12.3 Statistical tests

The following are tests that we have done throughout the semester. Notice, that code examples are random, so the input may vary, e.g., not the fitted values but residuals can be put in.

Bresuch-Pagan test (BP)

• This is a test for heteroskedasticity
  • H0: Homoskedasticity
  • bptest(fit)

Jarque-Beta test

• This is an assessment of normality
  • H0: The data is normally distributed
  • jarque.bera.test(m.arima$residuals)

Durbin-Watson test (DW)

• This is a test for serial correlation (autocorrelation).
  • H0: No autocorrelation
  • dwtest(fit)

Ljung-Box test

• Test for absence or serial correlation, i.e., autocorrelation, accounting for p and q lags.
  • H0: No autocorrelation
  • Box.test(ARIMAmod$residuals,type = "Ljung-Box",fitdf = p+q), must define p and q

ACF correlogram

• Test for autocorrelation. Visual inspection, see if there are spikes over the confidence level
  • acf(), tsdisplay() will also show it

Augmented Dickey-Fuller test (ADF)

• Test for stationarity
  • H0: Non-stationary series
  • adf.test(y)

Portmanteau test (symptotic)

• The Portmanteau statistic for testing the absence of up to the order h serially correlated disturbances in a stable VAR(p).
  • H0: No autocorrelation
  • serial.test(fit, lags.pt=10, type="PT.asymptotic")
  • This was applied with VAR(p) only

Phillips-Ouliaris test (PO)

• Test for cointegration (follows theh 2 tep EG test)
  • H0: No cointegration
  • serial.test(var1,lags.pt = 10,type = "PT.asymptotic"), notice, that the lags.pt. may be adjusted, e.g., take one or two seasonal cycles.

Diebold-Mariano test (DM)

• The tests whether two tests have the same accuracy
  • H0: Forecast a and b have the same accuracy
  • dm.test(e1 = resid(HW)e2 = resid(arima.bc)[25:2016],alternative = "two.sided")

Variance Inflation Factor (VIF)

• Test for multicollinearity
  • If larger than 9, then assume multicollinearity
  • vif(fit)