Final Report Summary - CHANGE-POINT TESTS (New Results on Structural Change Tests: Theory and Applications)
The project has the following objectives and outcomes:
(a) In econometrics as well as many other fields, we specify and estimate statistical models in order to quantify theories, to evaluate hypothesis related to our theories, to forecast a variable of interest or generally to make statistical inference. One of the elements of reliable statistical inference is the validity of the assumptions of the model. Hence one important aspect of model evaluation is the development of residual based tests in order to evaluate whether our model specification assumptions are valid. This project develops a novel, general alternative asymptotic analysis of test statistics with estimation error for residual specification tests or two stage estimators. The asymptotic theory of these tests is developed under general assumptions for the models and estimators. The theory developed can be applied to various econometric specifications as long as they satisfy certain conditions. We provide applications of our asymptotic analysis to time series models as well as discrete choice models.
(b) Most economic phenomena undergo through periods of structural change. A family of tests for structural changes in the mean of a time series phenomena can exhibit non-monotonic power which can even go to zero as the alternative considered is further away from the null value. A number of such tests suffer from this problem. These tests are widely used in both Econometrics and Statistics fields. The non-monotone power is not only an important problem of any statistical test but it can have significant consequences in applications given that it will fail to detect any large or multiple changes in an economic process. Failure to detect structural changes has (i) statistical inference implications related e.g. to the properties of the estimators and forecasting based on a given model, (ii) economic policy decisions e.g. investment misallocation decisions. In this project we proposed a solution to the non-monotone power problem/puzzle of a family structural change or change point tests which directly deals with the source of the problem namely the long-run variance estimator or the Heteroskedastic and Autocorrelation consistent estimator used in these tests. Using this alternative long-run variance estimator the existing change-point tests no longer suffer from the non-monotone problem. In addition, this new estimator can also be used in other types of tests.
(c) We evaluate the properties of a new recently proposed family of time series models where the regressand is observed at a different sampling frequency from the regressors. We relate the theoretical properties of these models to the traditional models of temporal aggregation in econometrics. We show that generally ignoring the different sampling frequencies of the various economic variables can lead to statistical inference problems. We apply these models in different fields of economics ranging from forecasting to testing various hypotheses related to economic theory relationships.
The results of the project have been published in top field journals. They have been used by other researchers in the area of Economics and have been cited by other papers. Moreover some of the results of the project are of interest to the research departments of Central Banks both in Europe and in the US for economic policy analysis.
(a) In econometrics as well as many other fields, we specify and estimate statistical models in order to quantify theories, to evaluate hypothesis related to our theories, to forecast a variable of interest or generally to make statistical inference. One of the elements of reliable statistical inference is the validity of the assumptions of the model. Hence one important aspect of model evaluation is the development of residual based tests in order to evaluate whether our model specification assumptions are valid. This project develops a novel, general alternative asymptotic analysis of test statistics with estimation error for residual specification tests or two stage estimators. The asymptotic theory of these tests is developed under general assumptions for the models and estimators. The theory developed can be applied to various econometric specifications as long as they satisfy certain conditions. We provide applications of our asymptotic analysis to time series models as well as discrete choice models.
(b) Most economic phenomena undergo through periods of structural change. A family of tests for structural changes in the mean of a time series phenomena can exhibit non-monotonic power which can even go to zero as the alternative considered is further away from the null value. A number of such tests suffer from this problem. These tests are widely used in both Econometrics and Statistics fields. The non-monotone power is not only an important problem of any statistical test but it can have significant consequences in applications given that it will fail to detect any large or multiple changes in an economic process. Failure to detect structural changes has (i) statistical inference implications related e.g. to the properties of the estimators and forecasting based on a given model, (ii) economic policy decisions e.g. investment misallocation decisions. In this project we proposed a solution to the non-monotone power problem/puzzle of a family structural change or change point tests which directly deals with the source of the problem namely the long-run variance estimator or the Heteroskedastic and Autocorrelation consistent estimator used in these tests. Using this alternative long-run variance estimator the existing change-point tests no longer suffer from the non-monotone problem. In addition, this new estimator can also be used in other types of tests.
(c) We evaluate the properties of a new recently proposed family of time series models where the regressand is observed at a different sampling frequency from the regressors. We relate the theoretical properties of these models to the traditional models of temporal aggregation in econometrics. We show that generally ignoring the different sampling frequencies of the various economic variables can lead to statistical inference problems. We apply these models in different fields of economics ranging from forecasting to testing various hypotheses related to economic theory relationships.
The results of the project have been published in top field journals. They have been used by other researchers in the area of Economics and have been cited by other papers. Moreover some of the results of the project are of interest to the research departments of Central Banks both in Europe and in the US for economic policy analysis.