Chapter 5 (The forecaster’s toolbox)

Question 1

Mean method

Answer 1

Forecasts of all future values are equal to the average of the historical data

• often not preferred

Question 2

Naïve method

Answer 2

All forecasts to be the value of the last observation

• use when no trend, no seasonality

Question 3

Seasonal naïve method

Answer 3

Each forecast to be equal to the last observed value from the same season

• use when seasonality is strong

Question 4

Drift method

Answer 4

amount of change over time (called the drift) is set to be the average change

drawing a line between first and last observations, and extrapolating it

• use when there is trend

Question 5

Why have the 4 simple forecasting methods?

Answer 5

Any forecasting methods that are developed will be compared to these simple methods to ensure new method is better than them

if not, new method is not worth considering

Question 6

Fitted values

Answer 6

Predicted values for the outcome variable

forecasts that uses previous observations

Question 7

Residuals

Answer 7

difference between the observations and the corresponding fitted/predicted values

Question 8

Residual diagnostics

Answer 8

uz-cn

good forecasting method will yield innovation residuals with the following properties:
1. innovation residuals are uncorrelated
2. innovation residuals have zero mean

useful (but not necessary) for the residuals to also have the following two properties:
3. innovation residuals have constant variance
4. innovation residuals are normally distributed
- these impact prediction intervals

Question 9

Portmanteau tests (Ljung-Box test) for autocorrelation

Answer 9

If p-value greater than 0.05 –> accept hypothesis of white noise
- white noise present, ideal

If p-value less than 0.05 –> reject hypothesis of white noise
- autocorrelation present, not ideal

Question 10

Prediction intervals

Answer 10

an interval within which we expect yt to lie with a specified probability

1.96 for 95%
1.28 for 80%

Question 11

accuracy of forecasts

Answer 11

determined by considering how well a model performs on new data that were not used when fitting the model

Question 12

Forecast errors

Answer 12

difference between an observed value and its forecast

• residuals are calculated on the training set while forecast errors are calculated on the test set
• residuals are based on one-step forecasts while forecast errors can involve multi-step forecasts

Question 13

RMSE

Answer 13

Root Mean Square Error

Minimising the RMSE will lead to forecasts of the mean

Question 14

Time series cross-validation

Answer 14

uses several training and testing sets at different points to achieve a possible forecast

training and testing uses known data, thus will perform slightly better