Time Series in Economics and Finance

Contents
Chapter 1: Introduction
Part I: Subject of Time Series
	Chapter 2: Random Processes
		2.1 Random Processes as Models for Time Series
		2.2 Specific Problems of Time Series Analysis
			2.2.1 Problems of Economic and Financial Data Observed in Time
				2.2.1.1 Problems Due to Choice of Observation Time Points
				2.2.1.2 Problems Due to Calendar
				2.2.1.3 Problems Due to Length of Time Series
			2.2.2 Methodological Problems
				2.2.2.1 Decomposition of Time Series
				2.2.2.2 Box-Jenkins Methodology
				2.2.2.3 Analysis of Multivariate Time Series
				2.2.2.4 Spectral Analysis of Time Series
				2.2.2.5 Special Methods of Time Series Analysis
			2.2.3 Problems with Construction of Predictions
				2.2.3.1 Point Prediction and Interval Prediction
				2.2.3.2 Quantitative Prediction and Qualitative Prediction
				2.2.3.3 Prediction in Structural Model and Prediction in Time Series Model
				2.2.3.4 In-Sample Prediction and Out-of-Sample Prediction
				2.2.3.5 Single-Prediction and Multi-prediction
				2.2.3.6 Static Prediction and Dynamic Prediction
				2.2.3.7 Measures of Prediction Accuracy
				2.2.3.8 Prediction Combinations
		2.3 Random Processes with Discrete States in Discrete Time
			2.3.1 Binary Process
			2.3.2 Random Walk
			2.3.3 Branching Process
			2.3.4 Markov Chain
		2.4 Random Processes with Discrete States in Continuous Time
			2.4.1 Poisson Process
			2.4.2 Markov Process
		2.5 Random Processes with Continuous States in Continuous Time
			2.5.1 Goniometric Function with Random Amplitude and Phase
			2.5.2 Wiener Process
		2.6 Exercises
Part II: Decomposition of Economic Time Series
	Chapter 3: Trend
		3.1 Trend in Time Series
			3.1.1 Subjective Methods of Elimination of Trend
			3.1.2 Trend Modeling by Mathematical Curves
				3.1.2.1 Linear Trend
				3.1.2.2 Exponential Trend
				3.1.2.3 Modified Exponential Trend
				3.1.2.4 Logistic Trend
				3.1.2.5 Gompertz Trend
				3.1.2.6 Splines
		3.2 Method of Moving Averages
			3.2.1 Construction of Moving Averages by Local Polynomial Fitting
			3.2.2 Other Types of Moving Averages
				3.2.2.1 Arithmetic Moving Averages
				3.2.2.2 Centered Moving Averages
				3.2.2.3 Robust Moving Averages
		3.3 Exponential Smoothing
			3.3.1 Simple Exponential Smoothing
			3.3.2 Double Exponential Smoothing
			3.3.3 Holt´s Method
		3.4 Exercises
	Chapter 4: Seasonality and Periodicity
		4.1 Seasonality in Time Series
			4.1.1 Simple Approaches to Seasonality
				4.1.1.1 Additive Decomposition
				4.1.1.2 Multiplicative Decomposition
			4.1.2 Regression Approaches to Seasonality
				4.1.2.1 Seasonality Modeled by Dummies
				4.1.2.2 Seasonality Modeled by Goniometric Functions
			4.1.3 Holt-Winters´ Method
				4.1.3.1 Additive Holt-Winters´ Method
				4.1.3.2 Multiplicative Holt-Winters´ Method
			4.1.4 Schlicht´s Method
		4.2 Tests of Periodicity
		4.3 Transformations of Time Series
			4.3.1 Box-Cox Transformation
			4.3.2 Transformation Based on Differencing
		4.4 Exercises
	Chapter 5: Residual Component
		5.1 Tests of Randomness
			5.1.1 Test Based on Signs of Differences
			5.1.2 Test Based on Turning Points
			5.1.3 Test Based on Kendall Rank Correlation Coefficient τ
			5.1.4 Test Based on Spearman Rank Correlation Coefficient ρ
			5.1.5 Test Based on Numbers of Runs Above and Below Median
		5.2 Exercises
Part III: Autocorrelation Methods for Univariate Time Series
	Chapter 6: Box-Jenkins Methodology
		6.1 Autocorrelation Properties of Time Series
			6.1.1 Stationarity
			6.1.2 Autocovariance and Autocorrelation Function
			6.1.3 Estimated Autocovariance and Autocorrelation Function
			6.1.4 Partial Autocorrelation Function and Its Estimate
		6.2 Basic Processes of Box-Jenkins Methodology
			6.2.1 Linear Process
			6.2.2 Moving Average Process MA
			6.2.3 Autoregressive Process AR
			6.2.4 Mixed Process ARMA
		6.3 Construction of Models by Box-Jenkins Methodology
			6.3.1 Identification of Model
				6.3.1.1 Identification Based on Autocorrelation and Partial Autocorrelation Function
				6.3.1.2 Identification Based on Information Criteria
			6.3.2 Estimation of Model
			6.3.3 Verification of Model
				6.3.3.1 Check of Stationarity
				6.3.3.2 Check of ARMA Structure
				6.3.3.3 Graphical Examination of Estimated White Noise
				6.3.3.4 Tests of Uncorrelatedness for Estimated White Noise
		6.4 Stochastic Modeling of Trend
			6.4.1 Tests of Unit Root
				6.4.1.1 Dickey-Fuller Test
				6.4.1.2 Augmented Dickey-Fuller Test
				6.4.1.3 Phillips-Perron Test
				6.4.1.4 KPSS Test
			6.4.2 Process ARIMA
		6.5 Stochastic Modeling of Seasonality
		6.6 Predictions in Box-Jenkins Methodology
		6.7 Long Memory Process
		6.8 Exercises
	Chapter 7: Autocorrelation Methods in Regression Models
		7.1 Dynamic Regression Model
		7.2 Linear Regression Model with Autocorrelated Residuals
			7.2.1 Durbin-Watson Test
			7.2.2 Breusch-Godfrey Test
			7.2.3 Construction of Linear Regression Model with ARMA Residuals
		7.3 Distributed Lag Model
			7.3.1 Geometric Distributed Lag Model
			7.3.2 Polynomial Distributed Lag Model
		7.4 Autoregressive Distributed Lag Model
			7.4.1 Intervention Analysis
			7.4.2 Outliers
		7.5 Exercises
Part IV: Financial Time Series
	Chapter 8: Volatility of Financial Time Series
		8.1 Characteristic Features of Financial Time Series
		8.2 Classification of Nonlinear Models of Financial Time Series
		8.3 Volatility Modeling
			8.3.1 Historical Volatility and EWMA Models
			8.3.2 Implied Volatility
			8.3.3 Autoregressive Models of Volatility
			8.3.4 ARCH Models
				8.3.4.1 Identification of Order of Model ARCH
				8.3.4.2 Estimation of Model ARCH
				8.3.4.3 Verification of Model ARCH
				8.3.4.4 Prediction of Volatility in Model ARCH
			8.3.5 GARCH Models
			8.3.6 Various Modifications of GARCH Models
				8.3.6.1 IGARCH
				8.3.6.2 GJR GARCH
				8.3.6.3 EGARCH
				8.3.6.4 GARCH-M
				8.3.6.5 Models of Stochastic Volatility SV
		8.4 Exercises
	Chapter 9: Other Methods for Financial Time Series
		9.1 Models Nonlinear in Mean Value
			9.1.1 Bilinear Models
			9.1.2 Threshold Models SETAR
			9.1.3 Asymmetric Moving Average Models
			9.1.4 Autoregressive Models with Random Coefficients RCA
			9.1.5 Double Stochastic Models
			9.1.6 Switching Regimes Models MSW
		9.2 Further Models for Financial Time Series
			9.2.1 Nonparametric Models
			9.2.2 Neural Networks
		9.3 Tests of Linearity
		9.4 Duration Modeling
		9.5 Exercises
	Chapter 10: Models of Development of Financial Assets
		10.1 Financial Modeling in Continuous Time
			10.1.1 Diffusion Process
			10.1.2 Ito´s Lemma and Stochastic Integral
			10.1.3 Exponential Wiener Process
		10.2 Black-Scholes Formula
		10.3 Modeling of Term Structure of Interest Rates
		10.4 Exercises
	Chapter 11: Value at Risk
		11.1 Financial Risk Measures
			11.1.1 VaR
			11.1.2 Other Risk Measures
		11.2 Calculation of VaR
		11.3 Extreme Value Theory
			11.3.1 Block Maxima
			11.3.2 Threshold Excesses
		11.4 Exercises
Part V: Multivariate Time Series
	Chapter 12: Methods for Multivariate Time Series
		12.1 Generalization of Methods for Univariate Time Series
		12.2 Vector Autoregression VAR
		12.3 Tests of Causality
		12.4 Impulse Response and Variance Decomposition
		12.5 Cointegration and EC Models
		12.6 Exercises
	Chapter 13: Multivariate Volatility Modeling
		13.1 Multivariate Models EWMA
		13.2 Implied Mutual Volatility
		13.3 Multivariate GARCH Models
			13.3.1 Models of Conditional Covariance Matrix
			13.3.2 Models of Conditional Variances and Correlations
			13.3.3 Factor Models
			13.3.4 Estimation of Multivariate GARCH Models
		13.4 Conditional Value at Risk
		13.5 Exercises
	Chapter 14: State Space Models of Time Series
		14.1 Kalman Filter
			14.1.1 Recursive Estimation of Multivariate GARCH Models
		14.2 State Space Model Approach to Exponential Smoothing
		14.3 Exercises
References
Index