Two aggregate series of heart disease cases are employed in the empirical study. Table 1 below includes some descriptive data, such as the mean, median, lowest and maximum values of cases. According to the table's outcome, there were 3 heart disease cases at a minimum every month during the study period. In Tamilnadu, there were 9.935 heart disease cases on average every month. The median number of instances of hypertension and heart disease is 65 and 6, respectively, according to the sample data for the five years, which consists of 60 data points.

**Table – 1: Descriptive Analysis of Heart Disease**

Disease | Observation | Mean | Median | Min. | Max. |

Heart | 60 | 9.9330 | 8 | 0 | 56 |

When looking at the average number of instances each month, the month of March had the greatest average number (16.8) while the month of November had the lowest average number of cases (ie 4.4 average number of cases). The largest number of heart disease cases—57 cases—occurred in the month of March, while the lowest number—0 cases—occurred in the month of June.

**Table-2**:

Month | Mean | Min. | Max. | Median |

**January** **February** **March** **April** **May** **June** **July** **August** **September** **October** **November** **December** | 10.4 11.6 16.8 14.4 5.4 12 9.2 12.4 11.6 5.2 4.4 5.8 | 2 1 1 1 1 0 2 5 1 4 1 1 | 25 34 57 54 12 33 18 39 24 7 14 12 | 7 6 8 5 3 9 7 6 115 2 6 |

## 3.1. Unit root properties of individual series

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Time series plots, the Augmented Dickey Fuller (ADF) test, the Philip Perrons (PP) test, and the Kwiatkowski-Phillip-Schmidt-Shin (KPSS) test is the series stationary. Unit Root Test Results for this appear to indicate that the series is stationary for both the ADF test and the PP test. The ACF plots do not gradually decay, despite the fact that there is a sizable spike at the initial lag of the PACF, which is a careful observation to support this finding. But until the numerous unit is verified these observations, they can only be considered hypotheses. The ADF test, PP test, and KPSS test were among the stationarity tests used in this study.

**Figure − 1: A time series display of the heart disease cases at levels in Tamilnadu**

**Table − 3: ADF unit root test results for heart disease cases**

HEART DISEASE | TEST STATISTIC | P-VALUE |

**CONSTANT** **CONSTANT + TREND** **NONE** | -4.2458 -4.4031 -3.0821 | 0.0013 0.0045 0.0026 |

**Table − 4: PP unit root test results for heart disease cases**

HEART DISEASE | TEST STATISTIC | P-VALUE |

**CONSTANT** **CONSTANT + TREND** **NONE** | -4.2153 -4.2973 -2.9628 | 0.0014 0.0061 0.0037 |

**Table − 5: KPSS unit root test results for heart disease cases**

TEST | TEST STATISTIC | P-VALUE |

**KPSS** | 0.3962 | 0.0788 |

Results from Tables 3, 4, and 5, indicate that the heart cases just like the hypertension cases are stationary at levels.

## 3.2. Stability Test

The OLS-CUSUM test was used to assess the parameters. Figure 3.2.1 shows that the model's cumulative residuals are within the 95% confidence interval. Therefore, it may be said that the model's parameters are structurally stable.

:Forecast for heart disease and hypertension cases. The model was used to forecast heart disease and hypertension because it passed nearly all of the pertinent diagnostic tests. The tables below display the findings as follows:

Table 6

Monthly forecasts of heart disease cases.

Month | Forecasts | LCL | UCL |

January February March April May June July August September October November December | 7 5 7 8 9 10 10 10 10 10 10 10 | -11.0340 -14.0400 -15.4183 -15.51935 -14.8445 -14.4445 -14.3964 -14.4355 -14.4422 -14.4190 -14.3935 -14.3792 | 24.95995 25.05432 28.67774 32.43230 34.19446 34.70181 34.75353 34.71623 34.71005 34.73432 34.76046 34.77487 |

## 3.3. Estimation of the VAR order

The order of a VAR model is the number of lags included in the model. The appropriate lag length (𝑝), should be estimated long enough for the residuals not to be serially correlated. The lag length plays a crucial role in diagnostic tests as well as in the estimation of VAR models for impulse response analysis and variance decomposition (Bhasin, 2004). Four of the selection criteria i.e. the Final Prediction Error (FPE), Akaike Information Criterion (AIC), the Schwarz Information Criterion(SC), and the Hannan-Quinn Information Criterion(HQ) support the inclusion of 2 lags for the VAR order. The fact that the majority of the criteria support the inclusion of two lags, the AIC which was the main guideline also supports that. Therefore the estimated VAR is VAR(2) model is as presented Table − 11.

**Table − 7: The long run estimation results for heart disease cases**

variable | Lag | Estimate | Std. error | t-value | p-value |

**Heart** **Heart** **Constant** | 1 2 | 0.4084 -0.0923 2.9840 | 0.0931 0.1871 1.9300 | 3.0983 -0.0983 1.2300 | 0.0023** 0.2331 0.3891 |

## 3.4. Granger Causality Test

An effective method for identifying whether a time series is suitable for forecasting. It is used when the coefficient of the lag of the other variable is greater than zero. At the usual significance level of 5%, the result demonstrates that hypertension Granger-causes heart illnesses. This indicates that future values of heart disease can be predicted using the past data on hypertension. But according to this study, the contrary is not true.

**Table − 8: presents the result from the Granger causality tests.**

NULL HYPOTHESIS | F-STATISTIC | P-VALUE |

Hypertension does not Granger-cause Heart Disease | -28.938 | 0.0005 |

Heart Disease does not Granger-cause Hypertension | -20.3293 | 0.7209 |

Granger At the usual significance level of 5%, the result demonstrates that hypertension Granger-causes heart illnesses. This indicates that future values of the past data on hypertension. But according to this study, the contrary is not true. The aforementioned test clearly showed that the claim that "heart disease does not Granger cause Hypertension" was untrue.

In the VAR model, the dependent variables are subject to shocks from each of the variables. Knowing how the variables interact with one standard deviation of positive shock applied to the error terms allows for the identification of the variable's response. Thus, a unit shock is calculated for each variable from each equation separately. applied to the erroneous terms, and the long-term impacts on the VAR system are indicated. The endogenous variables in the shocks on level are identified using a conventional decomposition.

## 3.5. **Impulse Response Function.**

Impulse responses show how well the dependant variables in the VAR model are able to respond to shocks from each of the variables. Knowing how the variables interact with one standard deviation of positive shock applied to the error terms allows for the identification of the variable's response. Therefore, a unit shock is administered to the erroneous terms for each variable from each equation independently, and the consequences on the VARsystem over time are observed. The endogenous variables on level are identified using a conventional decomposition.

The impulsive response is graphically depicted. The y-axis displays the direction and magnitude of the impulse, or the percentage deviation in the dependent variable from its baseline level, while the x-axis displays the time horizon, or the duration of the shock. The black lines inside the red dashed lines show the % variance, while the red dashed lines show the lower and upper bounds of the confidence interval. Figure 4.4 depicts how heart illnesses react to hypertension standard deviation innovations and to their own shocks (Heart Disease shocks).

## 3.6. Analysis of the Response from Heart Disease cases

Figure 3.2 shows that when a shock of one standard deviation is applied to the cases of heart disease, the response to the shock (by the cases of heart disease) is a gradual decrease in the number of cases from period one to period three, after which it maintains uniformity until the conclusion. The response of cardiac instances to a one standard deviation shock to hypertension cases is also an instant decrease followed by a gradual increase from period one to period four, following which it remains constant the entire time until the end.