I am on chapter 5.4 residual diagnostics.
In the chapter, there is a test for autocorrelation, with an example for a ljung_box test (below), the p value is 0.637 and it is concluded that the residuals are not distinguishable from a white noise series. My query is that if it was the other way round and if the p value was low eg <0.05, does this mean that any forecasting that you do would be inaccurate?
aug %>% features(.innov, ljung_box, lag = 10, dof = 0)
#> # A tibble: 1 x 4
#> Symbol .model lb_stat lb_pvalue
#> <chr> <chr> <dbl> <dbl>
#> 1 GOOG NAIVE(Close) 7.91 0.637
Residuals are useful in checking whether a model has adequately captured the information in the data. A good forecasting method will yield residuals with the following properties:
The residuals are uncorrelated. If there are correlations between residuals, then there is information left in the residuals which should be used in computing forecasts.
The residuals have zero mean. If the residuals have a mean other than zero, then the forecasts are biased.
Any forecasting method that does not satisfy these properties can be improved.
An ARIMA model is one way to improve a forecast with residual autocorrelation. Bias can be corrected. Residual autocorrelation may lead to wider prediction intervals.