TIME SERIES ANALYSIS
CE 78505

Course Objectives:
To enhance the students understanding and the possibilities and limitation of different types of time series models through lectures and practical model application.

1. Introduction(2 hours)

Stochastic processes and time series, Time series modeling, Physical basis of time series modeling in hydrology, Applicability

2. Characteristics of Hydrologic Series(2 hours)

Type of hydrologic series, General properties of hydrologic time series

3. Statistical Principles and Techniques for Time Series Modeling(8 hours)

Probability function and distribution function, Derived distributions, Chebyshev's Inequality, moment generating function, normal distribution, Central limit theorem, Estimation of the parameters of the distribution; Methods of moments, Method of maximum likelihood, selection of distribution

4. Auto-correlation Analysis(8 hours)

Classification of time series, Components of time series, Method of investigation, estimation of the auto-correlation coefficient, Correlogram of an independent process

5. Time Series Models(12 hours)

Moving average process, Auto regressive process, Goodness of fit for annual AR models; Test on the assumptions of the model, Comparison of the historical and model correlograms, Test of Parsimony of parameters, Generation and forecasting using annual AR models; Thomas-fiering model; Auto regressive moving average process, application in flood forecasting system, Auto-regressive integrated moving average process,

6. Seasonal Models(8 hours)

Univariate seasonal models, Daily flow model, spectral analysis; introduction, Line spectrum

7. Generation of Random Variates(5 hours)

Uniformly distributed random numbers; Mid-square technique, Mid-product technique, Mixed congruential method, testing the random numbers sequence, generation of normal random numbers; The inverse transformation method, the central limit theorem method, Box-muller method

Tutorial:

1. Statistical Principles and Techniques(2 hours)
2. Auto Correlation Analysis(4 hours)
3. AR models, Thomas Fiering Models(5 hours)
4. ARMA, ARIMA(2 hours)
5. Generation of Random Variates(2 hours)

Practical:

1. Non seasonal modeling of River system of Nepal
2. Daily flow modeling of River System of Nepal

References:

1. P. Jayarami Reddy, 'Stochastic Hydrology', Laxmi Publications, New Delhi
2. Salas, Delleur, Yevjwich and Lane, "Applied Modelling of Hydrologic Time Series', Water Resources Publications, Colorado, USA

Evaluation Scheme:
The questions will cover all the chapters in the syllabus. The evaluation scheme will be as indicated in the table below:

Chapter	Hours	Marks Distribution*
1	2	8
2	2	8
3	8	12
4	8	12
5	12	20
6	8	12
7	5	8
Total	45	80

*There could be minor deviation in mark distribution.