Department of Statistics #### ST-303 Stochastic Practicals

In this course we will be studying some practicals from Stochastic Processes #### Statistical Methods for Bio-Computing

It is the first course on application of statistics to biological sequence data. It is developed via algorithmic approach. ST O23 - Advanced Time Series Analysis

1.   Spectral Analysis of Stationary Time Series

Fourier analysis, Fourier representation of periodic and non-periodic series, Discrete Fourier Transforms, Spectral theory of stationary processes, Spectrum of common processes, Estimation of the spectral density and spectrum, Examples & data analysis

(10 L + 2 Lab)

2.   Time Series Models for Non-Gaussian and Count Data

Non Gaussian Time Series Models, Estimation, Properties, Applications

Thinning-based approach, POINAR models, INAR, INARMA models, Categorical time-series models, Estimation of parameters and Forecasting, Mode of the predictive distribution, Models which do not require thinning.  Examples & Data Analysis

(8 L + 2 Lab)

3. State-Space Models

State-space models, State-space representations, local-trend model, The basic structural model, State-space representation of ARIMA models, Filtering and smoothing, The Kalman recursions, Estimation for State-Space models, Generalized state-space models, Parameter & observation driven models, Non-Gaussian state-space models, CAPM with time varying parameters, Examples & data analysis

(8      L + 2 Lab)

4.   Non-Stationarity, Granger Causality and Co-integration

Test for stationarity and unit roots, DF, ADF, PP and KPSS tests, Granger causality, Cointegration and ECM, Cointegrating VAR, Cointegration tests, Applications to the purchasing power parity (PPP), Other Applications. Examples & Data analysis

(10 L + 2 Lab)

5.   Quantile Methods in Time Series

Introduction to Quantile Regression, Quantile Autoregression, Issues in Quantile Autoregression

(4 L + 1 Lab)

6.   Some Advanced Topics in Time Series

Estimating Functions in Time Series, Bootstrapping in Time Series, Long Memory Time Series Models, Examples & Data Analysis

(8 L + 3 Lab)

Reference Books/Papers:

1.      Bera, A. K., Bilias, Y., Simlai, P. (2006). Estimating functions and equations: An essay on historical developments with applications to econometrics. In: Mills, T. C., Patterson, K., eds. Palgrave Handbook of Econometrics. Vol. 1. NSW: Palgrave MacMillan, pp. 427–476

2.       Brockwell, P.J. and Davis, R. A. (2003). Introduction to Time Series Analysis, Springer

3.      Chandra, S. A. and Taniguchi, M. (2001). Estimation functions for nonlinear time series model, Annals of Institute of Statistical Mathematics, Vol. 53, 125-141.

4.      Commandeur, J. J. F. and Koopman, S. J. (2007). An Introduction to State Space Time Series Analysis, Oxford University Press

5.      Fuller, W. A. (1996). Introduction to Statistical Time Series, 2nd Ed. Wiley.

6.      Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis, Springer

7.      Palma, W. (2007). Long-Memory Time Series: Theory & Methods, Wiley.

8.      Peters, G. W. (2018). General Quantile Time Series Regressions for Applications in Population Demographics. Risks, 6, 97; doi:10.3390/risks6030097

9.      Rajarshi, M. B. (2012). Statistical Inference for Discrete Time Stochastic Processes, Springer.

10.  Roger Koenker & Zhijie Xiao (2006) Quantile Autoregression, Journal of the American Statistical Association, 101:475, 980-990, DOI: 10.1198/016214506000000672

11.  Shimizu, K. (2010). Bootstrapping Stationary ARMA-GARCH Models, Vieweg+Teubner

12.  Shumway, R. H. and Stoffer, D. S. (2010). Time Series Analysis & Its Applications, Springer.

13.  Thavaneswaran, A., Abraham, B. (1988). Estimation for non-linear time series models using estimating equations. Journal of Time Series Analysis 9:99–108.

14.  Tsay, R. S. (2010). Analysis of Financial Time Series, Third Edition, Wiley, New York.

15.  Weiss, C., H. (2018). An Introduction to Discrete-Valued Time Series, Wiley.