CUSUM Of Squares Test Research Articles

Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.

The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes

In this paper we consider the problem of testing for a scale change in the infinite order moving average process Xj=Σ∞i=0aiεj−i, where εj are i.i.d. r.v.s with Eε1α < ∞ for some α > 0. In performing the test, a cusum of squares test statistic analogous to Inclan & Tiao’s (1994) statistic is considered. It is well‐known from the literature that outliers affect test procedures leading to false conclusions. In order to remedy this, a cusum of squares test based on trimmed observations is considered. It is demonstrated that this test is robust against outliers, is valid for infinite variance processes as well. Simulation results are given for illustration.

On the Cusum test for parameter changes in garch(1,1) Models

This paper considers the problem of testing parameter constancy in GARCH(1,1) models. A cusum of squares test is propesed in analogy Of Incl´n and Tiao (1394)'s statistic. its limiting distribution is derived via using the invariance principle for mixingaie sequences obtained by McLeish(1975). Simulation results are illustrated to demonstrate the validity of the cusumtest.

Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets : Mico Loretan, Peter C.B. Phillips

Abstract We investigate methods of testing the proposition that the unconditional variance of a time series is constant over time. Motivated by the observation that many financial datasets are “heavy-tailed,” we focus on the properties of statistical tests of covariance stationarity when unconditional fourth and second moments of the data are not finite. We find that sample split prediction tests and cusum of squares tests have nonstandard limiting distributions when fourth unconditional moments are infinite. These tests are consistent provided that variances are finite. However, the rate of divergence under the alternative hypothesis and hence the power of these tests is sensitive to the index of tail thickness in the data. We estimate the maximal moment exponent (which measures tail thickness) for a number of stock market return and exchange rate return series, and conclude that fourth unconditional moments of these series do not appear to be finite. In our formal tests of covariance stationarity, we reject the null hypothesis of constancy of the unconditional variance of these series. This raises questions about the nature of the observed volatility in economic time series, and about appropriate methods of statistically modeling this volatility.

An analysis of the structural change in the exchange market pressure: Korea, 1980-89

This paper tests the stability of the exchange market pressure model in the case of Korea under a managed floating exchange rate. Using the cusum of squares test, we show that the structural stability was broken in about mid-1986. This is plausible given that there was a sudden surplus in the balance of payments in Korea in late 1985. Estimation results show that the exchange market pressure model works very well where there is a surplus in balance of payments; however, its explanatory power is poor in periods of deficit.

Intertemporal Changes in the Riskiness of REITs

This study investigates the variability in the risk components of REITs over the 1973-1989 period using the cusum test, the cusum of squares test, and the Quandt's log-likelihood ratio method. Four...

Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets

We investigate methods of testing the proposition that the unconditional variance of a time series is constant over time. Motivated by the observation that many financial datasets are “heavy-tailed,” we focus on the properties of statistical tests of covariance stationarity when unconditional fourth and second moments of the data are not finite. We find that sample split prediction tests and cusum of squares tests have nonstandard limiting distributions when fourth unconditional moments are infinite. These tests are consistent provided that variances are finite. However, the rate of divergence under the alternative hypothesis and hence the power of these tests is sensitive to the index of tail thickness in the data. We estimate the maximal moment exponent (which measures tail thickness) for a number of stock market return and exchange rate return series, and conclude that fourth unconditional moments of these series do not appear to be finite. In our formal tests of covariance stationarity, we reject the null hypothesis of constancy of the unconditional variance of these series. This raises questions about the nature of the observed volatility in economic time series, and about appropriate methods of statistically modeling this volatility.

Testing for Disequilibrium in the Hired Farm Labor Market: Comment

In a recent article, Duffield and Coltrane use an econometric model to test for disequilibrium in the hired farm labor market. Cusum and cusum of squares tests show that the estimated parameters are stable. Estimated shortand long-run elasticities of adjustment suggest that the national hired labor market adequately adjusts to changes in farm and nonfarm wages, of farms, farm prices, and family labor. The methodology used is sound and appropriate for testing for disequilibrium in a market. However, we have three comments. The first is to question whether their model using time series data from 1948 through 1989 successfully captures the dramatic structural changes that occurred in the farm sector over this period. Among the many changes affecting farm labor are mechanical innovations, production system modifications, and child labor laws. The authors include a number of farms variable and a trend to reflect these structural changes, but it would have been preferable to test for significant differences between blocks of time, and then use a shorter, recent time period for the analysis, say, since 1975. The second is to ask if the results of this model are subject to the Lucas critique (Lucas). The parameters of the model were estimated over a period when the government was continually interfering. Between 1948 and 1989 we've seen the Bracero and H2A programs and special agricultural programs under the 1986 Immigration Reform and Control Act (IRCA). These government programs affected employment levels of hired farm labor. In fact they were designed specifically to increase or maintain the supply of agricultural labor (Heppel and Amendola). So how can this model be used to indicate how well the market adjusts without government interference? The third and probably most important comment is to question the appropriateness of using aggregate U.S. data to model the hired farm labor market. The bulk of the hired farm labor force is found in a handful of states: In California, three-fourths of the farm work force is hired; in Florida, 68%; while in the Cornbelt, only 15% is hired (USDA, NASS). Aggregate U.S. data wash out the heterogeneity of U.S. agriculture and the diversity of farm labor use. The contrast between a salaried hired worker on a Wisconsin dairy farm and a seasonal migrant worker from Mexico who picks California grapes could not be more striking. How meaningful is it to lump them together to analyze an overall labor market? There are many labor markets in the nation, differing markedly by crop and region of the country. In some of these labor markets, for example, where a high minimum wage is enforced, the observed labor quantity may be on the demand curve and there would be a surplus of labor. In other markets where farmers demand more labor than is supplied at the prevailing wage, the observed quantity may lie on the supply curve meaning a labor shortage. In still other markets where temporary workers are attracted at the prevailing wage, a downward supply shift could lead to the observed quantity hired being at or near the intersection of supply and demand. The point is that aggregate U.S. data homogenize these interesting differences. Evidence of labor market equilibrium nationally clearly is not evidence for local equilibria where regional differences are pronounced. Further, it is not true that labor moves easily from shortage to surplus areas. In a recent survey of farmworkers in Oregon (Mason, Cross, and Nuckton), we find that workers don't even shift readily between crops located in close proximity, such as between strawberries and Christmas trees in Oregon's Willamette Valley. Rather, they develop skills in one (or a few related) crop(s) and follow that crop through the production season. Given the heterogeneity of the U.S. farm labor markets, we question the author's use of aggregate U.S. data over four decades to draw the particular policy conclusions for the early 1990s that they suggest (p. 419):

The Cusum Test with Ols Residuals

We show that the CUSUM test of the stability over time of the coefficients of a linear regression model, which is usually based on recursive residuals, can also be applied to ordinary least squares residuals. We derive the limiting null distribution of the resulting test and compare its local power to that of the standard procedure. It turns out that neither version is uniformly superior to the other. henceforth BDE) on the CUSUM and CUSUM of squares tests for the constancy over time of the coefficients of a linear regression model. Both tests are based on recursive residuals, which are independent N(O, o.2) under Ho, and therefore ideal ingredients for all types of tests. While the CUSUM of squares test has been generalized to ordinary least squares (OLS) residuals (McCabe and Harrison (1980)), a generalization of the CUSUM test to OLS residuals, which are dependent and heteroskedastic even under Ho, has not yet been made except for a very special case (MacNeill (1978)). In fact, both BDE (1975, p. 151) and McCabe and Harrison (1980, p. 142) argue that a least squares variant of the CUSUM test poses intractable problems, due to an alleged difficulty in assessing the significance of the departure of the cumulated OLS residuals from their mean value zero. Below we show that it is no more difficult to derive the limiting distribution for a CUSUM test based on OLS residuals than for a CUSUM test based on recursive residuals. While the CUSUMs of the recursive residuals, properly standardized, tend in distribution to a standard Wiener process (Sen (1982); Krimer, Ploberger, and Alt (1988), henceforth KPA), we show that the OLS- based CUSUMs tend in distribution to a Brownian bridge (or tied-down- Brownian-motion; see Billingsley (1968, p. 64)). This generalizes MacNeill's (1978) polynomial regression result to arbitrary regressor sequences. We also demonstrate that the resulting CUSUM test has higher (local) power for certain types of structural change than the one based on recursive residuals, though neither variant is uniformly superior to the other.

A Bayesian Significance Test of the Stationarity of Regression Parameters

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens- Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

A Bayesian significance test of the stationarity of regression parameters

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the BehrensFisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

Some comparisons of the relative power of simple tests for structural change in regression models

AbstractThe power of Chow, linear, predictive failure and cusum of squares tests to detect structural change is compared in a two‐variable random walk model and a once‐for‐all parameter shift model. In each case the linear test has greatest power, followed by the Chow test. It is suggested that the linear test be used as the basic general test for structural change in time series data, and tests of forecasting performance be confined to the last few observations. Analysis of recursive residuals and recursive parameter estimates should be regarded as forms of exploratory data analysis and tools for understanding discrepancies with previous results rather than a basis for formal tests of structural change.

The Local Power of the CUSUM and CUSUM of Squares Tests

We consider the local power of the cusum and cusum of squares tests for structural change in the linear regression model. We show that the local power of the cusum of squares test equals its size for a wide class of structural changes, as compared to a nontrivial local power for the cusum test. The conventional ranking of these procedures is thus reversed.

A new test for structural stability in the linear regression model

Abstract We propose a new test for the constancy of regression coefficients in linear models. The test does not require that possible change points be known. We derive the limiting null distribution of the test statistic, prove that the test has non-trivial power against many local alternatives, and show that it compares favourably to both the CUSUM and CUSUM of squares tests.

On studentizing a test for structural change

We show that the asymptotic null distribution of the CUSUM of squares test is not robust against deviations from normality, and propose a modification which overcomes this deficiency.

Evidence of the Structural Stability of Short-Term Capital Flow

IN an earlier study, Hodgson and Holmes (1977) provided empirical evidence on the structural stability of short-term capital flow using the case of U.S.-Canadian net bank claims for the period 1955-I to 1974-I.1 Their findings indicated that the short-term capital flow underwent a significant structural change, and that the instability in the short-term capital flow may have been due to changes in interest rate sensitivity over time. However, as Garbade (1977) shows, the test procedure used by Hodgson and Holmes, labeled the cusum of squares test, has limitations for detecting structural change in the coefficients. The primary purpose of this paper is to present additional empirical evidence on the stability of U.S.-Canadian capital flow, obtained not only from the cusum of squares test, but also from the variable parameter regression technique. The use of the latter test is well justified in that it is somewhat more powerful and has the advantage of being able to isolate instability in individual regression coefficients. In section I we develop an analytical framework for short-term capital flow based on the portfolio balance approach. Section II presents the regression results for the U.S.-Canadian short-term capital flow. In section III we present a brief and heuristic description of the two stability test procedures as well as the results of these tests. Major conclusions are presented in section IV.

Testing for parameter stability in structural econometric relationships

This letter discusses CUSUM and CUSUM of squares tests for parameter stability in an equation which forms part of a structural simultaneous equations model.

On the Strong Mixing Property for Linear Sequences

On the Strong Mixing Property for Linear Sequences