Time Series
Analysis

Deterministic
Models


Models

Components of TS

Stationary Stochastic
Processes

Models

Correlation Functions

ARMA Models

Non-Stationary
Stochastic Processes

ARIMA Models

Unit Root Tests

Non-stationary and Trends

Seasonal ARIMA

Additive Model

Multiplicative Model

Cyclical Component

Long-Term Component

Forecasting/Extrapolation

Deterministic Models

Linear Models

Non-Linear Models

Smoothing Techniques

Moving Averages

Structure

Choice of Order

Exponential
Weighted Moving Average

Centered

Holt-Winter's Two
Parameter

Hodrick-Prescott Filter

Pros/Cons

Calculation from
Long Term Component

Seasonal Component

Multiplicative Model

Trigonometric Function (FYI)

"Elimination" Procedure

Regression with dummy variables

Introduction

Definition Stochastic Process

Stationary vs Non-Stationary

Implications of Stationarity
for estimation

Non-Stationary Process Transformation

Autocorrelation Function

AR with lag k

Introduction

Wolds Decomposition Theorem

Autoregressive Model

AR(p)

AR(1)

Wold Descomposition

Random walk with drift

First-Order Difference Equiation

Gaussian AR(1)

AR(2)

Covariance and ACF

Sample vs Population models

Partial Autocorrelation Function

Population PACF

Linear Projection

Introduction

Sample PACF

Estimation mth PACF

Introduction

ARMA(1,1)

ACF

Sample vs Population

PACF

Estimation

Least Square

Maximum Likelihood

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Standard Approach

Alternative:
Joint Density=f(conditional density)

Exact ML of AR(1)

Hessian Matrix

Conditional ML

vs Exact

AR(p)

MA(q)

ARMA(p,q)

AR(2) and OLS

Introduction

(Gaussian) White Noise

Moving Average

MA(q)

MA(2)

MA(1)

Diagnostic Checking

Residuals: ACF of Residuals

Misspecification

Joint test of (P)ACF

Model Selection

Box and Pierce

Box and Ljung

Aikake's Information Criterion

Bayesian Information Criterion

Forecasting

Optimal Forecast

AR(1)

MA(1)

Finite Sample Prediction and Invertibility

MA(1)

ARMA(1,1)

ARMA(p,q)

Forecast Intervals

Prediction Interval

PRediction with Estimated Parameters

General Solution

Definition and Implications

Lag Operator

MA

ARMA

AR

Inverse of Lag Operator polynomial

Condition for Stationarity

Unit Root

Definitions and Implications

Trend-Stationary (TS)

Difference-Stationary (DS)

Logarithmic Transformation

Stationary vs non-stationary AR(1)

Wold Decomposition

Comparison of Forecasts

Predictions of Intervals

Unit Root processes (DS models)

Stationarity and ACF

Detecting Non-stationarity

AR model

Testing for unit roots for simple AR(1)

Testing for unit roots for simple AR(p)

ARMA Model

Dickey Fuller Test

Augmented Dickey Fuller Test

Uncentered

Unsymmetric

Centered

MA as filter technique

Adaptive Forecasting