Indicative Module Content:
The Detailed Syllabus:
• Introduction and basic concepts
Expected value and variance of a time series.
Autocovariance and autocorrelation (sample and theoretical).
Stationarity: weak and strict.
Backshift operator.
• Box-Jenkins Modelling: ARIMA Models
ARIMA models
Polynomials in B and root of the equations
Yule-Walker equations
Solving recurrent difference equations
• Model Identification
The sample autocorrelation function (ACF)
Convergence of the sample ACF
ACF of ARIMA models
Partial autocorrelation function (PACF)
Durbin-Levinson equations
PACF of ARIMA models
Overdifferencing
• Model Estimation
ARIMA model with drift or trend
Estimating the trend.
Estimation of centered ARIMA
Method of moments
Least squares
Maximum likelihood estimation
• Model Bootstrapping
Bootstrapping for ARIMA models
• Diagnostics
Residuals
qq-plot of residuals
Shapiro-Wilk test
ACF and Ljung-Box-Pierce tests
• Forecasting
Conditional expectations
Minimum mean square error forecast
Forecasting error
Confidence intervals
• Time Series Decomposition
Components of a time series
Seasonality and trend
Estimate the trend and seasonality
Moving average
Additive decomposition
Multiplicative decomposition
• Non-stationary Time Series
Difference-stationary series
Trend-stationary series
Dickey-Fuller unit root tests
Augmented Dickey-Fuller test (ADF)
• Heteroscedasticity
Heteroskedasticity versus Homoskedasticity
McLeod-Li test to check cluster volatility for ARMA
Autoregressive Conditionally Heteroscedastic models (ARCH)
Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH)
ARMA-GARCH Models
• Spurious Regressions
Cross-Correlation function (CCF)
Sample cross-correlation function
Causes of spurious regressions
Whitening (prewhitening)
How to recognize spurious correlations?
• Multivariate Time Series
Vector AutoRegressive (VAR) models
Companion Form of VAR models
Stability for VAR model
Cointegrated time series
Error Correction Model (ECM)
Engle-Granger method