• Forecasting: Principles and Practice Book Club
  • Welcome
    • Book club meetings
    • Pace
  • 1 Getting started
    • 1.1 SLIDE 1
    • 1.2 Meeting Videos
      • 1.2.1 Cohort 1
      • 1.2.2 Cohort 2
  • 2 Time series graphics
    • 2.1 SLIDE 1
    • 2.2 Meeting Videos
      • 2.2.1 Cohort 1
      • 2.2.2 Cohort 2
  • 3 Time series decomposition
    • 3.1 Transformations and adjustments
    • 3.2 Time series components
      • 3.2.1 Additive decomposition
      • 3.2.2 Multiplicative decomposition
      • 3.2.3 Example: Employment in the US retail sector
    • 3.3 Classical decompositions
      • 3.3.1 Moving average smoothing
      • 3.3.2 Moving averages of moving averages
      • 3.3.3 Weighted moving averages
      • 3.3.4 Additive decomposition
      • 3.3.5 Multiplicative decomposition
    • 3.4 Methods used by official statistics agencies
      • 3.4.1 X-11 method
      • 3.4.2 The SEATS method
    • 3.5 Exercises
      • 3.5.1 Exercise 5
      • 3.5.2 Exrecise 10
      • 3.5.3 Exrecise 10
    • 3.6 Further reading
    • 3.7 Meeting Videos
      • 3.7.1 Cohort 1
      • 3.7.2 Cohort 2
  • 4 Time series features
    • 4.1 Some simple statistics
      • 4.1.1 Five summary statistics
    • 4.2 ACF features
    • 4.3 STL features
    • 4.4 Other features
    • 4.5 Exploring Australian tourism data
      • 4.5.1 Principal Component Analysis (PCA)
    • 4.6 Meeting Videos
      • 4.6.1 Cohort 1
      • 4.6.2 Cohort 2
  • 5 The forecaster’s toolbox
    • 5.1 EXRCISE 1
      • 5.1.1 Australian Population (global_economy)
      • 5.1.2 Bricks (aus_production)
      • 5.1.3 NSW Lambs (aus_livestock)
      • 5.1.4 Household wealth (hh_budget)
      • 5.1.5 Australian takeaway food turnover (aus_retail)
    • 5.2 Meeting Videos
      • 5.2.1 Cohort 1
      • 5.2.2 Cohort 2
  • 6 Judgmental forecasts
    • 6.1 SLIDE 1
  • 7 Time series regression models
    • 7.1 Linear Regression Model
    • 7.2 US consumption expenditure
    • 7.3 Multiple Linear Regression Model
    • 7.4 Least squares estimation
      • 7.4.1 Example
    • 7.5 Exercises
    • 7.6 Meeting Videos
      • 7.6.1 Cohort 2
  • 8 Exponential smoothing
    • 8.1 Simple Exponential smoothing
    • 8.2 Methods
      • 8.2.1 Trend
    • 8.3 Exercises
      • 8.3.1 Exercise 5
    • 8.4 Meeting Videos
      • 8.4.1 Cohort 2
  • 9 ARIMA models
    • 9.1 Exercise 7
      • 9.1.1 a. Use ARIMA() to find an appropriate ARIMA model. What model was selected.
      • 9.1.2 b. Write the model in terms of the backshift operator.
      • 9.1.3 c. Plot forecasts from an ARIMA(0,1,0) model with drift and compare these to part a.
      • 9.1.4 d. Plot forecasts from an ARIMA(2,1,2) model with drift and compare these to parts a. and c.
      • 9.1.5 e. Plot forecasts from an ARIMA(0,2,1) model with a constant. What happens?
    • 9.2 Exercise 11
      • 9.2.1 Do the data need transforming?
      • 9.2.2 Are the data stationary?
      • 9.2.3 Which of the models is the best according to their AIC values?
      • 9.2.4 Do the residuals resemble white noise?
      • 9.2.5 Compare the forecasts obtained using ETS()
    • 9.3 Meeting Videos
      • 9.3.1 Cohort 2
  • 10 Dynamic regression models
    • 10.1 White Noise and Autocorrelation
    • 10.2 What is the Difference Between ARIMA and ARMA Model?
    • 10.3 Example: US Personal Consumption and Income
    • 10.4 Forecast
    • 10.5 Difference between Stochastic and deterministic trends
    • 10.6 Dynamics
    • 10.7 Impact of a predictor
    • 10.8 Forecast with different levels of TVadverts
    • 10.9 Meeting Videos
      • 10.9.1 Cohort 2
  • 11 Forecasting hierarchical and grouped time series
    • 11.1 SLIDE 1
    • 11.2 Meeting Videos
      • 11.2.1 Cohort 2
  • 12 Advanced forecasting methods
    • 12.1 Complex seasonality
      • 12.1.1 Case Study 1
      • 12.1.2 Case Study 2
    • 12.2 Prophet model
      • 12.2.1 Case Study 3
      • 12.2.2 Case Study 4
    • 12.3 Vector autoregressions (VAR)
      • 12.3.1 Case Study 5
    • 12.4 Neural network models
      • 12.4.1 Case Study 6
    • 12.5 Bootstrapping and bagging
      • 12.5.1 Case Study 7
      • 12.5.2 Bagging = bootstrap aggregating
    • 12.6 Exercises
    • 12.7 Meeting Videos
      • 12.7.1 Cohort 2
  • 13 Some practical forecasting issues
    • 13.1 SLIDE 1
    • 13.2 Meeting Videos
      • 13.2.1 Cohort 2
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Forecasting: Principles and Practice Book Club

10.5 Difference between Stochastic and deterministic trends

\[y_t=\beta_0+\beta_1x+\eta_t\]

  • Deterministic \(\eta_t \sim ARIMA(p,0,q)\)
  • Stochastic \(\eta_t \sim ARIMA(p,1,q)\)
fit_deterministic <- aus_airpassengers |>
  model(deterministic = ARIMA(Passengers ~ 1 + trend() +
                                pdq(d = 0)))

fit_stochastic <- aus_airpassengers |>
  model(stochastic = ARIMA(Passengers ~ pdq(d = 1)))
## Scale for fill_ramp is already present.
## Adding another scale for fill_ramp, which will replace the existing scale.