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Topics for Time Series
- Second-order, Strict, Autocovariance sequence, Gaussianity, Toeplitz covariance matrix, Positive semidefiniteness, Lag, Examples of discrete stationary processes, Harmonic with random amplitude, Generalized autoregressive conditionally heteroscedastic , Autoregressive conditionally heteroscedastic , Autoregressive-moving average , Autoregressive (AR), Moving average (MA), White noise.
- Trend removal and seasonal adjustment, Seasonal adjustment, Differencing, Residuals, The general linear process, z-polynomial, Directionality and reversibility, Invertibility, Stationarity, Spectral representation, Classification of spectra, Spectral density function (sdf), Integrated spectrum, Linear filtering, Sampling and aliasing, Determination of sdfs via linear filtering, Impulse response.
- Frequency response function, gain and phase, Estimation of mean and autocovariance, Sample mean, Ces`, Ergodic property, aro summability, consistency, ‘Biased’ and ‘unbiased’ autocovariance estimators, A naive spectral estimator — the periodogram, Mean as convolution of true spectrum with F´, Derivation, ejer’s kernel, Sidelobe leakage, Parametric model fitting, autoregressive processes, Bias reduction by tapering, Forward, backward and forward/backward least squares, Tapering, Yule-Walker method, Bivariate time series.
- Magnitude squared coherence, Cross-spectra, Cross-covariances, Forecasting, Bivariate autoregressive processes, Forecasting errors and updating, AR, ARMA and MA examples, economic and financial time series, asset returns, Basic models, white noise, random walk, Stationary time series, Autocovariance and autocorrelation functions, Linear Prediction, Yule-Walker equations
- Estimation of autocorrelation and partial autocorrelation functions, Models for stationary time series , autoregressive (AR) models, moving average (MA) models, autoregressive moving average (ARMA) models, Seasonal ARMA models, Properties, estimation and model building, Diagnostic checking, Non-stationary time series, Non-stationarity in variance , logarithmic and power transformations
- Non-stationarity in mean. Determinisitic trends, Integrated time series, ARIMA and seasonal ARIMA models, Modelling seasonality and trend with ARIMA models, Filtering, exponential smoothing, seasonal adjustments, Non-linear models , threshold AR, bilinear models, Cointegration, Multivariate time series, Stationarity, autocorrelation and crosscorrelation, Multivariate autoregressive model, Markov property, Representation of univariate autoregressive models in Markov form, Model based forecasting, ARMA and ARIMA, Conditionally heteroskedastic models , ARCH-type models, Volatility forecasting, Regime switching models.