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On the Distribution of Quadratic Form of Sample Mean and Variance

100%
Wywiał J., Kończak G., The Karol Adamiecki University of Economics K.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2006
|
vol. 196
EN
The quadratic form of the sample mean and sample variance was considered. The sample is from normal distribution. The density function of the quadratic form has been derived. The quadratic form can be applied as the test statistic for the hypothesis on expected value and variance of normal distribution. The table with approximated critical values of the test statistic has been derived.
2
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Sequential Tests with Power Equal to 1 for Chosen Location Parameters

100%
Pekasiewicz D., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2007
|
vol. 206
EN
We often verify hypotheses about random variable distribution parameters, when the variable distribution is unknown. In these cases we apply nonparametric tests, in particular nonparametric sequential tests. This paper presents sequential tests for the mean and median. These tests have important property - their power is equal to 1.
PL
Nieparametryczne testy sekwencyjne mogą służyć do weryfikacji hipotez o wartościach parametrów zmiennej losowej, takich jak wartość oczekiwana i mediana, w przypadku gdy nie znamy klasy rozkładu badanej zmiennej. W pracy przedstawione zostały przykłady testów sekwencyjnych, których moc, przy dużej liczebności próby, jest równa 1. Testy tego typu mogą znaleźć zastosowanie zarówno w kontroli jakości produkcji, jak i badaniach medycznych.
3
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Joint Monitoring of the Mean, Dispersion and Asymmetry in Process Control

88%
Kończak G., Department of Statistics U. o. E. K., koncz@ae.katowice.pl
Acta Universitatis Lodziensis. Folia Oeconomica
|
2007
|
vol. 206
EN
In this paper the quadratic form of sample mean, sample variance and sample asymmetry is considered. This quadratic form can be used for testing hypothesis on the expected value, variance and asymmetry of observed variable. This statistic can be used for constructing a control chart for monitoring these three parameters in process control or in acceptance sampling by variables. It is very difficult to find the exact distribution of the proposed statistic. The asymptotic distribution of the proposed statistic is presented. The quantiles of exact distributions have been derived using Monte Carlo study for the case of normal distribution of the monitored variable.
PL
W artykule analizowano rozkład formy kwadratowej średniej, wariancji oraz asymetrii z próby. Przyjęto założenie, że próba pochodzi z populacji o rozkładzie normalnym. Proponowana statystyka może być wykorzystana w procesach sterowania jakością do jednoczesnego monitorowania poziomu przeciętnego, rozproszenia oraz asymetrii rozkładu badanej zmiennej. Trudne jest wyznaczenie rozkładu dokładnego proponowanej statystyki. Podano asymptotyczny rozkład rozważanej zmiennej oraz, wykorzystując symulacje komputerowe, wyznaczono kwantyle dla rozkładów dokładnych, uwzględniając różne liczebności prób.
4

To What Extent are Stock Returns Driven by Mean and Volatility Spillover Effects? – Evidence from Eight European Stock Markets

63%
Alikhanov A.
Review of Economic Perspectives
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2013
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vol. 13
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issue 1
3-29
EN
The paper investigates mean and volatility spillover effects from the U.S and EU stock markets as well as oil price market into national stock markets of eight European countries. The study finds strong indication of volatility spillover effects from the US-global, EU-regional, and the world factor oil towards individual stock markets. While both mean and volatility spillover transmissions from the US are found to be significant, EU mean spillover effects are negligible. To evaluate the magnitude of volatility spillovers, the variance ratios are also computed and the results draw to attention that the individual emerging countries’ stock returns are mostly influenced by the U.S volatility spillovers rather than EU or oil markets. Additionally, examination of only global and regional stock markets spillover transmissions into European stock markets also confirms the dominating presence of the U.S spillover transmissions. Furthermore, I also implement asymmetric tests on stock returns of eight markets. The stock market returns of Hungary, Poland, Russia and the Ukraine are found to respond asymmetrically to negative and positive shocks in the US stock returns. The weak evidence of asymmetric effects with respect to oil market shocks is found only in the case of Russia and the quantified variance ratios indicate that presence of oil market shocks are relatively higher for Russia. Moreover, a model with dummy variable confirms the effect of European Union enlargement on stock returns only for Romania. Finally, a conditional model suggests that the spillover effects are partially explained by instrumental macroeconomic variables, out of which exchange rate fluctuations play the key role in explaining the spillover parameters rather than total trade to GDP ratios in most investigated countries.
5

Eurusd Intraday Price Reversal

63%
Wiśniewska M.
Folia Oeconomica Stetinensia
|
2014
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vol. 14
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issue 2
152-162
EN
The study investigates the mean reversion in 1-minute EURUSD. Intraday patters in FX seem of particular interest as more and more trades in the FX market are automated high frequency trades (HFT). The study reveals that the mean reversion is present in the intraday EURUSD. ADF test rejects unit root. The average of the deviation of EURUSD from its (moving) mean is close to zero. Furthermore when short and long positions are simultaneously open, the average maximum return achieved through 24 hour period is similar, providing yet another evidence for mean reversion and lack of weak form of market efficiency.
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