Residual plots5/3/2023 ![]() In any case, the autocorrelation is not particularly large, and at lag 7 it is unlikely to have any noticeable impact on the forecasts or the prediction intervals. The autocorrelation plot shows a significant spike at lag 7, but it is not quite enough for the Breusch-Godfrey to be significant at the 5% level. The histogram shows that the residuals seem to be slightly skewed, which may also affect the coverage probability of the prediction intervals. This heteroscedasticity will potentially make the prediction interval coverage inaccurate. ![]() The time plot shows some changing variation over time, but is otherwise relatively unremarkable. (The checkresiduals() function will use the Breusch-Godfrey test for regression models, but the Ljung-Box test otherwise.) #> data: Residuals from Linear regression modelįigure 5.8 shows a time plot, the ACF and the histogram of the residuals from the multiple regression model fitted to the US quarterly consumption data, as well as the Breusch-Godfrey test for jointly testing up to 8th order autocorrelation. #> Breusch-Godfrey test for serial correlation of order up to 8 The Breusch-Godfrey test is similar to the Ljung-Box test, but it is specifically designed for use with regression models.įigure 5.8: Analysing the residuals from a regression model for US quarterly consumption. A small p-value indicates there is significant autocorrelation remaining in the residuals. It is used to test the joint hypothesis that there is no autocorrelation in the residuals up to a certain specified order. Therefore we should always look at an ACF plot of the residuals.Īnother useful test of autocorrelation in the residuals designed to take account for the regression model is the Breusch-Godfrey test, also referred to as the LM (Lagrange Multiplier) test for serial correlation. The forecasts from a model with autocorrelated errors are still unbiased, and so are not “wrong”, but they will usually have larger prediction intervals than they need to. In this case, the estimated model violates the assumption of no autocorrelation in the errors, and our forecasts may be inefficient - there is some information left over which should be accounted for in the model in order to obtain better forecasts. Therefore when fitting a regression model to time series data, it is common to find autocorrelation in the residuals. With time series data, it is highly likely that the value of a variable observed in the current time period will be similar to its value in the previous period, or even the period before that, and so on. We will now discuss each of them in turn. There are a series of plots that should be produced in order to check different aspects of the fitted model and the underlying assumptions. (This is not necessarily true when the intercept is omitted from the model.)Īfter selecting the regression variables and fitting a regression model, it is necessary to plot the residuals to check that the assumptions of the model have been satisfied. The differences between the observed \(y\) values and the corresponding fitted \(\hat.Īs a result of these properties, it is clear that the average of the residuals is zero, and that the correlation between the residuals and the observations for the predictor variable is also zero. 12.9 Dealing with missing values and outliers.12.8 Forecasting on training and test sets.12.7 Very long and very short time series.12.5 Prediction intervals for aggregates.12.3 Ensuring forecasts stay within limits.10.7 The optimal reconciliation approach.10 Forecasting hierarchical or grouped time series.9.4 Stochastic and deterministic trends.7.5 Innovations state space models for exponential smoothing.7.4 A taxonomy of exponential smoothing methods.6.7 Measuring strength of trend and seasonality.5.9 Correlation, causation and forecasting.1.7 The statistical forecasting perspective.1.6 The basic steps in a forecasting task.
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