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| ADF | Merit | (i) Test is reliable for high time series length. |
| Demerits | (i) Calculates low power for a smaller time series length, often resulting in unit root conclusions even for a stationary time series |
| (ii) Inappropriate choice of lag number adversely affects the test results |
| Suggestion | (i) Reliable for apt selection of lag number |
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| KPSS | Merits | (i) Test is nonparametric |
| (ii) Test outcome indicates stationary if the time series is strongly stationary |
| Demerit | (i) The test statistic is vulnerable to type-I errors lowering the test’s reliability |
| Suggestion | (i) Reliable for low time series lengths and recommended to be used along with another test |
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| PP | Merits | (i) Test is reliable for high time series lengths |
| (ii) Test is nonparametric |
| Demerit | (i) Low reliability for small and moderately large time series lengths due to severe size distortions |
| Suggestion | (i) Reliable for higher time series lengths and shorter time series lengths having low parameter value |
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| Breitung | Merits | (i) Reliable for any time series length |
| (ii) Test result is unbiased by any time series characteristics |
| Demerit | (i) Fails to detect the presence of unit root for = 1 in absence of other nonstationary components for lower lengths |
| Suggestion | (i) The test is helpful in accurately understanding the impacts of trend, seasonality, and volatility effects through test results |
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| MK | Merit | (i) Presence of the slightest trend component can be effectively detected |
| Demerit | (i) Test is not reliable, particularly for higher time series length |
| Suggestion | (i) Test cannot be solely used for assessing stationarity |
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| Levene’s | Merit | (i) Completely reliable |
| Demerits | (i) Test is parametric |
| (ii) Cannot detect the presence of trend component if the variance is constant throughout |
| Suggestion | (i) Test is very effective for assessing variance and is recommended for use with some other tests for trend assessment |
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| KW | Merits | (i) Test is nonparametric |
| (ii)Test is fairly reliable for higher time series lengths |
| Demerits | (i) Cannot detect small differences in mean values |
| (ii) Low reliability for lower time series lengths |
| Suggestion | (i) Recommended for use with higher time series lengths |
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| SW | Merits | (i) Test is reliable |
| (ii) Best performing test in all normality tests |
| Demerits | (i) Nonstationary outcome does not mean that the time series is not stationary |
| (ii) Low reliability with respect to skewness |
| (iii) Significant type-I error for 0 kurtosis |
| Suggestion | (i) This test is to be used first. If the test outcome is nonstationary, then other tests are to be used |
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| KS | Merit | (i) Test is nonparametric (two-way) and low type-I errors |
| Demerit | (i) Very low reliability with respect to skewness and kurtosis |
| Suggestion | (i) Two-way KS test is useful for stationarity assessment, but the use of other tests for confirmation of results is recommended |
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