ECON
ECON301_Handout_12_1213_02

# A cusum and cusumsq tests we may have no strong prior

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A. CUSUM and CUSUMSQ tests We may have no strong prior knowledge of specific structural breaks. Another method used to avoid arbitrary breakpoints (structural change points) is based on recursive estimation . This involves estimating the equation by OLS; starting with a small sample and allow the data period to increase by one period each estimate. It therefore produces a time series of estimates for the coefficients. These can be plotted with confidence intervals. Under the null hypothesis of parameter stability CUSUM should have zero mean and variance approximately equal to the number of normalised residuals being summed. Reject the null hypothesis of parameter stability if the CUSUM plot cross's any of the two lines. 5 You are not responsible from this test.

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 16 An alternative similar test is based on the cumulated sums of squared residuals, CUSUMSQ . Reject the null hypothesis of parameter stability if the CUSUMSQ plot cross's any of the two lines. It is generally recognized that the power of the tests is low (are not reliable for small samples) and in practice they are often used as a diagnostic tool. It is advisable to complement these parameter stability indicators with a formal Chow test (ACOV or Predictive). Example As an example of some of the tests discussed in this section the following price linkage equation from the cheese retail price to the wholesale price was estimated by OLS Y t 0 1 X t +u t where Y t is the cheese wholesale price and X t is the cheese retail price.
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 17

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 18
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 19 The CUSUM suggests no parameter instability. The CUSUMSQ suggest parameter instability between 1980-85. Hence according to CUSUMSQ test there can be a structural change after 1980 or between 1980-1985. These two possibility can be tested by usual Chow structural change test.
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