WJWJ Maths
Time Series Analysis
  • Introduction
  • Types of Time Series
  • Objectives of Time Series
  • Descriptive Techniques
  • Stationary Time Series
  • Transformation
  • Auto correlation
  • Stochastic Process
  • Second Order Stationary
  • Random Process
  • Random Walk
  • Moving Average (Ma)
  • Invertibility
  • Autoregressive Process
  • General Order Of an AR Process
  • Mixed Arma Models
  • Integrated Arma
  • Forecasting
  • The Partial Autocorrelation Function
  • Estimation Of Models
  • Fitting an AR Model
  • Fitting an MA Process
  • Box-Jenkins Seasonal (SARIMA) Model
  • Forecasting: (Box-Jenkins Procedure)
  • Computation of Forecast
  • The Frequency Domain
  • The Spectral Density
  • The Periodogram
  • State Space Models And The Kalman Filter
  • The Linear Model
  • The Kalman Filter
  • Nonlinear Models: ARCH And Volatility
  • Practice Problems

Time Series Analysis

Lecture Notes

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\[\rho (\tau ) = \frac {\gamma (\tau )}{\gamma (0)}, \qquad \gamma (\tau ) = \Cov \left (X_t,\,X_{t+\tau }\right )\]

Contents
1 Introduction
1.1 Types of Time Series
1.2 Objectives of Time Series
1.3 Descriptive Techniques
1.4 Stationary Time Series
1.5 Transformation
1.6 Auto correlation
2 Stochastic Process
2.1 Second Order Stationary
3 Random Process
4 Random Walk
5 Moving Average (Ma)
6 Invertibility
7 Autoregressive Process
7.1 General Order Of an AR Process
8 Mixed Arma Models
9 Integrated Arma
10 Forecasting
10.1 The Partial Autocorrelation Function
11 Estimation Of Models
11.1 Fitting an AR Model
11.2 Fitting an MA Process
11.3 Box-Jenkins Seasonal (SARIMA) Model
11.4 Forecasting: (Box-Jenkins Procedure)
11.5 Computation of Forecast
12 The Frequency Domain
12.1 The Spectral Density
12.2 The Periodogram
13 State Space Models And The Kalman Filter
13.1 The Linear Model
13.2 The Kalman Filter
14 Nonlinear Models: ARCH And Volatility
15 Practice Problems