Week 1: Pendahuluan dan Metode Sederhana
- About Cross-section Data
- About Time Series Data
- Pooled Data
- Definition: Stochastic Process
- About Time Series Components
- Definition: Autocovariance and Autocorrelation
- Definition: Weakly Stationary
- Definition: Strictly Stationary
- Theorem: Strict stationary implies weak stationary
- Naive method
- Averaging method
- Smoothing methods
- Single Moving Average (SMA)
- Double Moving Average (DMA)
- Single Exponential Smoothing (SES)
- Double Exponential Smoothing (Holt’s Linear Trend)
- Holt-Winter Seasonal Method
- Procedure: Selecting a model using data splitting
- Accuracy Measures (MAD, MSD, MAPE)
- Definition: Univariate vs Multivariate Models
- Procedure: Building models with the Box-Jenkins strategy
Week 2: Konsep Dasar dan Sifat Proses Stokastik
- Example: Economic and Natural Time Series Examples
- Definition: Lag
- Definition: White Noise
- Definition: Moving Average Process (Stochastic)
- Definition: Random Walk
- Definition: Stochastic vs Deterministic Trend
- Definition: Linear and Quadratic Deterministic Trends
- Procedure: Estimating Constant Mean
- Accuracy Measures (MAD, MSE, MAPE, MPE)
Week 3: Metode Regresi dan Model AR(1)
- Procedure: Least Squares for Linear Trend Estimation
- Procedure: Least Squares for Quadratic Trend Estimation
- Definition: Seasonal Average Model
- Definition: Sample Autocorrelation (ACF)
- About: Correlogram
- Definition: General Linear Process
- Property: Stationarity Condition for General Linear Process
- Definition: Autoregressive (AR) Process Definition
- Definition: AR(1) Process Model
- Property: Stationarity Condition for AR(1)
- Property: ACF of AR(1)
- Definition: Backshift Operator (B)
- Definition: AR Characteristic Equation
Week 4: Model AR(p), MA(q), dan ARMA(p,q)
- Definition: AR(p) Process Model
- Property: Stationarity Condition for AR(p)
- Property: Yule-Walker Equations for AR(p)
- Property: Variance of AR(p)
- Definition: Moving Average Process (MA(q))
- Definition: MA(1) Process Model
- Property: Bounds of MA(1) Autocorrelation
- Property: Non-uniqueness of MA(1) Model
- Property: Invertibility Condition for MA(1)
Week 5: Model ARIMA dan Non-Stasioneritas
- About: Rationale for Non-Stationary Models
- Example: Explosive AR(1) Process
- Procedure: Differencing to Achieve Stationarity
- Definition: ARIMA(p,d,q) Model Definition
- Definition: ARIMA(p,1,q) Formulation
- Property: Characteristic Polynomial of ARIMA(p,1,q)
Week 6: Model IMA, ARI, dan Transformasi Data
- Definition: IMA(d,q) Model
- Definition: ARI(p,d) Model
- Definition: IMA(1,1) Model
- Definition: IMA(2,2) Model
- Definition: ARI(1,1) Model
- Procedure: Determining Weights for ARI(1,1)
- Definition: Constant Term in ARIMA Models
- Procedure: Log Transformation for Variance Stabilization
- Procedure: Percentage Changes Transformation
Week 7: Uji Stasioneritas dan Spesifikasi Model
Uji Stasioneritas
- Procedure: Visual Stationarity Test
- Definition: Bartlett’s Test for ACF
- Definition: Box-Pierce Test
- Definition: Ljung-Box Test
- About: Box-Pierce vs Ljung-Box Comparison
- Definition: Dickey-Fuller Test
- Definition: Augmented Dickey-Fuller Test
Spesifikasi Model
- Procedure: Visual Stationarity Test
- Definition: Bartlett’s Test for ACF
- Definition: Box-Pierce Test
- Definition: Ljung-Box Test
- About: Box-Pierce vs Ljung-Box Comparison
- Definition: Dickey-Fuller Test
- Definition: Augmented Dickey-Fuller Test
- Definition: Partial Autocorrelation (PACF)
- PACF
- Definition: Extended ACF (EACF)
- Definition: AIC Criterion
- Definition: BIC Criterion
Week 9: Parameter Estimation
Method of Moments
Noise Variance Estimation
Least Square Method
- Definition: Conditional Sum of Squares Function
- Procedure: Conditional Least Squares
- About: Least Square Method
Maximum Likelihood Method
- Definition: Unconditional Sum-of-Squares Function
- Procedure: Unconditional Least Squares
- About: Maximum Likelihood Method
Properties of the Estimates
Week 11
Same material as Week 9 Parameter Estimation
Week 12: Model Volatilitas (ARCH dan GARCH)
- About: Volatility Clustering
- About: Leverage Effect
- About: Principle of Parsimony in Econometric Modeling
- GARCH Relationship
- Definition: Log-Returns
- Definition: Continuously Compounded Return
- Definition: Conditional Variance
- Definition: ARCH(m) Model
- Definition: GARCH(m,s) Model
- Definition: Standardized Residuals
- Procedure: Building a Volatility Model
- Procedure: Testing for ARCH Effects
- GARCH
- GARCH
- Procedure: Forecasting with ARCH(m)
- Procedure: Forecasting with GARCH(m,s)
Week 13: Forecasting
- Definition: Minimum Mean Square Error Forecast
- Property: Deterministic Trends Forecast
- Procedure: ARIMA Forecasting
- Property: Prediction Limits
- Procedure: Updating ARIMA Forecasts
- Procedure: Forecasting Transformed Series