# 1 - 2 Model ﬁtting(or parameter estimation 3 Model...

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NOTES 1 Introduction : What is a time series? Previous Statistics courses focus on independent data. For example, 5 crops from diﬀerent farms are studied to determine the mean yield μ . The crop yields X 1 ,X 2 ,X 3 ,X 4 ,X 5 can be viewed as independent. Summary statistics ¯ X, S 2 can be used to make inferences about μ . Now we may have the following situation: A plant is weighed each week, for T weeks. Put X t = weight at the end of t th week. Then { X 1 ,X 2 ,...,X T } are dependent (corre- lated). Problems of interest : 1. Estimating μ t = mean weight at time t . 2. Forecast future size X T + t , given data { X 1 ,X 2 ,...,X T } . Examples of Time Series : 1. Annual Sales 2. Unemployment 3. Temperature 4. Hang Seng index Model-Building Strategy : 1. Model speciﬁcation (or identiﬁcation)
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Unformatted text preview: 2. Model ﬁtting (or parameter estimation) 3. Model diagnostics (or residual analysis) Remark: Principle of parsimony Statistical Package to be used : SPlus. Some good features of SPlus: (1) Easy to use; (2) High quality graphical outputs (3) Built in statistical analysis. In the beginning, we need to know how to do: 1. Import data into SPlus 2. Make simple plots 3. Do linear (simple and multiple) regression 4. Handle output (obtain relevant material only) 5. How to get help Remark : The students are expected to be familiar with the basics properties of the expectation, variance, covariance and correlation. 1...
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