Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian
Time Series Modelling and Forecasting
by
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:
Box, George E. P., Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung. (2015). Time Series Analysis, Forecasting and Control, Wiley.
Brockwell, P.J. and R.A. Davis, (2009). Time Series: Theory and Methods (Second Edition), Springer-Verlag.
Chatfield, C. (1975). The Analysis of Time Series: Theory and Practice Springer-Verlag.
Cowpertwait, Paul S.P and Andrew V. Metcalfe (2008). Introductory Time Series with R, Springer
Cryer, Jonathan D. Kung-Sik Chan (2008). Time Series Analysis: With Applications in R, Springer Texts in Statistics.
Granger, C.W.J. and M. Hatanka, (1964). Spectral Analysis of Economic Time Series, Princeton Univ. Press, N.J.
Kirchgassner, G. and J. Wolters, (2007). Introduction to Modern Time Series Analysis, Springer.
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 |