Diagnostic-tests

Breusch-Pagan Test

Breusch Pagan Test was introduced by Trevor Breusch and Adrian Pagan in 1979. It is used to test for heteroskedasticity in a linear regression model and assumes that the error terms are normally distributed. It tests whether the variance of the errors from a regression is dependent on the values of the independent variables. Null hypothesis states that error variances are constant.

model <- lm(real_gdp ~ imp + exp + poil + eurkzt,macroKZ)
bp(model)
#>                                Breusch-Pagan test                                
#> Heteroskedasticity presents.
#> Please use other tests additionally.
#> In case of opposite results study the case further.
#> 
#> --------------------
#> BP            15.152 
#> p-value        0.004 
#> --------------------

Diagnostic-tests.R

Goldfeld-Quandt Test

The Goldfeld Quandt Test is a test used in regression analysis to test for homoscedasticity. It compares variances of two subgroups; one set of high values and one set of low values. If the variances differ, the test rejects the null hypothesis that the variances of the errors are not constant.

model <- lm(real_gdp ~ imp + exp+poil+eurkzt, macroKZ)
gq(model)
#>                               Goldfeld-Quandt test                               
#> Homoskedasticity presents.
#> Please use other tests additionally.
#> In case of opposite results study the case further.
#> 
#> -------------------
#> GQ            1.951 
#> p-value       0.057 
#> df1              24 
#> df2              23 
#> -------------------

Diagnostic-tests.R

VIF Test

The VIF of the linear regression is defined as VIF = 1/T. With VIF > 5 there is an indication that multicollinearity may be present; with VIF > 10 there is certainly multicollinearity among the variables.

model <- lm(real_gdp ~ imp + exp + poil + eurkzt,macroKZ)
vif_reg(model)
#>                            Variance Inflation Factor                             
#> 
#> If statistics exceeds 5, please be aware of multicollinearity.
#> 
#>    imp    exp   poil eurkzt 
#>  2.062 14.815 16.244  2.328 
#> 
#> This value 14.815 exceeds acceptable threshold.
#> This value 16.244 exceeds acceptable threshold.

Diagnostic-tests.R

Durbin-Watson Test

The Durbin Watson (DW) statistic is a test for autocorrelation in the residuals from a statistical model or regression analysis. The Durbin-Watson statistic will always have a value ranging between 0 and 4. A value of 2.0 indicates there is no autocorrelation detected in the sample. Values from 0 to less than 2 point to positive autocorrelation and values from 2 to 4 means negative autocorrelation.

model <- lm(real_gdp ~ imp + exp + poil + eurkzt,macroKZ)
dwtest(model)
#> 
#>  Durbin-Watson test
#> 
#> data:  model
#> DW = 2.1296, p-value = 0.5525
#> alternative hypothesis: true autocorrelation is greater than 0

Diagnostic-tests.R

Breusch-Godfrey Test

Alternatively, there is Breusch-Godfrey Test for autocorrelation check.It tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests or that sub-optimal estimates of model parameters would be obtained.Null hypothesis states that there is no autocorrelation.

model <- lm(real_gdp ~ imp + exp + poil + eurkzt,macroKZ)
bg(model)
#>           Breusch-Godfrey test for serial correlation of order up to 1           
#> 
#> Residuals are not autocorrelated. 
#> -------------------
#> LM test       0.324 
#> p-value       0.569 
#> -------------------

Diagnostic-tests.R

Shapiro-Wilk statistic

The null-hypothesis of this test is that the population is normally distributed. Thus, if the p value is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not normally distributed. On the other hand, if the p value is greater than the chosen alpha level, then the null hypothesis (that the data came from a normally distributed population) can not be rejected.

Kolmogorov-Smirnov statistic

The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample case) or that the samples are drawn from the same distribution (in the two-sample case).Since the p-value is less than .05, we reject the null hypothesis.

Cramer-Von Mises test

Alternative to Kolmogorov-Smirnov test, Cramer-von Mises statistic is a measure of the mean squared difference between the empirical and hypothetical cumulative distribution functions. It is also used as a part of other algorithms, such as minimum distance estimation.The Cramér–von Mises test can be seen to be distribution-free if empirical distribution is continuous and the sample has no ties. Otherwise, statistic is not the true asymptotic distribution.

Anderson test

The Anderson-Darling test is used to test if a sample of data comes from a population with a specific distribution.The null hypothesis is that your data is not different from normal. Your alternate or alternative hypothesis is that your data is different from normal. You will make your decision about whether to reject or not reject the null based on your p-value.

For additional information please address:

Wooldridge, Jeffrey M. 2012. Introductory Econometrics: A Modern Approach, Fifth Edition.

Hyndman, Rob J and George Athanasopoulos. 2018. Forecasting: Principles and Practice, 2nd Edition.