Case TS: Test of Significance



Case TS: Tests of Significance of Coefficients

For the following series, suppose that the forecaster fits a quadratic trend.

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|Dependent Variable: Y | | |

|Sample: 1 40 | | | |

|Included observations: 40 | | |

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|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

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|C |2.545662 |2.746653 |0.926823 |0.3600 |

|T |0.001570 |0.308960 |0.005081 |0.9960 |

|T*T |0.012973 |0.007308 |1.775139 |0.0841 |

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|R-squared |0.589935 |    Mean dependent var |9.758133 |

|Adjusted R-squared |0.567769 |    S.D. dependent var |8.370830 |

|S.E. of regression |5.503342 |    Akaike info criterion |6.320626 |

|Sum squared resid |1120.610 |    Schwarz criterion |6.447292 |

|Log likelihood |-123.4125 |    F-statistic |26.61477 |

|Durbin-Watson stat |2.043732 |    Prob(F-statistic) |0.000000 |

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It appears that both t and t*t are not significant, using 5% significance level.

However R-squared and Adjusted R-squared are quite high. Here an F-test gives provides an insight:

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The critical value of F-statistic is 95 percentile of the F distribution with the numerator degrees of freedom=2 and the denominator degrees of freedom=37, which equals 3.25 (using Eviews function @qfdist(0.95, 2, 37)). This can also be verified from the p-value of the F-statistic which is less than 5%.

Note that DW is close to 2. This means that the residuals are not positively auto-correlated. The test is thus valid.

The test rejects H0 and this implies that at least one coefficient is not zero. So, a natural next step is to fit a linear trend as follows:

|Dependent Variable: Y | | | |

|Sample: 1 40 | | | | |

|Included observations: 40 | | | |

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|Variable |Coefficient |Std. Error |t-Statistic |Prob.   | |

| | | | | | |

| | | | | | |

|C |-3.259866 |1.689106 |-1.929936 |0.0611 | |

|T |0.507448 |0.071796 |7.067952 |0.0000 | |

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|R-squared |0.567966 |    Mean dependent var |7.142819 | |

|Adjusted R-squared |0.556596 |    S.D. dependent var |7.871580 | |

|S.E. of regression |5.241572 |    Akaike info criterion |6.199827 | |

|Sum squared resid |1044.015 |    Schwarz criterion |6.284271 | |

|Log likelihood |-121.9965 |    F-statistic |49.95595 | |

|Durbin-Watson stat |2.184679 |    Prob(F-statistic) |0.000000 | |

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