**6. Conclusions**

**Model Distributions Alpha Expected**

eGARCH (1,1)

NGARCH (1,1)

NGARCH (2,1)

apARCH (2,2)

TGARCH (2,1)

**Table 5.**

**116**

*stock returns.*

Skewed student t

> Skewed student t

**Exceed**

*Linked Open Data - Applications,Trends and Future Developments*

Student t 1% 10.7 10 LR.uc Statistic: 0.047

**Actual VaR Exceed**

5% 53.5 67 LR.uc Statistic: 3.332

1% 10.7 10 LR.uc Statistic: 0.047

5% 53.5 74 LR.uc Statistic: 7.425

5% 53.5 135 LR.uc Statistic: 93.627

1% 10.7 74 LR.uc Statistic: 163.466

5% 53.5 141 LR.uc Statistic:

Student t 1% NA NA NA NA

5% 53.5 92 LR.uc Statistic: 24.225

*Note: uc.LRstat: the unconditional coverage test likelihood-ratio statistic; uc.critical: the unconditional coverage test critical value; uc.LRp: the unconditional coverage test p-value; cc.LRstat: the conditional coverage test likelihood-ratio statistic; cc. critical: the conditional coverage test critical value; cc.LRp: the conditional coverage test p-value; NA: not available.*

*Backtesting of the GARCH models: GARCH roll forecast (backtest length: 1070) for the log daily zenith Bank*

Student t 1% 10.7 31 LR.uc Statistic: 25.744

5% NA NA NA NA

Student t 1% 10.7 76 LR.uc Statistic: 171.505

**Unconditional Coverage (Kupiec) H0: Correct Exceedances**

LR.uc Critical: 6.635 LR.uc p-value: 0.828 Reject Null: NO

LR.uc Critical: 3.841 LR.uc p-value: 0.068 Reject Null: NO

LR.uc Critical: 6.635 LR.uc p-value: 0.828 Reject Null: NO

LR.uc Critical: 3.841 LR.uc p-value: 0.006 Reject Null: YES

LR.uc Critical: 6.635 LR.uc p-value: 0 Reject Null: YES

LR.uc Critical: 3.841 LR.uc p-value: 0 Reject Null: YES

LR.uc Critical: 6.635 LR.uc p-value: 0 Reject Null: YES

106.038 LR.uc Critical: 3.841 LR.uc p-value: 0 Reject Null: YES

LR.uc Critical: 6.635 LR.uc p-value: 0 Reject Null: YES

LR.uc Critical: 3.841 LR.uc p-value: 0 Reject Null: YES

**Conditional Coverage (Christoffersen) H0: Correct Exceedances and independence of Failure**

LR.cc Statistic: 0.236 LR.cc Critical: 9.21 LR.cc p-value: 0.889 Reject Null: NO

LR.cc Statistic: 3.497 LR.cc Critical: 5.991 LR.cc p-value: 0.174 Reject Null: NO

LR.cc Statistic: 0.236 LR.cc Critical: 9.21 LR.cc p-value: 0.889 Reject Null: NO

LR.cc Statistic: 7.428 LR.cc Critical: 5.991 LR.cc p-value: 0.024 Reject Null: YES

LR.cc Statistic: 175.258 LR.cc Critical: 9.21 LR.cc p-value: 0 Reject Null: YES

LR.cc Statistic: 101.753 LR.cc Critical: 5.991 LR.cc p-value: 0 Reject Null: YES

LR.cc Statistic: 171.614 LR.cc Critical: 9.21 LR.cc p-value: 0 Reject Null: YES

LR.cc Statistic: 111.739 LR.cc Critical: 5.991 LR.cc p-value: 0 Reject Null: YES

LR.cc Statistic: 25.755 LR.cc Critical: 9.21 LR.cc p-value: 0 Reject Null: YES

LR.cc Statistic: 24.823 LR.cc Critical: 5.991 LR.cc p-value: 0 Reject Null: YES

This book chapter investigated the place of backtesting approach in financial time series analysis in choosing a reliable GARCH Model for analyzing stock returns. To achieve this, The chapter used a secondary data that was collected from www.cashcraft.com under stock trend and analysis. Daily stock price was collected on Zenith bank stock price from October 21st 2004 to May 8th 2017. The chapter used nine different GARCH models (sGARCH, gjrGARCH, eGARCH, iGARCH, aPARCH, TGARCH, NGARCH, NAGARCH and AVGARCH) with maximum lag of 2. Most the information criteria for the sGARCH model were not available because the model could to converged. The lowest information criteria were associated with apARCH (2,2) with Student t distribution followed by NGARCH(2,1) with skewed student t distribution. The caution here is that GARCH model should not be selected only based on information criteria only but the significance value of the coefficients, goodness-of-test fit and backtesting should be considered also [3].

The backtesting result of the apARCH (2,2) was not available while eGARCH (1,1) with Skewed student t distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student t distribution passed the backtesting approach. Therefore with the backtesting approach, eGARCH(1,1) with student distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria [30, 31]. This chapter recommended the backtesting approach to selecting reliable GARCH model.
