2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 2, Hilbert Spaces
1.
2.
3.
4.
5.
6.
7.
Inner-product spaces
Hilbert spaces
Projection theorem
Orthonormal sets
Projection in
Linear regression and general linear model
Me
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 1, Stationary Time Series
Examples of time series
Stochastic processes
Stationarity and strict stationarity
Estimation and elimination of trend and seasonal
components
Aut
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
1.
2.
3.
4.
Causal and invertible ARMA processes
Moving average processes of infinite order
Computing ACVF of an ARMA(p, q) process
Partial autocorrelation function
Chapter 3, Sta
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 5, Prediction of Stationary
Processes
1. Prediction equations in the time domain
2. Recursive methods for computing best linear
predictors
3. Recursive prediction of an AR
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 9, Model Building and Forecasting
with ARIMA Processes
1.
2.
3.
4.
5.
6.
ARIMA models for nonstationary time series
Identification techniques
Order selection
Diagnostic ch
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 4, Spectral Representation of a
Stationary Process
1. Complex-valued stationary time series
2. Spectral distribution of a linear combination of
sinusoids
3. Herglotz's the
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
1. Estimation of
2. Estimation of
and
Chapter 7, Estimation of Mean and ACVF
3
1. Estimation of
A natural estimator of
4
Properties of
is the sample mean
=
1
.
is unbiased.
If
is
2
Outline
STATISTICS G6503: STATISTICAL INFERENCE
AND TIME SERIES MODELLING
Chapter 8, Estimation for ARMA Models
1. Yule-Walker equations and parameter estimation
for AR processes
2. Preliminary estimation for AR processes using
Durbin-Levinson algorithm