Time Series Analysis and Forecasting with ADAM
Preface
What is ADAM?
1
Introduction
2
Forecasting process and forecasts evaluation
2.1
Measuring accuracy of point forecasts
2.2
Measuring uncertainty
2.3
Rolling origin
2.4
Statistical tests
3
A short introduction to main statistical ideas
3.1
Properties of estimators
3.1.1
Bias
3.1.2
Efficiency
3.1.3
Consistency
3.1.4
Asymptotic normality
3.1.5
Asymptotics and Likelihood
3.2
Typical assumptions of statistical models
3.2.1
Model is correctly specified
3.2.2
The expectation of residuals is zero, no matter what
3.2.3
Residuals are i.i.d.
3.2.4
The explanatory variables are not correlated with anything but the response variable
3.2.5
The variable follows the specified distribution
3.3
Theory of distributions
3.3.1
Normal distribution
3.3.2
Laplace distribution
3.3.3
S distribution
3.3.4
Generalised Normal distribution
3.3.5
Asymmetric Laplace distribution
3.3.6
Log Normal, Log Laplace, Log S and Log GN distributions
3.3.7
Inverse Gaussian distribution
3.4
Model selection mechanism
3.4.1
Information criteria idea
3.4.2
Calculating number of parameters in models
4
Time series decomposition and ETS taxonomy
4.1
Time series components
4.2
Classical Seasonal Decomposition
4.3
ETS taxonomy
5
Exponential smoothing methods and their connection to ETS
5.1
Simple Exponential Smoothing
5.2
SES and ETS
5.2.1
ETS(A,N,N)
5.2.2
ETS(M,N,N)
5.3
Sevaral examples of exponential smoothing methods and ETS
5.3.1
ETS(A,A,N)
5.3.2
ETS(A,Ad,N)
5.3.3
ETS(A,A,M)
6
Conventional ETS model
6.1
Models in the ETS taxonomy
6.2
ETS assumptions, estimation and selection
6.3
State space form of ETS
7
ADAM: Pure additive ETS
7.1
General formulation of pure additive ETS
7.2
Local level model, ETS(A,N,N)
8
ADAM: Pure multiplicative ETS
8.1
Local level model, ETS(M,N,N)
References
Published with bookdown
Time Series Analysis and Forecasting with ADAM
Chapter 7
ADAM: Pure additive ETS