Fitted values and residuals

Forecasting in R

Rob J. Hyndman

Professor of Statistics at Monash University

Fitted values and residuals

A fitted value is the forecast of an observation using all previous observations

That is, they are one-step forecasts
Often not true forecasts since parameters are estimated on all data

A residual is the difference between an observation and its fitted value

That is, they are one-step forecast errors

Example: oil production

fc <- naive(oil)
autoplot(oil, series = "Data") + xlab("Year") +
  autolayer(fitted(fc), series = "Fitted") +
  ggtitle("Oil production in Saudi Arabia")

Example: oil production

autoplot(residuals(fc))

Residuals should look like white noise

Essential assumptions

They should be uncorrelated
They should have mean zero

Useful properties (for computing prediction intervals)

They should have constant variance
They should be normally distributed

We can test these assumptions using the checkresiduals() function.

checkresiduals()

checkresiduals(fc)

    Ljung-Box test
data:  residuals
Q* = 12.59, df = 10, p-value = 0.2475
Model df: 0.   Total lags used: 10

Let's practice!

Forecasting in R