STAT 4825/5825: Applied Time Series
Seasonal ARIMA Models
Copyright: Nalini Ravishanker, Univ. of Connecticut
Seasonal ARIMA Models
Multiplicative seasonal ARIMA(p, d, q) (P, D, Q)s model:
(B)(B s )(1 B)d (1 B s )D Xt ) = (B)(B s )Wt
(10.1)
where Wt WN(0,
STAT 4825/5825: Applied Time Series
Forecasting ARMA Processes
Copyright: Nalini Ravishanker, Univ. of Connecticut
Forecasting ARMA Processes
Consider a stationary and invertible ARMA(p,q) process
(B)Xt = (B)wt with MA representation given by
Xt =
j=0 j w
STAT 4825/5825: Applied Time Series
Time Series Regression
Copyright: Nalini Ravishanker, Univ. of Connecticut
Deterministic Time Series Regression Methods
We will study the following:
Structural Decomposition
Trend Fitting by Polynomial Trend Models
Tren
STAT 4825/5825: Applied Time Series
Time Series Smoothing Methods
Copyright: Nalini Ravishanker, Univ. of Connecticut
Time Series Smoothing Methods
In tting polynomial trend models, we assume that the parameter
values are constant, and use of least square
STAT 4825/5825: Applied Time Series
Conditional Heteroscedasticity - ARCH/GARCH
Models
Copyright: Nalini Ravishanker, Univ. of Connecticut
Conditional Heteroscedasticity - ARCH/GARCH Models
In some applications (nancial), we are interested not only in the
STAT 4825/5825: Applied Time Series
Stochastic Properties of Time Series
Copyright: Nalini Ravishanker, Univ. of Connecticut
Stationarity, Strict and Weak Stationarity
Stationarity. A time series cfw_Xt , t = 0 1, 2, is stationary if
its statistical prop
STAT 4825/5825: Applied Time Series
Fitting ARIMA Models
Copyright: Nalini Ravishanker, Univ. of Connecticut
Fitting ARIMA Models
There are three broad phases in tting ARIMA models:
Model Identication
Model Estimation
Model Diagnostics - Model Adequacy an
STAT 4825/5825: Applied Time Series
ARIMA Processes
Copyright: Nalini Ravishanker, Univ. of Connecticut
ARIMA Processes
We discuss AR, MA, ARMA and ARIMA models and their
properties
The process cfw_Xt is an AutoRegressive Moving Average process
with AR o
STAT 4825/5825: Applied Time Series
State Space Models
Copyright: Nalini Ravishanker, Univ. of Connecticut
Examples of Time Series
Let yt denote a possibly vector-valued time series.
Goal: model patterns in yt and predict future values.
In some examples,
STAT 4825/5825: Applied Time Series
Vector Time Series
Copyright: Nalini Ravishanker, Univ. of Connecticut
Vector Time Series
Let cfw_Xt , t = 0, 1, 2, and cfw_Yt , t = 0, 1, 2, be two
time series, with respective means x and y respectively.
Joint Stati
STAT 5825 HW4
Heng Yan
Problem 1.
[
( s , t )=E ( x sE [ x s ] )( x t E [ x t ] )
]
E [ ( x su s ) ( x tu t ) ]
E ( x s x t ut x sus xt +us ut )
E ( x s x t )E ( ut x s ) E ( u s x t ) + E ( u s ut )
E ( x s x t )ut E ( x s ) u s E ( x t ) +u s ut
E