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Time Series Analysis (Stationary Stochastic Processes (Models (ARMA…
Time Series
Analysis
Deterministic
Models
Models
Additive Model
Multiplicative Model
Components of TS
Cyclical Component
Calculation from
Long Term Component
Long-Term Component
Forecasting/Extrapolation
Deterministic Models
Linear Models
Non-Linear Models
Smoothing Techniques
Moving Averages
Structure
Choice of Order
Uncentered
Unsymmetric
Centered
MA as filter technique
Adaptive Forecasting
Exponential
Weighted Moving Average
Centered
Holt-Winter's Two
Parameter
Hodrick-Prescott Filter
Pros/Cons
Seasonal Component
Multiplicative Model
"Elimination" Procedure
Regression with dummy variables
Trigonometric Function (FYI)
Stationary Stochastic
Processes
Models
ARMA Models
Introduction
ARMA(1,1)
ACF
PACF
Sample vs Population
Introduction
Wolds Decomposition Theorem
(Gaussian) White Noise
Autoregressive Model
AR(p)
Covariance and ACF
AR(1)
Wold Descomposition
Random walk with drift
First-Order Difference Equiation
Gaussian AR(1)
AR(2)
Moving Average
MA(q)
MA(2)
MA(1)
Correlation Functions
Autocorrelation Function
AR with lag k
Sample vs Population models
Introduction
Partial Autocorrelation Function
Population PACF
Linear Projection
Introduction
Sample PACF
Estimation mth PACF
AR(2) and OLS
Introduction
Definition Stochastic Process
Stationary vs Non-Stationary
Implications of Stationarity
for estimation
Non-Stationary Process Transformation
Estimation
Least Square
Maximum Likelihood
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)
Diagnostic Checking
Residuals: ACF of Residuals
Misspecification
Joint test of (P)ACF
Box and Pierce
Box and Ljung
Model Selection
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
Non-Stationary
Stochastic Processes
ARIMA Models
Unit Root processes (DS models)
Stationarity and ACF
Unit Root Tests
Detecting Non-stationarity
AR model
Testing for unit roots for simple AR(1)
Dickey Fuller Test
Testing for unit roots for simple AR(p)
Augmented Dickey Fuller Test
ARMA Model
Non-stationary and Trends
Trend-Stationary (TS)
Difference-Stationary (DS)
Logarithmic Transformation
Stationary vs non-stationary AR(1)
Wold Decomposition
Comparison of Forecasts
Predictions of Intervals
Seasonal ARIMA
Definition and Implications
Lag Operator
MA
ARMA
AR
Inverse of Lag Operator polynomial
Condition for Stationarity
Unit Root
Definitions and Implications