Introduction to Linear Time series Analysis
Tran Vu Duc
Department of Mathematics
Hoa Sen University
Tran Vu Duc (HSU)
Time Series Analysis
13/03/2014
1 / 66
Outline
1
Linear Time Series Analysis
Definition
Stationarity
Autocorrelation Function - ACF
Part
Astrostats 2013 Lecture 2
Bayesian time series analysis and stochastic processes
C.A.L. Bailer-Jones
Max Planck Institute for Astronomy, Heidelberg
http:/www.mpia.de/~calj/
Last updated: 2013-06-17 22:20
Contents
1 Key points
2
2 Introduction
3
3 Sinusoid
Time Series Analysis of Aviation
Data
Dr. Richard Xie
February, 2012
What is a Time Series
A time series is a sequence of observations in
chorological order, such as
Daily closing price of stock MSFT in the past ten
years
Weekly unemployment claims in
Using Statistical Data to Make Decisions
Module 6: Introduction to Time Series Forecasting
Titus Awokuse and Tom Ilvento,
University of Delaware, College of Agriculture and Natural Resources,
Food and Resource Economics
The last module examined the multip
Chapter 22
Page 1
Time Series and Forecasting
A time series is a sequence of observations of a random variable. Hence, it is a stochastic
process. Examples include the monthly demand for a product, the annual freshman
enrollment in a department of a unive
Compositional Time Series Analysis: A Review
Aguilar Zuil, Luca
Universidad de Extremadura, Dept. de Matem
aticas, Escuela Politecnica
Avda. de la Universidad s/n
10071 C
aceres, Spain
E-mail: [email protected]
Barcelo-Vidal, Carles
Universitat de Girona, Dep
TIME SERIES ANALYSIS
A time series is a sequence of data indexed by time, often comprising uniformly spaced
observations. It is formed by collecting data over a long range of time at a regular time interval
(data points should be at the same interval on t
SOME BASICS OF TIME-SERIES ANALYSIS
John E. Floyd
University of Toronto
December 18, 2006
An excellent place to learn about time series analysis is from Walter
Enders textbook.1 For a basic understanding of the subject one should
read pages 211 to page 22
ST221:
Introduction to Probability
Chapter 2 - Axioms of Probability
Seung Jun Shin
Department of Statistics
Korea University
Sample Space and Events
Chapter 2
Sample space is the set of all possible outcomes of an
experiment and denoted by S.
- Sex of a
STAT221: INTRODUCTION TO PROBABILITY THEORY
Solutions to Homework 3
1. The daily demand, D is Binomial (10, 1/3). Let Y denote the number of papers
sold during the day, and b denote the number of papers he purchased.
Consider possible bs.
(i) When b=2,
y
ST221:
Introduction to Probability
Chapter 6 - Jointly Distributed RV (part II)
Seung Jun Shin
Department of Statistics
Korea University
Sum of Indep RVs
Chapter 6
Suppose X and Y are independent continuous RVs having
PDF fX and fY . Then
FX +Y (a) = P(X
ST221:
Introduction to Probability
Chapter 4 - Random Variables (part I)
Seung Jun Shin
Department of Statistics
Korea University
Random Variables
Chapter 4
We are often interested in some function of outcome.
ex) When tossing two dice, we may be interest
ST221:
Introduction to Probability
Chapter 5 - Continuous Random Variables (part II)
Seung Jun Shin
Department of Statistics
Korea University
Exponential Random Variables
Chapter 5
An exponential random variable X has the PDF f (x )
defined as
f (x ) = e
ST221:
Introduction to Probability
Chapter 3 - Conditional Probability and
Independence (part II)
Seung Jun Shin
Department of Statistics
Korea University
Independent Events
Chapter 3
In general, the conditional probability P(E |F ) is
different from the
ST221:
Introduction to Probability
Chapter 5 - Continuous Random Variables (part I)
Seung Jun Shin
Department of Statistics
Korea University
Continuous Random Variable
Chapter 5
A random variable X is said to be continuous or have
a continuous distributio
ST221:
Introduction to Probability
Chapter 3 - Conditional Probability and
Independence (part I)
Seung Jun Shin
Department of Statistics
Korea University
Introduction
Chapter 3
Conditional probability is one of the most important
concept in probability an
STAT221: INTRODUCTION TO PROBABILITY THEORY
Solutions to Homework 5
1. For any nonnegative integers m and n,
P( X = m, Y = n) = (1 p)m p(1 p)n p = (1 p)m+n p2 .
Thus, the joint mass function of X and Y is
(
p( x, y) =
2.
(1 p ) x + y p2
for x, y = 0, 1,
ST221:
Introduction to Probability
Chapter 7 - Expectation and Its Properties
Seung Jun Shin
Department of Statistics
Korea University
Expectation
Chapter 7
Recall that
E (X ) =
X
xp(x ),
for discrete X
x
Z
=
xf (x )dx ,
for continuous X
x
If X and Y have
ST221:
Introduction to Probability
Chapter 6 - Jointly Distributed RV (part I)
Seung Jun Shin
Department of Statistics
Korea University
Joint Distribution Functions
Chapter 6
The joint cumulative probability distribution function
of two random variables X
ST221 - Homework 4
1. The PDF of X, the lifetime of a certain type of electronic device (measured in hours), is given by
f (x) = 10/x2 ,
x > 10
(a) Find P (X > 20).
(b) What is the CDF of X?
(c) What is the probability that of 6 such types of devices, at
ST221:
Introduction to Probability
Chapter 1 - Combinatorial Analysis
Seung Jun Shin
Department of Statistics
Korea University
Introduction
Chpater 1
Counting plays an essential role in computing
probability.
Mathematical theory of counting is formally kn
ST221 - Homework 3
1. A newsboy purchases papers at 10 cents and sells them at 15 cents. However, he is not allowed to return
unsold papers. If his daily demand is a binomial random variable with n = 10 and p = 1/3, approximately
how many papers should he
ST221 - Homework 6
1. The time that it takes to service a car is an exponential random variable with rate 1.
(a) If A.J. brings his car in at time 0 and M.J. brings her car in at time t, what is the probability that M.J.s
care is ready before A.J.s care?
STAT221: INTRODUCTION TO PROBABILITY THEORY
Solutions to Homework 4
1.
(a)
(b)
(c)
R
10
= 1/2
dx = x10 ]20
20 x2
R y 10
F (y) = 10 x2 dx = 1 10
y, y >
6 i
i
6
= 1 73/36
6i=3 ( i )( 23 ) ( 13 )
10
since F (15) = 15 .
10. F (y) = o f or y < 10.
= 1 0.10013
ST221 - Homework 1
1. Give an analytic proof of
n
n1
n1
=
+
,
r
r1
r
1 r n.
2. Provide a combinatorial argument to prove
X
r
n+m
n
m
=
.
r
i
ri
i=0
Hint: Consider a group of n men and m women. How many groups of size r are possible?
3. Using the bin
ST221:
Introduction to Probability
Chapter 4 - Random Variables (part II)
Seung Jun Shin
Department of Statistics
Korea University
Poisson Random Variable
Chapter 4
A random variable X cfw_0, 1, 2, is said to be a
Poisson Random Variable with parameter >
STAT221: INTRODUCTION TO PROBABILITY THEORY
Solutions to Homework 6
1.
1 t
e .
2
(b) 1 3e2 .
(a)
2. Let X denote Jills score and let Y be Jacks score. Also, let Z denote a standard
normal random variable.
(a)
P (Y > X ) = P (Y X > 0 )
= P(Y X > 0.5)
"
#
Y
ST221 - Homework 2
1. Suppose that an insurance company classifies people into one of three classes: good risks, average risks, and
bad risks. The companys records indicate that the probabilities that good-, average-, and bad-risk persons
will be involved
STAT221: INTRODUCTION TO PROBABILITY THEORY
Solutions to Homework 2
1. Choose a person at random
Pcfw_they have accident = Pcfw_ acc. | good Pcfw_ g + Pcfw_ acc. | ave. Pcfw_ ave.
+ Pcfw_ acc. | badP(b)
= (.05)(.2) + (.15)(.5) + (.30)(.3) = .175
.95(2)
Pc