}$ | 2.8315 × 10${}^{-5}$ | −0.0444 | 0.96463 | |

ARIMAX 4 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ma1 | 1.5643 × 10${}^{-1}$ | 2.7021 × 10${}^{-2}$ | 5.7892 | 7.074 × 10${}^{-9}$ | *** |

ma2 | 1.4215 × 10${}^{-1}$ | 2.4340 × 10${}^{-2}$ | 5.8402 | 5.214 × 10${}^{-9}$ | *** |

intercept | 1.6379 × 10${}^{-2}$ | 8.0711 × 10${}^{-4}$ | 20.2929 | <2.2 × 10${}^{-16}$ | *** |

Vol Neg News | −9.4690 × 10${}^{-6}$ | 2.9785 × 10${}^{-5}$ | −0.3179 | 0.7506 | |

ARIMAX 5 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ma1 | 0.15708778 | 0.02698884 | 5.8205 | 5.868 × 10${}^{-9}$ | *** |

ma2 | 0.14238103 | 0.02429455 | 5.8606 | 4.612 × 10${}^{-9}$ | *** |

intercept | 0.01624505 | 0.00077884 | 20.8579 | <2.2 × 10${}^{-16}$ | *** |

All Impact | 0.00404174 | 0.00199765 | 2.0232 | 0.04305 | * |

**Table 16.**z-test of coefficients for ARIMAX models in Germany for first difference of mean country spread. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Germany | |||||
---|---|---|---|---|---|

ARIMAX 1 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | −3.6493 × 10${}^{-2}$ | 9.4180 × 10${}^{-2}$ | −0.3875 | 0.6984003 | |

ar2 | −1.0804 × 10${}^{-1}$ | 3.8524 × 10${}^{-2}$ | −2.8045 | 0.0050388 | ** |

ma1 | −3.1595 × 10${}^{-1}$ | 9.3749 × 10${}^{-2}$ | −3.3702 | 0.0007512 | *** |

intercept | −4.5338 × 10${}^{-5}$ | 4.4661 × 10${}^{-4}$ | −0.1015 | 0.9191406 | |

ARIMAX 2 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | −0.0396688 | 0.0944553 | −0.4200 | 0.6745037 | |

ar2 | −0.1085231 | 0.0385408 | −2.8158 | 0.0048656 | ** |

ma1 | −0.3132387 | 0.0941024 | −3.3287 | 0.0008725 | *** |

Estimate | Std. Error | z value | Pr (>|z|) | ||

intercept | −0.0028227 | 0.0033941 | −0.8317 | 0.4055958 | |

Pos Impact | 0.0042479 | 0.0057224 | 0.7423 | 0.4578843 | |

Neg Impact | −0.0014718 | 0.0042487 | −0.3464 | 0.7290285 | |

ARIMAX 3 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | −4.0451 × 10${}^{-2}$ | 9.3563 × 10${}^{-2}$ | −0.4323 | 0.6654925 | |

ar2 | −1.0967 × 10${}^{-1}$ | 3.8287 × 10${}^{-2}$ | −2.8644 | 0.0041780 | ** |

ma1 | −3.1253 × 10${}^{-1}$ | 9.3140 × 10${}^{-2}$ | −3.3555 | 0.0007923 | *** |

intercept | 2.9294 × 10${}^{-4}$ | 8.2730 × 10${}^{-4}$ | 0.3541 | 0.7232734 | |

All Impact | −5.6466 × 10${}^{-4}$ | 2.4362 × 10${}^{-3}$ | −0.2318 | 0.8167073 | |

Vol All News | −6.1672 × 10${}^{-6}$ | 3.2677 × 10${}^{-5}$ | −0.1887 | 0.8503033 | |

ARIMAX 4 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | −3.8931 × 10${}^{-2}$ | 9.3731 × 10${}^{-2}$ | −0.4154 | 0.6778841 | |

ar2 | −1.0907 × 10${}^{-1}$ | 3.8331 × 10${}^{-2}$ | −2.8455 | 0.0044348 | ** |

ma1 | −3.1403 × 10${}^{-1}$ | 9.3339 × 10${}^{-2}$ | −3.3644 | 0.0007672 | *** |

intercept | 1.0767 × 10${}^{-4}$ | 5.8730 × 10${}^{-4}$ | 0.1833 | 0.8545389 | |

Vol Neg News | −7.9893 × 10${}^{-6}$ | 3.1632 × 10${}^{-5}$ | −0.2526 | 0.8006021 | |

ARIMAX 5 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | −4.0580 × 10${}^{-2}$ | 9.3979 × 10${}^{-2}$ | −0.4318 | 0.6658911 | |

ar2 | −1.0948 × 10${}^{-1}$ | 3.8339 × 10${}^{-2}$ | −2.8556 | 0.0042957 | ** |

ma1 | −3.1199 × 10${}^{-1}$ | 9.3603 × 10${}^{-2}$ | −3.3332 | 0.0008587 | *** |

intercept | −2.7963 × 10${}^{-5}$ | 4.5456 × 10${}^{-4}$ | −0.0615 | 0.9509479 | |

All Impact | −4.9344 × 10${}^{-4}$ | 2.4336 × 10${}^{-3}$ | −0.2028 | 0.8393225 |

**Table 17.**z-test of coefficients for ARIMAX models in Italy for first difference of mean country spread. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Italy | |||||
---|---|---|---|---|---|

ARIMAX 1 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.46133768 | 0.12335966 | 3.7398 | 0.0001842 | *** |

ar2 | 0.03544736 | 0.03389688 | 1.0457 | 0.2956806 | |

ma1 | −0.62378812 | 0.12090617 | −5.1593 | 2.479 × 10${}^{-7}$ | *** |

intercept | 0.00018773 | 0.00197467 | 0.0951 | 0.9242594 | |

ARIMAX 2 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.46277654 | 0.12319101 | 3.7566 | 0.0001723 | *** |

ar2 | 0.03559929 | 0.03388776 | 1.0505 | 0.2934856 | |

ma1 | −0.62498542 | 0.12072233 | −5.1770 | 2.254 × 10${}^{-7}$ | *** |

intercept | −0.00176552 | 0.00760684 | −0.2321 | 0.8164635 | |

Pos Impact | −0.00014615 | 0.01336217 | −0.0109 | 0.9912732 | |

Neg Impact | −0.00470141 | 0.01234966 | −0.3807 | 0.7034323 | |

ARIMAX 3 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 5.0517 × 10${}^{-1}$ | 1.0053 × 10${}^{-1}$ | 5.0250 | 5.034 × 10${}^{-7}$ | *** |

ar2 | 4.0360 × 10${}^{-2}$ | 3.1541 × 10${}^{-2}$ | 1.2796 | 0.2006900 | |

ma1 | −6.7218 × 10${}^{-1}$ | 9.7445 × 10${}^{-2}$ | −6.8980 | 5.273 × 10${}^{-12}$ | *** |

intercept | −4.1680 × 10${}^{-3}$ | 2.0572 × 10${}^{-3}$ | −2.0261 | 0.0427560 | * |

All Impact | −3.0439 × 10${}^{-2}$ | 9.1134 × 10${}^{-3}$ | −3.3400 | 0.0008377 | *** |

Vol All News | 1.0598 × 10${}^{-4}$ | 3.4367 × 10${}^{-5}$ | 3.0837 | 0.0020445 | ** |

ARIMAX 4 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 5.3473 × 10${}^{-1}$ | 8.6187 × 10${}^{-2}$ | 6.2043 | 5.494e-10 | *** |

ar2 | 4.3724 × 10${}^{-2}$ | 3.0037 × 10${}^{-2}$ | 1.4557 | 0.14549 | |

ma1 | −7.0321 × 10${}^{-1}$ | 8.2556 × 10${}^{-2}$ | −8.5180 | <2.2 × 10${}^{-16}$ | *** |

intercept | −3.6287 × 10${}^{-3}$ | 1.9272 × 10${}^{-3}$ | −1.8829 | 0.05971 | . |

Vol Neg News | 2.3325 × 10${}^{-4}$ | 4.2094 × 10${}^{-5}$ | 5.5412 | 3.003e-08 | *** |

ARIMAX 5 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.4378483 | 0.1385411 | 3.1604 | 0.0015754 | ** |

ar2 | 0.0345230 | 0.0358910 | 0.9619 | 0.3361083 | |

ma1 | −0.6024669 | 0.1363825 | −4.4175 | 9.986 × 10${}^{-6}$ | *** |

intercept | −0.0010503 | 0.0020071 | −0.5233 | 0.6007710 | |

All Impact | −0.0353804 | 0.0091396 | −3.8711 | 0.0001083 | *** |

**Table 18.**z-test of coefficients for ARIMAX models in Spain for first difference of mean country spread. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

Spain | |||||
---|---|---|---|---|---|

ARIMAX 1 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.95264611 | 0.07344346 | 12.9711 | <2.2 × 10${}^{-16}$ | *** |

ar2 | −0.31051240 | 0.02587822 | −11.9990 | <2.2 × 10${}^{-16}$ | *** |

ma1 | −0.60989499 | 0.07476256 | −8.1578 | 3.413 × 10${}^{-16}$ | *** |

intercept | 0.00025918 | 0.00170650 | 0.1519 | 0.8793 | |

ARIMAX 2 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.95221352 | 0.07374859 | 12.9116 | <2.2 × 10${}^{-16}$ | *** |

ar2 | −0.31029570 | 0.02594255 | −11.9609 | <2.2 × 10${}^{-16}$ | *** |

ma1 | −0.60927154 | 0.07510366 | −8.1124 | 4.963 × 10${}^{-16}$ | *** |

intercept | 0.00087810 | 0.00519333 | 0.1691 | 0.8657 | |

Pos Impact | 0.00032176 | 0.00824912 | 0.0390 | 0.9689 | |

Neg Impact | 0.00162662 | 0.00748399 | 0.2173 | 0.8279 | |

ARIMAX 3 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 9.5654 × 10${}^{-1}$ | 7.2633 × 10${}^{-2}$ | 13.1694 | <2.2 × 10${}^{-16}$ | *** |

ar2 | −3.0813 × 10${}^{-1}$ | 2.5501 × 10${}^{-2}$ | −12.0828 | <2.2 × 10${}^{-16}$ | *** |

ma1 | −6.2122 × 10${}^{-1}$ | 7.3874 × 10${}^{-2}$ | −8.4091 | <2.2 × 10${}^{-16}$ | *** |

intercept | −1.5055 × 10${}^{-3}$ | 1.9408 × 10${}^{-3}$ | −0.7757 | 0.437934 | |

All Impact | −1.4101 × 10${}^{-2}$ | 5.0149 × 10${}^{-3}$ | −2.8118 | 0.004926 | ** |

Vol All News | 3.3985 × 10${}^{-5}$ | 3.5864 × 10${}^{-5}$ | 0.9476 | 0.343331 | |

ARIMAX 4 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 9.5207 × 10${}^{-1}$ | 7.4309 × 10${}^{-2}$ | 12.8123 | <2.2 × 10${}^{-16}$ | *** |

ar2 | −3.0659 × 10${}^{-1}$ | 2.5850 × 10${}^{-2}$ | −11.8600 | <2.2 × 10${}^{-16}$ | *** |

ma1 | −6.1608 × 10${}^{-1}$ | 7.5588 × 10${}^{-2}$ | −8.1506 | 3.622 × 10${}^{-16}$ | *** |

intercept | −1.7347 × 10${}^{-3}$ | 1.8302 × 10${}^{-3}$ | −0.9478 | 0.34321 | |

Vol Neg News | 1.1917 × 10${}^{-4}$ | 4.7389 × 10${}^{-5}$ | 2.5148 | 0.01191 | * |

ARIMAX 5 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.95558588 | 0.07294917 | 13.0993 | <2.2 × 10${}^{-16}$ | *** |

ar2 | −0.30831923 | 0.02564519 | −12.0225 | <2.2 × 10${}^{-16}$ | *** |

ma1 | −0.61812569 | 0.07418126 | −8.3326 | <2.2 × 10${}^{-16}$ | *** |

intercept | −0.00035687 | 0.00170466 | −0.2093 | 0.834176 | |

All Impact | −0.01446756 | 0.00500825 | −2.8887 | 0.003868 | ** |

**Table 19.**z-test of coefficients for ARIMAX models in the UK for first difference of mean country spread. Signif. codes are: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’.

UK | |||||
---|---|---|---|---|---|

ARIMAX 1 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.09656998 | 0.13120808 | 0.7360 | 0.461727 | |

ar2 | −0.09876149 | 0.03400310 | −2.9045 | 0.003679 | ** |

ma1 | −0.28436253 | 0.13140202 | −2.1641 | 0.030459 | * |

intercept | −0.00027202 | 0.00086353 | −0.3150 | 0.752758 | |

ARIMAX 2 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.1178994 | 0.1301340 | 0.9060 | 0.364944 | |

ar2 | −0.0982591 | 0.0343999 | −2.8564 | 0.004285 | ** |

ma1 | −0.3081697 | 0.1303238 | −2.3646 | 0.018047 | * |

intercept | −0.0206728 | 0.0120786 | −1.7115 | 0.086985 | . |

Pos Impact | 0.0455152 | 0.0191331 | 2.3789 | 0.017366 | * |

Neg Impact | 0.0050737 | 0.0149431 | 0.3395 | 0.734205 | |

ARIMAX 3 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 1.0385 × 10${}^{-1}$ | 1.2953 × 10${}^{-1}$ | 0.8017 | 0.422719 | |

ar2 | −9.9086 × 10${}^{-2}$ | 3.4002 × 10${}^{-2}$ | −2.9141 | 0.003567 | ** |

ma1 | −2.9357 × 10${}^{-1}$ | 1.2972 × 10${}^{-1}$ | −2.2631 | 0.023629 | * |

intercept | −1.8931 × 10${}^{-3}$ | 1.9301 × 10${}^{-3}$ | −0.9808 | 0.326681 | |

All Impact | 1.0825 × 10${}^{-2}$ | 5.9305 × 10${}^{-3}$ | 1.8253 | 0.067958 | . |

Vol All News | 1.0817 × 10${}^{-5}$ | 3.2073 × 10${}^{-5}$ | 0.3373 | 0.735915 | |

ARIMAX 4 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 9.6457 × 10${}^{-2}$ | 1.3128 × 10${}^{-1}$ | 0.7347 | 0.462493 | |

ar2 | −9.8840 × 10${}^{-2}$ | 3.3976 × 10${}^{-2}$ | −2.9091 | 0.003624 | ** |

ma1 | −2.8410 × 10${}^{-1}$ | 1.3147 × 10${}^{-1}$ | −2.1610 | 0.030697 | * |

intercept | −5.5211 × 10${}^{-4}$ | 1.2299 × 10${}^{-3}$ | −0.4489 | 0.653489 | |

Vol Neg News | 6.1279 × 10${}^{-6}$ | 3.1030 × 10${}^{-5}$ | 0.1975 | 0.843450 | |

ARIMAX 5 | |||||

Estimate | Std. Error | z value | Pr (>|z|) | ||

ar1 | 0.09532101 | 0.13035263 | 0.7313 | 0.464623 | |

ar2 | −0.09991539 | 0.03394586 | −2.9434 | 0.003247 | ** |

ma1 | −0.28472486 | 0.13058831 | −2.1803 | 0.029233 | * |

intercept | −0.00033034 | 0.00086085 | −0.3837 | 0.701179 | |

All Impact | 0.01076473 | 0.00594057 | 1.8121 | 0.069975 | . |

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Erlwein-Sayer, C.
Macroeconomic News Sentiment: Enhanced Risk Assessment for Sovereign Bonds. *Risks* **2018**, *6*, 141.
https://doi.org/10.3390/risks6040141

**AMA Style**

Erlwein-Sayer C.
Macroeconomic News Sentiment: Enhanced Risk Assessment for Sovereign Bonds. *Risks*. 2018; 6(4):141.
https://doi.org/10.3390/risks6040141

**Chicago/Turabian Style**

Erlwein-Sayer, Christina.
2018. "Macroeconomic News Sentiment: Enhanced Risk Assessment for Sovereign Bonds" *Risks* 6, no. 4: 141.
https://doi.org/10.3390/risks6040141