Introduction to
STAT 3301/6002 Time Series
Analysis
Guodong Li
Assistant Professor
Department of Statistics & Actuarial Science
University of Hong Kong
Instructor and tutors
Guodong Li (Instructor)
Office: MW 502H; Tel: 2859 1986;
Email: gdli@hku.hk;
Offi
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2303 Probability Modelling & STAT2803 Stochastic Models
Assignment 2
(Due date: October 28, 2011)
11/12
1. Suppose that Zt = 5 + 2t + Xt , where cfw_Xt is a zero-mean stationa
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
11/12
STAT3301/6002 Time Series Analysis
Assignment 1
(Due date: October 7, 2011)
1. Let Z be a random variable with mean and variance 2 , and let Zt = Z for all t.
Show that Zt i
1
Fitting the Seasonal ARIMA Model to
The Airline Passenger Data
0. The data
The airline passenger data records the number of passengers traveling by air per month from
January, 1949 to December, 1960.
It is given as Series G in Box and Jenkins (1976), an
Using ARIMA Procedure to
Analyze a Real Data
Identification (Part I)
0. Simulate an AR(2) time series data
The model: Z(t)=0.5*Z(t-1)+0.4Z(t-2)+a(t)
The SAS program:
/* Create a new library */
libname ts 'D:/TimeSeries';
/* Simulate an AR(2) process */
da
STAT3301/6002 Time Series Analysis
Example Class 7
Example 1: How to use Time Series Forecasting System in SAS.
1. Get into Time Series Forecasting System
Solutions -> Analysis -> Time Series Forecasting System
2. Specify the Input Data Set
Browse (On the
Using ARIMA Procedure to Analyze a Real Data
(Part II)
3. Estimate the models
Candidate models: AR(3), ARMA(3,1) with AR coefficient at lag 2 suppressed and ARIMA(2,1,0)
without intercept.
The SAS program:
/* Identify some suitable models with minimum r
STAT3301/6002 Time Series Analysis
Tutorial 10: Model Diagnostic Checking and Forecasting
Review:
The steps of structuring a time series model:
Step1Model Specication
Tool:
(1) The graph of the raw data
If there exist obvious deterministic trend or period
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT3301/6002 Time Series Analysis
Solution of Example Class 9
1
Examples
Example1: Consider an MA(1) model for which it is known that the process mean is
zero. Based on a series o
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
11/12
STAT3301/6002 Time Series Analysis
Assignment 3
(Due date: November 22, 2011)
1. Consider the stationary MA(1) process Zt = (1 B)at , where | < 1. If we take the
rst dierenci
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT3301/6002 Time Series Analysis
Assignment 4
(Due date: December 6, 2011)
11/12
1. Consider the time series cfw_Zt in Additional exercise 2 in Chapter 5 with sample size
n = 10
Time Series Analysis with R Part I
Walter Zucchini, Oleg Nenadi c
Contents
1 Getting started 1.1 Downloading and Installing R . . . . . . . . . . . . . . . . . . . . 1.2 Data Preparation and Import in R . . . . . . . . . . . . . . . . . 1.3 Basic Rcommand
Quick Review about How to Use SAS to
Analyze Time Series Data
1. Get to know SAS
How to Start SAS?
If you use computer in this laboratory, please start SAS from Desktop or Start/programs.
You can use the SAS software at the laboratory of the Computer cent
Simulating AR, MA, and ARMA Time Series
R : Copyright 2003, The R Development Core Team
Version 1.7.1 (2003-06-16)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type `license()' or `
Content of this course
Part I. Linear time series models
Part II. How to fit linear time series models
Chapter 1. Some fundamental concepts;
Chapter 2. Stationary linear time series models;
Chapter 3. Non-stationary linear time series models.
Chapter 4. M
STAT3301/6002 TIME SERIES ANALYSIS
Department of Statistics & Actuarial Science
University of Hong Kong
(First Semester, 2011-2012)
Instructor:
Dr. Guodong Li
Office: Meng Wah Complex 502H; Email: gdli@hku.hk; Tel: 2859 1986
Tutors:
Mr. Yuan Li (liyuan@hk
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
11/12
STAT3301/6002 Time Series Analysis
Project
(Due date: November 30, 2010)
Find a time series with sample size n > 100, and delete the last 5 values for the sake of
comparison
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THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT3301/6002 Time Series Analysis
Example Class 9: Model Estimation and Forecasting
1
Key Points
1.1
Tool: CLSE, MLE, ULSE
(1) Understand the basic idea of each estimation method;
STAT 3301/6002 Time Series Analysis
Tutorial 8: Model Specication
1. SACFBartletts formula for MA(q)
Note that if cfw_Zt is a M A(q) process, then k = 0 for k > q, the SACF ,
1
rk N (0, n (1 + 2 q 2 ).
j=1 j
Suppose we are given a series of data, we have
STAT3301/4601/6002 Time Series Analysis
Example Class 3 Solution
MA(q) and AR(p) Models
1. A moving average process of order q, and abbreviated as MA(q), is dened as:
Zt = 0 + at 1 at1 2 at2 . . . q atq ,
2
where q 0 is an integer and cfw_at W N (0, a ).
STAT3301/4601/6002 Time Series Analysis
Example Class 2
Stationarity
1. Strict stationarity: A time series cfw_Zt is said to be strictly stationary if the joint
distribution of Zt1 , Zt2 , . . . , Ztn is the same as that of Zt1 k , Zt2 k , . . . , Ztn k