Checking time series residuals

When applying a forecasting method, it is important to always check that the residuals are well-behaved (i.e., no outliers or patterns) and resemble white noise. The prediction intervals are computed assuming that the residuals are also normally distributed. You can use the checkresiduals() function to verify these characteristics; it will give the results of a Ljung-Box test.

You haven't used the pipe function (%>%) so far, but this is a good opportunity to introduce it. When there are many nested functions, pipe functions make the code much easier to read. To be consistent, always follow a function with parentheses to differentiate it from other objects, even if it has no arguments. An example is below:

> function(foo)       # These two
> foo %>% function()  # are the same!

> foo %>% function    # Inconsistent

In this exercise, you will test the above functions on the forecasts equivalent to what you produced in the previous exercise (fcgoog obtained after applying naive() to goog, and fcbeer obtained after applying snaive() to ausbeer).

This exercise is part of the course

Forecasting in R

Exercise instructions

Using the above pipe function, run checkresiduals() on a forecast equivalent to fcgoog.
Based on this Ljung-Box test results, do the residuals resemble white noise? Assign googwn to either TRUE or FALSE.
Using a similar pipe function, run checkresiduals() on a forecast equivalent to fcbeer.
Based on this Ljung-Box test results, do the residuals resemble white noise? Assign beerwn to either TRUE or FALSE.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Check the residuals from the naive forecasts applied to the goog series
goog %>% naive() %>% ___

# Do they look like white noise (TRUE or FALSE)
googwn <- ___

# Check the residuals from the seasonal naive forecasts applied to the ausbeer series
___

# Do they look like white noise (TRUE or FALSE)
beerwn <- ___

Edit and Run Code

This exercise is part of the course

Forecasting in R

IntermediateSkill Level

4.9+

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The first thing to do in any data analysis task is to plot the data. Graphs enable many features of the data to be visualized, including patterns, unusual observations, and changes over time. The features that are seen in plots of the data must then be incorporated, as far as possible, into the forecasting methods to be used.

Exercise 1: Welcome to Forecasting Using R Exercise 2: Creating time series objects in R Exercise 3: Time series plots Exercise 4: Seasonal plots Exercise 5: Trends, seasonality, and cyclicity Exercise 6: Autocorrelation of non-seasonal time series Exercise 7: Autocorrelation of seasonal and cyclic time series Exercise 8: Match the ACF to the time series Exercise 9: White noise Exercise 10: Stock prices and white noise

In this chapter, you will learn general tools that are useful for many different forecasting situations. It will describe some methods for benchmark forecasting, methods for checking whether a forecasting method has adequately utilized the available information, and methods for measuring forecast accuracy. Each of the tools discussed in this chapter will be used repeatedly in subsequent chapters as you develop and explore a range of forecasting methods.

Exercise 1: Forecasts and potential futures Exercise 2: Naive forecasting methods Exercise 3: Fitted values and residuals Exercise 4: Checking time series residuals

Current Exercise

Exercise 5: Training and test sets Exercise 6: Evaluating forecast accuracy of non-seasonal methods Exercise 7: Evaluating forecast accuracy of seasonal methods Exercise 8: Do I have a good forecasting model?Exercise 9: Time series cross-validation Exercise 10: Using tsCV() for time series cross-validation

Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation, the higher the associated weight. This framework generates reliable forecasts quickly and for a wide range of time series, which is a great advantage and of major importance to applications in business.

Exercise 1: Exponentially weighted forecasts Exercise 2: Simple exponential smoothing Exercise 3: SES vs naive Exercise 4: Exponential smoothing methods with trend Exercise 5: Holt's trend methods Exercise 6: Exponential smoothing methods with trend and seasonality Exercise 7: Holt-Winters with monthly data Exercise 8: Holt-Winters method with daily data Exercise 9: State space models for exponential smoothing Exercise 10: Automatic forecasting with exponential smoothing Exercise 11: ETS vs seasonal naive Exercise 12: Match the models to the time series Exercise 13: When does ETS fail?

ARIMA models provide another approach to time series forecasting. Exponential smoothing and ARIMA models are the two most widely-used approaches to time series forecasting, and provide complementary approaches to the problem. While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data.

Exercise 1: Transformations for variance stabilization Exercise 2: Box-Cox transformations for time series Exercise 3: Non-seasonal differencing for stationarity Exercise 4: Seasonal differencing for stationarity Exercise 5: ARIMA models Exercise 6: Automatic ARIMA models for non-seasonal time series Exercise 7: Forecasting with ARIMA models Exercise 8: Comparing auto.arima() and ets() on non-seasonal data Exercise 9: Seasonal ARIMA models Exercise 10: Automatic ARIMA models for seasonal time series Exercise 11: Exploring auto.arima() options Exercise 12: Comparing auto.arima() and ets() on seasonal data

The time series models in the previous chapters work well for many time series, but they are often not good for weekly or hourly data, and they do not allow for the inclusion of other information such as the effects of holidays, competitor activity, changes in the law, etc. In this chapter, you will look at some methods that handle more complicated seasonality, and you consider how to extend ARIMA models in order to allow other information to be included in the them.

Exercise 1: Dynamic regression Exercise 2: Forecasting sales allowing for advertising expenditure Exercise 3: Forecasting electricity demand Exercise 4: Dynamic harmonic regression Exercise 5: Forecasting weekly data Exercise 6: Harmonic regression for multiple seasonality Exercise 7: Forecasting call bookings Exercise 8: TBATS models Exercise 9: TBATS models for electricity demand Exercise 10: Your future in forecasting!