• Preface
  • 1 Chapter 1: Time Series Fundamentals
    • 1.1 Definition
    • 1.2 White Noise: purely random process
    • 1.3 Random Walk: random but dependent
    • 1.4 Time Series Modelling
      • 1.4.1 Log Transformation
      • 1.4.2 Box-Cox Transformation
    • 1.5 Time Series Properties
      • 1.5.1 Mean function (if mean is constant)
      • 1.5.2 Variance function (if variance is constant)
      • 1.5.3 Autocovariance function (ACVF):
      • 1.5.4 Autocorrelation function (ACF):
      • 1.5.5 Properties
    • 1.6 Stationarity
  • 2 Chapter 1 Lab
    • 2.1 White Noise (WN)
    • 2.2 Random Walk (RW)
    • 2.3 Stationary
      • 2.3.1 Examples: CPI Data
    • 2.4 ACF to Time Series Plot
  • 3 Chapter 2: Modelling trends and seasonal patterns
    • 3.1 Method 1: Regression
      • 3.1.1 Examples
      • 3.1.2 Other common models
    • 3.2 Method 2: Moving Average Smoothing
    • 3.3 Method 3: Differencing
      • 3.3.1 Remove Trends
      • 3.3.2 Remove Seasonality
    • 3.4 Choosing a smoothing parameter
      • 3.4.1 Simplicity
      • 3.4.2 Objective criteria (AIC & BIC)
  • 4 Chapter 2 Lab
    • 4.1 Model choice and Residual analysis
    • 4.2 Data Example: Annual Varve Series
  • 5 Chapter 3: Autoregressive processes
    • 5.1 Definition
    • 5.2 First order Autoregressive process
      • 5.2.1 Mean
      • 5.2.2 Variance
      • 5.2.3 Examples
    • 5.3 \(AR(p)\) process
      • 5.3.1 Mean
      • 5.3.2 Stationarity
      • 5.3.3 Variance
      • 5.3.4 Autocorrelation Function
    • 5.4 When and how to use AR(p) model
      • 5.4.1 Definition of PACF
  • 6 Chapter 3 Lab
    • 6.1 Autoregressive model (AR)
    • 6.2 Chicken Price
    • 6.3 Chicken price
    • 6.4 Unemployment
  • 7 Chapter 4: Moving Average processes
    • 7.1 Definition
    • 7.2 Mean and Variance
    • 7.3 Autocorrelation functions
      • 7.3.1 Examples:
      • 7.3.2 Another example
    • 7.4 Invertibility
      • 7.4.1 Inveritibility Theorem
    • 7.5 MA Model Identification
      • 7.5.1 Example
    • 7.6 MA parameter estimation
    • 7.7 MA Example
  • 8 Chapter 4 Lab
    • 8.1 Moving Average model (MA)
  • 9 Chapter 5: More general time series processes
    • 9.1 ARMA model
      • 9.1.1 Mean of ARMA(p,q) process
      • 9.1.2 Variance and autocorrelation function
      • 9.1.3 Stationarity and Invertibility
      • 9.1.4 ARMA model identification
      • 9.1.5 ARMA parameter estimation
      • 9.1.6 ARMA simulation example
    • 9.2 ARIMA model
      • 9.2.1 Definition
      • 9.2.2 ARIMA model identification
      • 9.2.3 Example 1
      • 9.2.4 Example 2
  • 10 Chapter 5 Lab
    • 10.1 Oil Return
    • 10.2 Air Passengers
    • 10.3 Birth Rate
  • 11 Chapter 6: Forecasting
    • 11.1 General problem
    • 11.2 Regression
      • 11.2.1 Example 1
      • 11.2.2 Example 2
      • 11.2.3 Example 3
    • 11.3 Exponential smoothing
      • 11.3.1 Definition
      • 11.3.2 Choosing \(\alpha\)
      • 11.3.3 Measure uncertainty
    • 11.4 Forecasting from AR(p) models
      • 11.4.1 AR(1) forecasting
      • 11.4.2 AR(p) forecasting
      • 11.4.3 Example 1: Simulated data
      • 11.4.4 Example 2
      • 11.4.5 Example 3
    • 11.5 Forecasting from MA(q) models
      • 11.5.1 MA(1) forecast
      • 11.5.2 MA(q) forecasts
    • 11.6 Forecasting time series with trend, seasonality and correlation
      • 11.6.1 Example
  • 12 Chapter 6 Lab
    • 12.1 Forecasting with ARIMA
    • 12.2 Global Temp data
    • 12.3 Exponential smoothing
  • References

Time Series

References

Time Series Fundamentals https://bookdown.org/gary_a_napier/time_series_lecture_notes/ChapterOne.html