Reviews

Ch. 1 Overview

Ch. 2 Fundamental Concepts

Stationary time series

ACV

ACF and its properties.

PACF

White noise and its properties

Estimation of ACV, ACF and PACF

Ch. 3 Stationary Time Series Models

AR model

MA model

ARNA model

AR model + drift

MA model + drift

ARMA model + drift

Conditions for stationarity and invertibility

1

ACF, PACF and their properties

Ch. 4 Non-stationary Time Series Mod-

els

Deterministic trend model

Stochastic trend model

ARIMA model and its ACF and PACF

stationarity and invertibility

Remove the nonstationary components

Ch. 5 Forecasting

MSE forecasting

Best linear predictor

Forecasting error

Forecasting variance

Forecast interval

updating forecasts

ARMA model and ARIMA model

Ch.6 Model identification

Steps for model identification

Ch.7 Parameter estimation, diagnostic

checking and model selection

Yule-Walker estimator

CLSE

ULSE

MLE

Find the Log-likelihood functions for these

estimators

Test whether or not an estimator parame-

ter is zero

Test whether or not the model fitted is

adequate for the data

AIC, BIC and select the best model for

data

Procedure for model building

Ch.8 Seasonal time series model

Feature of seasonal data

Pure seasonal AR model

Pure seasonal MA model

Pure seasonal ARMA and ARIMA model

Seasonal period and seasonal correlation

Conditions for stationarity and invertibility

Remove the nonstationary component

ACF

Procedure for model building

Ch.9 GARCH model

ARCH and GARCH model

Expansion of GARCH(1,1)model

Condition for the model having finite vari-

ance

Testing whether or not the conditional vari-

ance is a constant

Write down the Log-likelihood function

Forecasting interval

Ch.14 Vector time series models

Mean

Covariance matrix and its properties

Vector white noise

Vector AR(1) model

Vector MA(1) model

Vector ARMA(1,1) model

Conditions for stationarity and invertibility

ACF, PACF and their properties.