• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.223-229
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• 2010

We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.10
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• pp.523-530
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• 2020

The efficient market hypothesis explains the random walk hypothesis suggesting that stock prices are independent of each other, hence, it is impossible to earn abnormal profits. The positive effect of a well-functioning and highly efficient stock market on the performance of an economy motivated the Philippine Stock Exchange to pursue massive modernization initiatives. This research provides evidence of the existence of random walk in the Philippine stock market employing the Augmented Dickey-Fuller (1981) and Phillips-Perron (1988) unit root tests, the Lo-MacKinlay's (1988) conventional variance ratio test, and Chow-Denning's (1993) simple multiple variance ratio test. Results of the ADF and PP unit root tests confirm the necessary condition for a random walk. The Chow-Denning (1993) maximum /z/ statistic and the Wald test statistic as in Richardson and Smith (1991) for the joint hypotheses and the Lo and MacKinlay (1988) individual statistics variance ratio test generally accepted the null hypothesis of a random walk. That is, the unit root and variance ratio tests consistently indicate that the null hypothesis of random walk cannot be rejected. The existence of a random walk in weak-form efficiency can be attributed to market liquidity as a result of continuous development and modernization of the Philippine equity market.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.457-469
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• 1996

In this paper, we propose a method for an exact test of H : $p_i$ = $r_i$ for all i against K : $p_i$ $\neq$ $r_i$ for some i in an unbalanced random effect linear model, where $p_i$ denotes the ratio of the i-th variance component to the error variance. Then we present a method to test H : $p_i$ $\leq$ r against K : $p_i$> r for some specific i by applying orthogonal projection on the model. We also show that any test statistic that follows an F-distribution on the boundary of the hypotheses is equal to the one given here.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.296-302
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• 1995

When heteroscedasticity occurs in random effects linear model, the error variance may depend on the values of one or more of the explanatory variables or on other relevant quantities such as time or spatial ordering. In this paper we derive a score test as a diagnostic tool for detecting non-constant error variance in random effefts linear model based on the model expansion on error variance. This score test is compared to loglikelihood ratio test.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.11-24
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• 1999

In this paper we propose a method to test $\textit{H}$:$\rho_i$=$\gamma_i$ for 1$\leq$$\textit{i}$$\leq$$\ell$ against $\textit{K}$:$\rho_i$$\neq$$\gamma_i$ for some ｉin k-variance component random or mixed linear model where $\rho$i denotes the ratio of the i-th variance component to the error variance and $\ell$$\leq$K. The test which we call Rao-Wald test is exact and does not depend upon nuisance parameters. From a numerical study of the power performance of the test of the interaction effect for the case of a two-way random model Rao-Wald test was seen to be quite comparable to the locally best invariant (LBI) test when the nuisance parameters of the LBI test are assumed known. When the nuisance parameters of the LBI test are replaced by maximum likelihood estimators Rao-Wald test outperformed the LBI test.

• Journal of the Korea Construction Safety Engineering Association
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• s.43
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• pp.98-106
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• 2007

In this paper, a ground disturbance effects, strength and consolidation characteristics of soft clay through using the large block samples($\theta$:300mm, H:400mm) and the piston samples, f hose which had been gathered in west coast and south coast. Especially, we have assessed the coefficient of horizontal consolidation when penetrating the mandrel considering the variance of ratio between diameter and height in drainage sample through the experiment of the oedometer test and Rowecell and also investigated the disturbance area in smear zone by interior model test, the strength originated by disturbance, the variance in characteristics of the consolidation. As the result, the large block sample has been investigated that ihe uniaxial compression test(qu) was shown bigger than the piston sample by about 11-19%. Under the size of anistropy in consolidation, the coefficient ratio of consolidation(ch/cv,) perfomed by standard consolidation test(SC) was shown bigger than that of (Cro/Cv) by the Rowecell test. And the coefficient ratio of consolidation(Cro/Cv) perfomed by piston sample was evaluated bigger than that Of (Cro/Cv) by the large block sample by about 0.9-1.9. The coefficient ratio of consolidation along with the variance in ratio of between diameter and height when penetrating the mandrel was shown big difference according to the characteristics of soil of the specimen. In addition, ds/dw of smear zone at the marine clay in west-south was ranged from 1.6 to 4.2. The width of variance in rat io[(qud)/(quud)] of strength n the area between disturbance and undisturbance was shown big as about 72-91% but the principle was judged with the similiar range when the decrease of the strength in smear zone become the zone under 25% in unditurbance area.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.101-109
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• 1997

For the detection on variance changes in the nonstationary time series with a unit root two types of test statistics are proposed, of which one is based on the cumulative sum of squares and the other is based on the likelihood ratio test. The properties of the cusum type test statistic are derived and the performance of two tests in small samples are compared through Monte Carlo study. It is ovserved that the test based on the cumulative sum of squares can detect a samll change in the variance faster than the one based on the likelihood ratio.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.899-905
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• 2000

The characteristics of air flow and engine performance with swirl ratio variance of intake port In a turbocharged DI diesel engine was studied in this paper. The intake port flow is important factor which have influence on the engine performance and exhaust emission because the properties in the injected fuel depend on the combustion characteristics. The swirl ratio for ports was modified by hand-working and measured by impulse swirl meter. For the effects on performance and emission, the brake torque and brake specific fuel consumption were measured by engine dynamometer and NOx, smoke were measured by gas analyzer and smoke meter. As a result of steady flow test, when the valve eccentricity ratio are closed to cylinder wall, the flow coefficient and swirl intensity are increased. And as the swirl ratio is increased, the mean flow coefficient is decreasing, whereas the gulf factor is increasing. Also, through engine test its can be expected to meet performance and emission by optimizing the main parameters; the swirl ratio of intake port, injection timing and compression ratio.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.171-175
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• 1990

A diagnostic test for detecting nonconstant variance in mixed linear models based on the score statistic is derived through the technique of model expansion, and compared to the log likelihood ratio test.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.