TD_PORTMAN (Portmanteau test) is a statistical test to determine if the passed-in residual series can be classified as being white noise. White noise is a series that has zero mean, no evidence of serial correlation, and homoscedastic variance. The TD_PORTMAN test is a suite of sub-tests. All the tests assume that the calculated statistic follows a chi-squared distribution.
- Data is a time series
- Time series model is linear
- Time series model is stationary
- Time series model is correctly specified
- Residuals of the time series model are normally distributed
- Residuals have constant variance over time, meaning they are homoscedastic
- Residuals are not correlated with each other, meaning they are independent
Serial correlation is the correlation between a time series and its lagged values. If the residuals of a time series model exhibit significant serial correlation at certain lags, it suggests that the model is not capturing patterns in the data, and there is some systematic variation that is not accounted for by the model.
A common test is the Ljung-Box test, based on the sum of the squared serial correlation coefficients of the residuals up to a certain lag. The Ljung-Box test is used to test the null hypothesis that the serial correlations are zero, against the alternative hypothesis that they are not. If the test statistic is significant, it suggests that the null hypothesis can be rejected and that the residuals are not white noise. Other tests include Box-Pierce test, Li-McLeod test, Monti test, and McLeod-Li test.
- Use TD_ARIMAESTIMATE with FIT_PERCENTAGE less than 100, to estimate the coefficients associated with an ARIMA model and produce an associated ART table.
- Use TD_ARIMAVALIDATE to validate the estimate ARIMA model produced by TD_ARIMAESTIMATE.
- Use TD_EXTRACT_RESULTS using the ARTFITRESIDUALS layer.
- Use TD_PORTMAN to check the residuals for zero mean white noise.