Time Series Analysis and Forecasting with ADAM
Preface
What is ADAM?
1
Introduction
2
A short introduction to main statistical ideas
2.1
Properties of estimators
2.1.1
Bias
2.1.2
Efficiency
2.1.3
Consistency
2.1.4
Asymptotic normality
2.1.5
Asymptotics and Likelihood
2.1.6
Law of Large Numbers and Central Limit Theorem
2.2
Typical assumptions of statistical models
2.2.1
Model is correctly specified
2.2.2
The expectation of residuals is zero, no matter what
2.2.3
Residuals are i.i.d.
2.2.4
The explanatory variables are not correlated with anything but the response variable
2.2.5
The variable follows the specified distribution
2.3
Theory of distributions
2.3.1
Normal distribution
2.3.2
Laplace distribution
2.3.3
S distribution
2.3.4
Generalised Normal distribution
2.3.5
Asymmetric Laplace distribution
2.3.6
Log Normal, Log Laplace, Log S and Log GN distributions
2.3.7
Inverse Gaussian distribution
2.4
Model selection mechanism
2.4.1
Information criteria idea
2.4.2
Calculating number of parameters in models
3
Forecasting process and forecasts evaluation
3.1
Measuring accuracy of point forecasts
3.2
Measuring uncertainty
3.3
Rolling origin
3.4
Statistical tests
4
From time series components to ETS
4.1
Time series components
4.2
Classical Seasonal Decomposition
4.2.1
How to do?
4.2.2
A couple of examples
4.2.3
Other techniques and "Why bother?"
4.3
ETS taxonomy
4.4
Mathematical models in the ETS taxonomy
5
Conventional Exponential Smoothing
5.1
Simple Exponential Smoothing
5.1.1
Examples of application
5.1.2
Why "exponential"?
5.1.3
Error correction form of SES
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)
5.4
ETS assumptions, estimation and selection
5.5
State space form of ETS
5.6
Parameters bounds
6
ADAM: Pure additive ETS
6.1
Model formulation
6.2
Recursive relation
6.3
Conditional expectation and variance
6.3.1
Example with ETS(A,N,N)
6.4
Stability and forecastability conditions
6.4.1
Example with ETS(A,N,N)
6.4.2
Comming back to the general case
6.5
Distributional assumptions in pure additive ETS
6.6
Examples of application
6.6.1
Non-seasonal data
6.6.2
Seasonal data
7
ADAM: Pure multiplicative ETS
7.1
Recursive relation
7.2
The problem with moments in pure multiplicative ADAM ETS
7.3
Smoothing parameters bounds
7.4
Distributional assumptions in pure multiplicative ETS
7.5
Examples of application
References
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Time Series Analysis and Forecasting with ADAM
7.5
Examples of application