The hidden models exit in the different data sets have been identified and fully tested for the independence as well as auto-correlations of the residuals are presented in the Tables 1 to 5.
3.1. Quadratic Trend
The results presented in the Table – 1 reveals that the hidden Quadratic trend model is commonly identified in the districts of Perumbalur, Ramanathapuram and Sivaganga data sets.
Table 1
List of Districts with Quadratic trend
Sr. No | District | Model |
1. | Perambalur | Quadratic trend = 31.56 − 0.37 t2 + 0.0032 t2 |
2. | Ramanathapuram | Quadratic trend = 57.81–0.77 t + 0.0027 t2 |
3. | Sivagangai | Quadratic trend = 66.23–0.73 t + 0.0022 t2 |
3.2. Holt’s Linear exponential smoothing
In Kancheepuram, Kanyakumari and Virudhunagar Districts the Holt’s Linear exponential smoothing with different values of α and β is hidden in these three districts data sets.
Table 2
List of Districts with Holt’s Linear Exp.Smoothing with different values of α and β
Sr. No | District | Model |
1. | Kancheepuram | Holt’s Linear Exp.Smoothing with α = 0.1772 and β = 0.0346 |
2. | Kanyakumari | Holt’s Linear Exp.Smoothing with α = 0.1413 and β = 0.1071 |
3. | Virudhunagar | Holt’s Linear Exp.Smoothing with α = 0.1775 and β = 0.0848 |
3.3. Simple Exponential Smoothing
In case of Cuddalore, Dharmapuri, Dindigul, Erode, Pudukottai, Thiruvarur and Tiruppur districts the Simple Exponential Smoothing with different values of α is hidden in these districts data sets commonly.
Table 3
List of Districts with Simple exponential smoothing with different α values
Sr. No | District | Model |
1. | Cuddalore | Simple Exponential Smoothing with α = 0.4511 |
2. | Dharmapuri | Simple Exponential Smoothing with α = 0.5453 |
3. | Dindigul | Simple Exponential Smoothing with α = 0.3588 |
4. | Erode | Simple Exponential Smoothing with α = 0.3172 |
5. | Pudukottai | Simple Exponential Smoothing with α = 0.2847 |
6. | Thiruvarur | Simple Exponential Smoothing with α = 0.3517 |
7. | Tiruppur | Simple Exponential Smoothing with α = 0.3328 |
3.4. Brown’s Linear Exponential Smoothing
In case of Namakkal and Vellore districts the Brown’s linear exponential smoothing with different values of α is hidden commonly in these two districts data sets.
Table 4
List of District with Brown’s linear exponential smoothing with different values of α
Sr. No | District | Model |
1. | Namakkal | Brown’s Linear exp.smoothing with α = 0.2062 |
2. | Vellore | Brown’s Linear exp.smoothing with α = .0855 |
3.5. ARIMA (p,d,q,) Model
In the remaining districts, the ARIMA (p,d,q) model with different values of p,d and q are hidden sets. In general in all the districts data sets shows the decreasing in COVID-19 infected new cases.
Table 5
List of Districts with ARIM(p,d,q) with different of p,d and q
Sr. No | District | Model |
1. | Ariyalur | ARIMA(2,2,1) |
2. | Chengalpattu | ARIMA(0,2,2) |
3. | Chennai | ARIMA(1,1,1) |
4. | Coimbatore | ARIMA(2,1,2) |
5. | Kallakurichi | ARIMA(2,1,0) |
6. | Karur | ARIMA(0,1,2) |
7. | Krishnagiri | ARIMA(0,1,1) |
8. | Madurai | ARIMA(0,1,2) |
9. | Nagapattinam | ARIMA(2,1,1) |
10. | Nilgiris | ARIMA(1,1,1) |
11. | Ranipet | ARIMA(2,1,2) |
12. | Salem | ARIMA(1,1,0) |
13. | Tenkasi | ARIMA(0,1,1) |
14. | Thanjavur | ARIMA(1,2,1) |
15. | Theni | ARIMA(2,1,2) |
16. | Thirupathur | ARIMA(0,1,1) |
17. | Thiruvallur | ARIMA(1,1,1) |
18. | Thiruvannamalai | ARIMA(0,1,1) |
19. | Thoothukudi | ARIMA(2,0,0) |
20. | Tirunelveli | ARIMA(2,2,2) |
21. | Trichy | ARIMA(0,1,2) |
22. | Villupuram | ARIMA(1,1,1) |