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STA621 : Time Series Analysis

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Course Info

Course Category

 Probability & Statistics

Course Level

 Undergraduate

Credit Hours

 3

Pre-requisites

 N/A

Instructor

 Dr.Sohail Chand
Ph.D
University of Nottingham, UK.

Course Contents

Introduction to time series analysis Various types of time series: Examples Objectives of time series analysis Explanatory versus time series forecasting Least squares estimation Least squares estimation: Example (Non-functional form) Discovering and describing existing relationships Discovering and describing existing relationships: Example (Functional form) Descriptive Statistics: Univariate Descriptive Statistics: Univariate: Example Descriptive Statistics: Bivariate Descriptive Statistics: Bivariate: Example Descriptive Statistics: Time series dependent structure Descriptive Statistics: Time series dependent structure: Example The Accuracy of forecasting methods Accuracy measures- Standard statistical measures Accuracy measures- Standard statistical measures: Example Accuracy measures- Relative statistical measures Accuracy measures- Relative statistical measures: Example Accuracy measures-Theil's U statistic Accuracy measures-Theil's U statistic Introduction to Smoothing methods-The foecast scenario Smoothing methods appraisal and their classification Time series data patterns Averaging methods and the Mean method Averaging methods: Example (The Mean) Single Moving Averages Single Moving Averages: Example Double (Linear) Moving Averages Double (Linear) Moving Averages Double (Linear) Moving Averages Double (Linear) Moving Averages: Example Double (Linear) Moving Averages: Example Exponential Smoothing methods and Simple Exponential Smoothing Simple Exponential Smoothing: Example Adaptive Rate Exponential Smoothing Adaptive Rate Exponential Smoothing Adaptive Rate Exponential Smoothing Adaptive Rate Exponential Smoothing: Example Adaptive Rate Exponential Smoothing: Example Adaptive Rate Exponential Smoothing: Example Brown's Linear Method based on Single and Double exponential smoothing Brown's Linear Method based on Single and Double exponential smoothing Brown's Linear Method based on Single and Double exponential smoothing Brown's Linear Method based on Single and Double exponential smoothing-Example Brown's Linear Method based on Single and Double exponential smoothing-Example Brown's Linear Method based on Single and Double exponential smoothing-Example Components of time series Decomposition Trend Fitting Trend Fitting-Example Trend Fitting-Example The Ratio-to-Moving Averages method The Ratio-to-Moving Averages method-Example The Ratio-to-Moving Averages method-Example Seasonal indices Seasonal indices-Example Seasonal indices-Example Forecasting using the components Forecasting using the components-Example Introduction to Box-Jenkins approach Stationary time series Transformations The Correlogram The Correlogram-Examples Handling real data Introduction to general linear process Purely random process Relationship between two equivalent forms of linear process Autoregressive process: Definition and Model Autoregressive process: Properties (Mean and Variance) Autoregressive process: Properties (Autocovariance and Autocorrelation function) Autoregressive process: Properties (Autocovariance and Autocorrelation function) Autoregressive process: Yule Walker Equations Autoregressive process: Yule Walker Equations Stationarity condition of autoregressive process Stationarity condition of autoregressive process Properties of AR(1) process: Mean and Variance Properties of AR(1) process: Autocovariance Function Properties of AR(1) process: Autocorrelation and Partial Autocorrelation Functions Stationarity condition of AR(1) process Properties of AR(2) process: Mean and Variance Properties of AR(2) process: Autocovariance Function Properties of AR(2) process: Autocorrelation and Partial Autocorrelation Functions Stationarity condition of AR(2) process Stationarity conditions of AR(2) process Importance of Partial Autocorrelation function for an Autoregressive function Behaviour of autocorrelation and partial autocorrelation of autoregressive process Exercises on autoregressive processes Exercises on autoregressive processes Exercises on autoregressive processes Exercises on autoregressive processes Exercises on autoregressive processes Exercises on autoregressive processes Exercises on autoregressive processes Moving average process: Definition and Model Moving average process: Properties (Mean and Variance) Moving average process: Properties (Autocovariance and Autocorrelation function) Moving average process: Properties (Autocovariance and Autocorrelation function) Invertibility condition of moving average process Invertibility condition of moving average process Properties of MA(1) process Properties of MA(1) process Properties of MA(2) process Properties of MA(2) process Exercises of moving average processes Exercises of moving average processes Exercises of moving average processes Exercises of moving average processes Exercises of moving average processes Exercises of moving average processes Duality between moving average and autoregressive processes Behaviour of autocorrelation and partial autocorrelation of moving average process Mixed autoregressive moving average process Mixed autoregressive moving average process-Properties Mixed autoregressive moving average process-Properties Behaviour of autocorrelation and partial autocorrelation functions of mixed autoregressive moving average process Exercises of mixed autoregressive moving average processes Exercises of mixed autoregressive moving average processes Exercises of mixed autoregressive moving average processes Exercises of mixed autoregressive moving average processes Exercises of mixed autoregressive moving average processes Exercises of mixed autoregressive moving average processes Mixed autoregressive integrated moving average process-Introduction Random walk Unit root test Unit root test: Examples Unit root test: Examples Box-Jenkins iterative model building procedure Model identification-Objectives Identifying the degree of differencing Identifying the order of moving average and autoregressive components Relationship between estimated and theoretical autocorrelations Standard error of autocorrelation and partial autocorrelation Examples on Model identification More Examples on Model identification Use of Model Selection Criteria for Model Identification Estimation of Model parameters Estimation of moving average parameters- Least squares estimation Iterative Least squares estimation-Challenges Iterative Least squares estimation-Graphical view Initial estimates to start the iterative estimation procedure Estimation of autoregressive parameters-Least squares estimation Least squares estimation of MA(1) process 1 Least squares estimation of MA(1) process 2 Least squares estimation of AR(1) process 1 Least squares estimation of AR(1) process 2 Least squares estimation of AR(1) process 3 Least squares estimation of AR(2) process 1 Least squares estimation of AR(2) process 2 Least squares estimation of AR(2) process 3 Least squares estimation of AR(p) process Estimation of autoregressive parameters-Maximum likelihood estimation Maximum likelihood estimation of AR(1) process 1 Maximum likelihood estimation of AR(1) process 2 Maximum likelihood estimation of AR(1) process 3 aximum likelihood estimation of AR(2) process 1 aximum likelihood estimation of AR(2) process 2 aximum likelihood estimation of AR(2) process 3 aximum likelihood estimation of AR(2) process 4 Maximum likelihood estimation of AR(p) process 1 Maximum likelihood estimation of AR(p) process 2 Maximum likelihood estimation of AR(p) process 3 Maximum likelihood estimation of AR(p) process 4 Yule-Walker estimates of autoregressive process Yule-Walker estimates of AR(1) process Yule-Walker estimates of AR(2) process Diagnostic checking of fitted model 1 Diagnostic checking of fitted model 2 Overfitting Overfitting: Example Autocorrelation check Autocorrelation check: Example 1 Autocorrelation check: Example 2 Box-Pierce test Box-Pierce test: Example Ljung-Box-Pierce test Ljung-Box-Pierce test: Example Monti's test Monti's test: Example Use of residuals to modify the model Minimum mean square error forecasts Three explicit forms for the model Derivation of minimum mean square error forecasts 1 Derivation of minimum mean square error forecasts 2 Derivation of minimum mean square error forecasts 3 Derivation of minimum mean square error forecasts 4 Three basic forms for the forecast Forecsts from difference equations Forecasts in integrated form Forecasts as a weighted average of previous observations Forecasts: Examples 1 Forecasts: Examples 2 Forecasts: Examples 3 Forecasts: Examples 4 Forecasts: Examples 5 Forecasts: Examples 6 Properties of forecast error 1 Properties of forecast error 2 Properties of forecast error 3 Properties of forecast error 4 Probability limits of the forecasts 1 Probability limits of the forecasts 2 Probability limits of the forecasts 3 Probability limits of the forecasts: Examples 1 Probability limits of the forecasts: Examples 2 Updating forecasts Updating forecasts: Examples 1 Updating forecasts: Examples 2 Applications to some real life data of Pakistan 1 Applications to some real life data of Pakistan 1
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