homework3 solution - QF5210 FINANCIAL TIME SERIES THEORY...

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QF5210: FINANCIAL TIME SERIES: THEORY AND COMPUTATION Homework Assignment 3: Solution 6 March 2014 Notes: Unless specifically assigned, all tests are based on the 5% significance level ( = 5%). Do not hand in whole computer output. Use copy-and-paste to summarise the output . To hand in before 19 March 2014. You can try your own models to gain further experience, in addition to the specified time series model in some of the problems. 1. Consider the Decile 10 portfolio of CRSP. The monthly simple returns are available in the file m-dec125910-5112.txt. Obtain the log returns of the Decile 10 portfolio. For simplicity, do NOT need to consider outliers in this problem. The solution is not unique. The main objective of this question is to handle the seasonal serial correlation by a dummy variable. (a) The sample ACF cuts at lag 14, implying an MA (14) model. However 13 and 14 are not very important. Then we can consider an MA (12) model, which has 2 less parameters, as an approximation. The PACF cuts at lag 13, so we can also consider an AR (13) model. Here I show the result for an MA (12) model. Initial estimates indicates most of the MA coe ffi cients are not significant so that we simplify the model. The fitted model becomes r t = 0 . 0096 + a t + 0 . 216 a t - 1 + 0 . 113 a t - 12 , σ 2 a = 0 . 00374 . Model checking indicates that the model is adequate. See Figure 1. (b) Using January dummy variable to handle the seasonal serial correlation, we have r t = 0 . 044 + 0 . 0624 J t + a t + 0 . 235 a t - 1 , σ 2 a = 0 . 00347 , where J t = 1 if t is January and zero, otherwise. This model also fits the data well. See Figure 2.
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