Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur, Kanpur - 208016 (India)

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Time Series Modelling and Forecasting

by

Professor Anoop Chaturvedi

Allahabad University

Swayam Prabha Course

The forty hours course is for the students in Bachelor's and Master's programmes and covers the topics of time series and forecasting.

Suggested books:

1. Box, George E. P., Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung. (2015). Time Series Analysis, Forecasting and Control, Wiley.

2. Brockwell, P.J. and R.A. Davis, (2009). Time Series: Theory and Methods (Second Edition), Springer-Verlag.

3. Chatfield, C. (1975). The Analysis of Time Series: Theory and Practice Springer-Verlag.

4. Cowpertwait, Paul S.P and Andrew V. Metcalfe (2008). Introductory Time Series with R, Springer

5. Cryer, Jonathan D. Kung-Sik Chan (2008). Time Series Analysis: With Applications in R, Springer Texts in Statistics.

6. Granger, C.W.J. and M. Hatanka, (1964). Spectral Analysis of Economic Time Series, Princeton Univ. Press, N.J.

7. Kirchgassner, G. and J. Wolters, (2007). Introduction to Modern Time Series Analysis, Springer.

8. Montgomery, D.C. and L.A. Johnson (1977). Forecasting and Time Series Analysis, McGraw Hill.

Language of the course: English

Duration of the course: 40 Hours

Swayam Prabha DTH Channel 16 Youtube link: The telecasted lectures are available at  YouTube (Click here). 

Slides and Videos used in the lectures: 

Lecture No.	Lecture videos download links	Lecture slides download links	Lecture Title	Brief Description
1	Click here Lecture 1	Click here Lecture 1	Introduction to Time Series	Introduction to time series, its various applications, Outline of the Course
2	Click here Lecture 2	Click here Lecture 2	Matrix Algebra and Regression Model	Some basic results of matrix algebra and regression analysis required for the course
3	Click here Lecture 3	Click here Lecture 3	Components of time series	Decomposition into Various Components, method of free hand curve fitting and method of semi averages for the determination of Secular Trend
4	Click here Lecture 4	Click here Lecture 4	Components of time series	Methods of mathematical curve fitting and method of moving averages for the determination of trend component
5	Click here Lecture 5	Click here Lecture 5	Components of time series	Seasonal plots, Simple Time Series or Run sequence plot, Seasonal plot, Seasonal subseries plot, Multiple box plots, Cyclical component and its graphical presentation
6	Click here Lecture 6	Click here Lecture 6	Components of time series	Methods for the determination of Seasonal Component and Variate Difference Method for estimating variance of irregular variations, Effect of elimination of trend on other components
7	Click here Lecture 7	Click here Lecture 7	Smoothing and Adaptive Forecasting	Exponential Smoothing, Forecasting for Trend processes and seasonal processes, Forecast error detection
8	Click here Lecture 8	Click here Lecture 8	Time series processes	Introduction to Time series processes and Stochastic process, Various descriptive measures, process mean and variance, ACVF and ACF, Partial autocorrelation function (PACF)
9	Click here Lecture 9	Click here Lecture 9	Time series processes	Strongly and weekly Stationary processes
10	Click here Lecture 10	Click here Lecture 10	Time series processes	Ergodicity in time series, Deterministic, purely non-deterministic Processes
11	Click here Lecture 11	Click here Lecture 11	Stationary Processes for Time Series Modelling	Wold Decomposition, General Linear Process, its ACF and other properties
12	Click here Lecture 12	Click here Lecture 12	Stationary Processes for Time Series Modelling	Moving Average Process and its properties, ACF, PACF
13	Click here Lecture 13	Click here Lecture 13	Stationary Processes for Time Series Modelling	Autoregressive Process and its properties, ACF, PACF, Yule-Walker equations
14	Click here Lecture 14	Click here Lecture 14	Stationary Processes for Time Series Modelling	Mixed ARMA processes and their properties, mean, autocovariances, ACF
15	Click here Lecture 15	Click here Lecture 15	Stationary Processes for Time Series Modelling	Stationarity and invertibility conditions for AR, MA and mixed ARMA processes
16	Click here Lecture 16	Click here Lecture 16	Estimation of Parameters	Estimation of parameters of autoregressive processes
17	Click here Lecture 17	Click here Lecture 17	Estimation of Parameters	Estimation of parameters of AR, MA and ARMA processes
18	Click here Lecture 18	Click here Lecture 18	Frequency Domain Analysis	Fourier transformation, Processes in Frequency Domain, Frequency domain analysis and time domain analysis, spectral representation of time series
19	Click here Lecture 19	Click here Lecture 19	Frequency Domain Analysis	Spectral density function, spectral density function of some stationary processes
20	Click here Lecture 20	Click here Lecture 20	Frequency Domain Analysis	Spectrum of filtered processes
21	Click here Lecture 21	Click here Lecture 21	Frequency Domain Analysis	Cross Spectrum for bivariate processes, Spectrum of Sinusoidal Models
22	Click here Lecture 22	Click here Lecture 22	Frequency Domain Analysis	Simple Sinusoidal Model, Periodogram Analysis and estimation of spectral density using Periodogram
23	Click here Lecture 23	Click here Lecture 23	Forecasting with Stationary Processes	Forecasting with stationary or invertible data generating process
24	Click here Lecture 24	Click here Lecture 24	Forecasting with Stationary Processes	Forecasting with AR, MA and ARMA Processes
25	Click here Lecture 25	Click here Lecture 25	Diagnostics Checking	Diagnostics Checking for Stationary Processes, residual analysis, graphical techniques for model validation, Tests of Serial Uncorrelatedness, Q test, tests for randomness, QQ plot
26	Click here Lecture 26	Click here Lecture 26	Non-Stationary and Long Memory Processes	ARIMA Processes, Random Walk, Unit Root Problem, Implications of presence of unit root, Weiner process, Geometric Brownian motion, Unit Root hypothesis and test for unit root
27	Click here Lecture 27	Click here Lecture 27	Nonstationary and Long Memory Processes	Dickey-Fuller test for unit root hypothesis, Augmented Dickey-Fuller (ADF) test for difference stationarity against trend stationarity
28	Click here Lecture 28	Click here Lecture 28	Nonstationary and Long Memory Processes	Phillips-Perron Test for unit root, KPSS Test
29	Click here Lecture 29	Click here Lecture 29	Non-Stationary and Long Memory Processes	Autoregressive Fractionally Integrated Moving Average (ARFIMA) models, ACF, and spectral density function, long memory property of ARFIMA processes, estimation of parameters
30	Click here Lecture 30	Click here Lecture 30	Non-Stationary and Long Memory Processes	Seasonal Autoregressive Integrated Moving Average (SARIMA) Processes
31	Click here Lecture 31	Click here Lecture 31	Multivariate Time Series Processes	Multivariate Time series processes, Moments, Cross Moments and Stationarity, Wold representation,
32	Click here Lecture 32	Click here Lecture 32	Multivariate Time Series Processes	Cross spectrum analysis of bivariate time series processes, cross spectrum, coherency spectrum and squared coherency, amplitude and phase spectrum
33	Click here Lecture 33	Click here Lecture 33	Multivariate Time Series Processes	Estimation of Spectral Density Function: Bivariate Periodogram, Spectral Analysis of Multivariate Processes, Coherency Spectrum,
34	Click here Lecture 34	Click here Lecture 34	Multivariate Time Series Processes	Vector ARMA processes, Stationarity and invertibility conditions, Vector moving average processes, Vector Autoregresive (VAR) Processes, Yule-Walker equations,
35	Click here Lecture 35	Click here Lecture 35	Multivariate Time Series Processes	Forecasting in VARMA processes, Granger Causality, definition and applications, different causal relations
36	Click here Lecture 36	Click here Lecture 36	Multivariate Time Series Processes	Causality Analysis and Causality Tests, Direct Granger Procedure, Haugh-Pierce Test, Hsiao Procedure
37	Click here Lecture 37	Click here Lecture 37	Multivariate Time Series Processes	Error Correction representation, Basic concept of cointegration
38	Click here Lecture 38	Click here Lecture 38	Multivariate Time Series Processes	Cointegration for bivariate time series, Cointegration tests, Engle and Granger two-step procedure for cointegration analysis, Cointegration for general Multivariate Processes, Johansen test
39	Click here Lecture 39	Click here Lecture 39	Stochastic Volatility Models: ARCH, GARCH Processes	Introduction of Stochastic Volatility Models, Autoregressive Conditional Heteroscedastic (ARCH) Models
40	Click here Lecture 40	Click here Lecture 40	Stochastic Volatility Models: ARCH, GARCH Processes	Order determination for ARCH models, Generalized ARCH (GARCH) Models, properties of GARCH models, Forecasting in ARCH and GARCH models