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STA621 : Time Series Analysis

Course Overview

Course Synopsis

Time Series consist of values of a variable recorded in an order over a period of time Such data arise in just about every area of science and the humanities, including econometric and finance, engineering, medicine, genetics, sociology, environmental science. What makes time series data special is the presence of dependence between observations in a series, and the fact that usually only one observation is made at any given point in time. This means that standard statistical methods are not appropriate, and special methods for statistical analysis are needed. This course provides an introduction to time series analysis using current methodology and software.

Course Learning Outcomes

At the end of the course, you should be able to understand:

  • Demonstrate the understanding of the concepts of time series and their application
  • Demonstrate familiarity with a range of examples for the different topics covered in the course.
  • Apply ideas to real time series data and interpret outcomes of analyses.

Course Calendar

1 Introduction to time series analysis
2 Various types of time series: Examples
3 Objectives of time series analysi
4 Explanatory versus time series forecasting
5 Least squares estimation
6 Least squares estimation: Example (Non-functional form)
7 Discovering and describing existing relationships
8 Discovering and describing existing relationships: Example (Functional form)
9 Descriptive Statistics: Univariate
10 Descriptive Statistics: Univariate: Example
11 Descriptive Statistics: Bivariate
12 Descriptive Statistics: Bivariate: Example

13 Descriptive Statistics: Time series dependent structure
14 Descriptive Statistics: Time series dependent structure: Example
15 The Accuracy of forecasting methods
16 Accuracy measures- Standard statistical measures
17 Accuracy measures- Standard statistical measures: Example
18 Accuracy measures- Relative statistical measures
19 Accuracy measures- Relative statistical measures: Example
20 Accuracy measures-Theil's U statistic 1
21 Accuracy measures-Theil's U statistic 2
22 Introduction to Smoothing methods-The forecast scenario
23 Smoothing methods appraisal and their classification
24 Time series data patterns
25 Averaging methods and the Mean method

26 Averaging methods: Example (The Mean)
27 Single Moving Averages
28 Single Moving Averages: Example
29 Double (Linear) Moving Averages 1
30 Double (Linear) Moving Averages 2
31 Double (Linear) Moving Averages 3
32 Double (Linear) Moving Averages: Example 1
33 Double (Linear) Moving Averages: Example 2
34 Exponential Smoothing methods and Simple Exponential Smoothing
35 Simple Exponential Smoothing: Example
36 Adaptive Rate Exponential Smoothing 1
37 Adaptive Rate Exponential Smoothing 2
38 Adaptive Rate Exponential Smoothing 3
39 Adaptive Rate Exponential Smoothing: Example 1
40 Adaptive Rate Exponential Smoothing: Example 2
Quiz no.1
41 Adaptive Rate Exponential Smoothing: Example 3

42 Brown's Linear Method based on Single and Double exponential smoothing 1
43 Brown's Linear Method based on Single and Double exponential smoothing 2
44 Brown's Linear Method based on Single and Double exponential smoothing 3
45 Brown's Linear Method based on Single and Double exponential smoothing-Example 1
46 Brown's Linear Method based on Single and Double exponential smoothing-Example 2
47 Brown's Linear Method based on Single and Double exponential smoothing-Example 3
48 Components of time series
49 Decomposition
50 Trend Fitting
51 Trend Fitting-Example 1
52 Trend Fitting-Example 2
53 The Ratio-to-Moving Averages method
54 The Ratio-to-Moving Averages method-Example 1
55 The Ratio-to-Moving Averages method-Example 2
56 Seasonal indices
57 Seasonal indices-Example 1

58 Seasonal indices-Example 2
59 Forecasting using the components
60 Forecasting using the components-Example
61 Introduction to Box-Jenkins approach
62 Stationary time series
63 Transformations
64 The Correlogram
65 The Correlogram-Examples
66 Handling real data
67 Introduction to general linear process
68 Purely random process
69 Relationship between two equivalent forms of linear process
Quiz no.2
70 Autoregressive process: Definition and Model
71 Autoregressive process: Properties (Mean and Variance)
72 Autoregressive process: Properties (Autocovariance and Autocorrelation function) 1

73 Autoregressive process: Properties (Autocovariance and Autocorrelation function) 2
74 Autoregressive process: Yule Walker Equations 1
75 Autoregressive process: Yule Walker Equations 2
76 Stationarity condition of autoregressive process 1
77 Stationarity condition of autoregressive process 2
78 Properties of AR(1) process: Mean and Variance
79 Properties of AR(1) process: Autocovariance Function
80 Properties of AR(1) process: Autocorrelation and Partial Autocorrelation Functions
81 Stationarity condition of AR(1) process
82 Properties of AR(2) process: Mean and Variance
83 Properties of AR(2) process: Autocovariance Function
84 Properties of AR(2) process: Autocorrelation and Partial Autocorrelation Functions
85 Stationarity condition of AR(2) process 1
86 Stationarity condition of AR(2) process 2
87 Importance of Partial Autocorrelation function for an Autoregressive function
88 Behaviour of autocorrelation and partial autocorrelation of autoregressive process
89 Exercises on autoregressive processes 1

90 Exercises on autoregressive processes 2
91 Exercises on autoregressive processes 3
92 Exercises on autoregressive processes 4
93 Exercises on autoregressive processes 5
94 Exercises on autoregressive processes 6
95 Exercises on autoregressive processes 7
Assignment no.1
96 Moving average process: Definition and Model
97 Moving average process: Properties (Mean and Variance)
98 Moving average process: Properties (Autocovariance and Autocorrelation function) 1
99 Moving average process: Properties (Autocovariance and Autocorrelation function) 2
100 Invertibility condition of moving average process 1
101 Invertibility condition of moving average process 2
102 Properties of MA(1) process 1
103 Properties of MA(1) process 2
104 Properties of MA(2) process 1
105 Properties of MA(2) process 2
Mid-Term Exams

106 Exercises of moving average processes 1
107 Exercises of moving average processes 2
108 Exercises of moving average processes 3
109 Exercises of moving average processes 4
110 Exercises of moving average processes 5
111 Exercises of moving average processes 6
112 Duality between moving average and autoregressive processes
113 Behaviour of autocorrelation and partial autocorrelation of moving average process
114 Mixed autoregressive moving average process
115 Mixed autoregressive moving average process-Properties 1
116 Mixed autoregressive moving average process-Properties 2
117 Behaviour of autocorrelation and partial autocorrelation functions of mixed autoregressive moving average process
118 Exercises of mixed autoregressive moving average processes 1
119 Exercises of mixed autoregressive moving average processes 2
120 Exercises of mixed autoregressive moving average processes 3
121 Exercises of mixed autoregressive moving average processes 4
122 Exercises of mixed autoregressive moving average processes 5
123 Exercises of mixed autoregressive moving average processes 6
124 Mixed autoregressive integrated moving average process-Introduction

125 Random walk
126 Unit root test
127 Unit root test: Examples 1
128 Unit root test: Examples 2
129 Box-Jenkins iterative model building procedure
130 Model identification-Objectives
131 Identifying the degree of differencing
132 Identifying the order of moving average and autoregressive components
133 Relationship between estimated and theoretical autocorrelations
134 Standard error of autocorrelation and partial autocorrelation
135 Examples on Model identification
136 More Examples on Model identification
137 Use of Model Selection Criteria for Model Identification
138 Estimation of Model parameters
139 Estimation of moving average parameters- Least squares estimation

140 Iterative Least squares estimation-Challenges
141 Iterative Least squares estimation-Graphical view
142 Initial estimates to start the iterative estimation procedure
143 Estimation of autoregressive parameters-Least squares estimation
144 Least squares estimation of MA(1) process 1
145 Least squares estimation of MA(1) process 2
146 Least squares estimation of AR(1) process 1
147 Least squares estimation of AR(1) process 2
148 Least squares estimation of AR(1) process 3
149 Least squares estimation of AR(2) process 1
150 Least squares estimation of AR(2) process 2
151 Least squares estimation of AR(2) process 3

152 Least squares estimation of AR(p) process
Quiz no.3
153 Estimation of autoregressive parameters-Maximum likelihood estimation
154 Maximum likelihood estimation of AR(1) process 1
155 Maximum likelihood estimation of AR(1) process 2
156 Maximum likelihood estimation of AR(1) process 3
157 Maximum likelihood estimation of AR(2) process 1
158 Maximum likelihood estimation of AR(2) process 2
159 Maximum likelihood estimation of AR(2) process 3
160 Maximum likelihood estimation of AR(2) process 4
161 Maximum likelihood estimation of AR(p) process 1
162 Maximum likelihood estimation of AR(p) process 2
163 Maximum likelihood estimation of AR(p) process 3

164 Maximum likelihood estimation of AR(p) process 4
165 Yule-Walker estimates of autoregressive process
166 Yule-Walker estimates of AR(1) process
167 Yule-Walker estimates of AR(2) process
168 Diagnostic checking of fitted model 1
169 Diagnostic checking of fitted model 2
Quiz no.4
170 Overfitting
171 Overfitting: Example
172 Autocorrelation check
173 Autocorrelation check: Example 1
174 Autocorrelation check: Example 2
175 Box-Pierce test

176 Box-Pierce test: Example
177 Ljung-Box-Pierce test
178 Ljung-Box-Pierce test: Example
179 Monti's test
180 Monti's test: Example
181 Use of residuals to modify the model
182 Minimum mean square error forecasts
183 Three explicit forms for the model
184 Derivation of minimum mean square error forecasts 1
185 Derivation of minimum mean square error forecasts 2
186 Derivation of minimum mean square error forecasts 3
187 Derivation of minimum mean square error forecasts 4
Assignment no.2

188 Three basic forms for the forecast
189 Forecsts from difference equations
190 Forecasts in integrated form
191 Forecasts as a weighted average of previous observations
192 Forecasts: Examples 1
193 Forecasts: Examples 2
194 Forecasts: Examples 3
195 Forecasts: Examples 4
196 Forecasts: Examples 5
197 Forecasts: Examples 6
198 Properties of forecast error 1
199 Properties of forecast error 2

200 Properties of forecast error 3
201 Properties of forecast error 4
202 Probability limits of the forecasts 1
203 Probability limits of the forecasts 2
204 Probability limits of the forecasts 3
205 Probability limits of the forecasts: Examples 1
206 Probability limits of the forecasts: Examples 2
207 Updating forecasts
208 Updating forecasts: Examples 1
209 Updating forecasts: Examples 2
210 Applications to some real life data of Pakistan 1
211 Applications to some real life data of Pakistan 2

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