Next consider the n up or backwards graph hendry

This preview shows page 24 - 25 out of 25 pages.

Next consider the N up (or backwards) graph. Hendry calls this the Forecast Chow tests, or N up- Step Chow tests. Here the chart shows a sequence of Chow forecast tests for a horizon increasing from M to T. This is implemented by first using observations T to T-M to predict periods 1 to M. Then periods are successively added until the sample for the last regression consists of observations T to 2 which are used to predict the first observation. Again, the values shown have been scaled by the appropriate critical value (we have chosen 1% here). This implies that the horizontal line at unity becomes the critical value to use for making inference about stability. Hendry suggests that the N up forecast test “shows that a ‘break’ occurred in 1974”.
Image of page 24

Subscribe to view the full document.

25 INTERPRETING THE OUTCOMES OF TEST STATISTICS A "failure" on any of these tests (in the sense that the test statistic is significant under the null hypothesis) can mean one of several things: (a) the null hypothesis is false and that the model is misspecified in the way indicated by the alternative hypothesis. (e.g. a significant serial correlation statistic COULD indicate the presence of serial correlation). (b) the null hypothesis is correct, but the model is misspecified in some other way (e.g. a significant serial correlation statistic might not result from a true serially correlated error, but could result from an omitted variable). (c) the null hypothesis is false AND the model is misspecified in one or more other ways. (d) a significant statistic may result from a type I error (that is the null is true but is rejected). Because explanation (a) is not always correct, it is best to interpret each test as a general misspecification test, which may give some clues as to the type of misspecification encountered. Thus, a significant normality test implies the model is misspecified in some way. The type of misspecification MAY result from an error process which is not normal, but COULD result from virtually any type of misspecification. A “conservative” way of proceeding is, then, to regard the set of misspecification tests as a set of necessary hurdles to be overcome: unless the model you specify and estimate is not rejected in terms of any test of misspecification, do not proceed. Respecify the model until a satisfactory one is found. An important point to note is the distinction between the residuals and the errors. While a significant serial correlation test statistic implies (with a given degree of significance) that the residuals are serially correlated, this does not necessarily imply that the true errors are such. In a misspecified model, the residuals will include all determinants of the dependent variable that are not explicitly modelled in the deterministic component of the equation. A significant serial correlation statistic may therefore reflect the omission of a relevant regressor. Unfortunately, this makes matters rather difficult as the tests can not be used to conclude decisively on the nature of any misspecification discovered.
Image of page 25
You've reached the end of this preview.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern