Stochastic Modeling: A Thorough Guide to Evaluate, Pre-Process, Model and Compare Time Series with MATLAB Software

Front cover
Half title
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
Abbreviations
Chapter 1 Introduction
	1.1 Time series
		1.1.1 Time series in environmental epidemiology
		1.1.2 Engineering and sequential data
		1.1.3 Historical data for forecasting future economy
	1.2 Stochastic and stochastic with exogenous variables
		1.2.1 Stochastic models
		1.2.2 Stochastic model structure
		1.2.3 Model classifications
	1.3 Data preprocessing
		1.3.1 Definition of preprocessing
		1.3.2 Relationship between forecasting and time series structure
		1.3.3 Distribution and its impact on time series forecasting
	References
Chapter 2 Preparation & stationarizing
	2.1 Missing data
		2.1.1 Linear interpolation
		2.1.2 Code for linear interpolation
		2.1.3 Spline interpolation
		2.1.4 Code for spline interpolation
		2.1.5 Modified Akima cubic Hermite interpolation
		2.1.6 Code for MAKIMA
	2.2 Detecting outliers
		2.2.1 Grubbs test
		2.2.2 Grubbs test code
		2.2.3 Generalized extreme studentized deviate test
		2.2.4 Generalized Extreme Studentized Deviate test code
		2.2.5 Moving average and moving median
		2.2.6 Moving average and moving median codes
		2.2.7 Quartiles and percentiles
		2.2.8 Quartiles and percentiles codes
	2.3 Time series structure and attributes
		2.3.1 Trend in time series
		2.3.2 Jump in time series
		2.3.3 Period in time series
	2.4 Stationarity
		2.4.1 Unit root tests for stationarity evaluation
		2.4.2 Augmented Dickey–Fuller test
		2.4.3 KPSS test
		2.4.4 Phillips–Perron test
		2.4.5 Complementary adjustments for stationary test functions
	2.5 Deterministic terms detection tests
		2.5.1 Mann–Kendal test
		2.5.2 Mann–Whitney test
		2.5.3 Fisher's g test
		2.5.4 Correlograms
		2.5.5 How to determine the nonseasonal or seasonal correlations and the periodicity in time series by using correlograms?
	2.6 Stationarizing methods
		2.6.1 Trend analysis
		2.6.2 Differencing
		2.6.3 Standardization
		2.6.4 Spectral analysis
	2.7 Exercise
	References
Chapter 3 Distribution evaluation and normalizing
	3.1 Distribution visualization
	3.2 Normal distribution definition
	3.3 Skewness
	3.4 Kurtosis
	3.5 Common tests and transforms
	3.6 Data distribution tests
		3.6.1 Graphical methods
		3.6.2 Skewness and kurtosis
		3.6.3 Anderson–Darling test
		3.6.4 Lillifors test
		3.6.5 Jarque–Bera test
		3.6.6 Shapiro–Wilk test
	3.7 Normalization transforms
		3.7.1 Logarithmic
		3.7.2 Standard logarithmic
		3.7.3 Box–Cox
		3.7.4 Yeo–Johnson
		3.7.5 John–Draper
		3.7.6 Manly
	3.8 Exercise
	References
Chapter 4 Stochastic modeling
	4.1 Modeling methods overview
	4.2 Deterministic models
	4.3 Probabilistic statistical models
	4.4 Stochastic concepts
	4.5 Differencing operators in stochastic models
		4.5.1 Nonseasonal differencing
		4.5.2 Seasonal differencing
	4.6 Stochastic models equations
		4.6.1 General relationships
		4.6.2 Polynomial equations
	4.7 Identify appropriate models and parameters’ orders
	4.8 Estimation of stochastic models’ parameters
	4.9 Univariate stochastic modeling
		4.9.1 Model creation
		4.9.2 Polynomial parameter estimation
		4.9.3 Extracting residuals and modeled series
		4.9.4 Presampling in stochastic models
		4.9.5 Optimization methods in stochastic models
		4.9.6 Forecasting future steps
	4.10 Stochastic models with exogenous inputs
		4.10.1 General relationships
		4.10.2 StochasticX models with initial parameters
	4.11 Fitting stochastic and stochasticX models by econometric modeler app
		4.11.1 Loading data in MATLAB environment and opening econometric modeler
		4.11.2 Using econometric modeler
	4.12 Invertibility constraint for MA models
	4.13 Chapter summary
	4.14 Exercise
	References
Chapter 5 Goodness-of-fit & precision criteria
	5.1 Model adequacy
		5.1.1 Visual tools: residuals ACF and cumulative periodogram
		5.1.2 Numerical tests
	5.2 Model parsimony
		5.2.1 Akaike’s information criterion
		5.2.2 Bayesian information criterion
		5.2.3 Parameters’ significance test
	5.3 Conventional performance measure
	5.4 Cross-validation in time series
		5.4.1 Hold-out method
		5.4.2 Leave-p-out cross-validation
(LPO-CV)
		5.4.3 Leave-one-out cross-validation
(LOO-CV)
		5.4.4 k-fold cross-validation
		5.4.5 Stratified k-fold cross-validation
		5.4.6 Time series cross-validation
	5.5 Exercise
	References
Chapter 6 Forecasting time series by deep learning and hybrid methods
	6.1 Deep learning introduction
		6.1.1 Long-short term memory modeling concepts
		6.1.2 Forecasting time series using long short-term memory model
		6.1.3 Forecast the time series using dynamic long short-term memory model
	6.2 Hybrid modeling
		6.2.1 Hybridization concepts
	6.3 Exercise
	References
Appendix MATLAB introduction and basic commands
	A.1 Introduction
	A.2 How to execute commands in MATLAB
	A.3 Write commands in the Command Window
	A.4 Frequently used commands
	A.5 Using MATLAB’s help
	A.6 Arithmetic operators
	A.7 Commonly used characters, variables, and constants
	A.8 Relational operators
	A.9 Logical operators
	A.10 m Files
	A.11 Functions
	A.12 MATLAB’s predefined functions
		A.12.1 Opening m file of predefined functions
	A.13 Anonymous functions
	A.14 Symbolic function
		A.14.1 double function
		A.14.2 Piecewise function
	A.15 The most common built-in functions
		A.15.1 Import/export functions
		A.15.2 figure function
		A.15.3 plot function
		A.15.4 legend function
		A.15.5 title, xlabel, ylabel functions
		A.15.6 Hold on/off functions
		A.15.7 xlim and ylim functions
		A.15.8 Subplot function
		A.15.9 disp function
		A.15.10 fprintf and sprint functions
		A.15.11 Timeseries function
		A.15.12 iddata function
		A.15.13 Size, length, and numel functions
		A.15.14 if, conditional functions and for, loop function
	A.16 Required ToolBoxes and dependencies
Index
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