Chapter 7 (Time series regression models)

Question 1

Linear regression

Answer 1

Linear relationship between forecast variable ‘y’ and predictor variables ‘x’

Question 2

Linear regression assumptions about errors

Answer 2

1. mean zero
2. not autocorrelated
3. unrelated to predictor variables
4. (useful) to have errors normal distributed

Question 3

Least square estimation

Answer 3

finds the best estimates of coefficients

Question 4

Coefficient of determination / R-squared

Answer 4

how well a linear regression model fits the data

Lies between 0 to 1

Question 5

Evaluating the regression model

Answer 5

• ACF plot of residual will likely show autocorrelation, still unbiased but will have larger prediction intervals (and short term forecasts may not be accurate)
• Histogram of residuals are normally distributed
• Residual plots against predictors should not show patterns
• Residual plots against fitted values should show no pattern
• Outliers

Question 6

Use of Fourier terms

Answer 6

Regression model containing Fourier terms is often called harmonic regression

Question 7

Piecewise linear

Answer 7

Introduce knots (points) where slope of f can change