Tests for departure from normality in the case of linear stochastic processes

Łomnicki, Z. A.

doi:10.1007/bf02613866

Cited by 64 publications

(40 citation statements)

References 4 publications

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“…Therefore, transforming u t such that the resulting y t has an arcsine distribution under the null tends to decrease the size distortions of theα Finally, one could modify the approach based on the INTs by using knowledge about the long-run covariance matrix under the null. According to Lomnicki (1961), the long-run covariance matrix of the raw moments of the INTs, Ω 1234 , is given by…”

Section: Extensionsmentioning

confidence: 99%

Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments

Knüppel¹

2014

Journal of Business & Economic Statistics

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Abstract:The evaluation of multi-step-ahead density forecasts is complicated by the serial correlation of the corresponding probability integral transforms. In the literature, three testing approaches can be found which take this problem into account.However, these approaches can be computationally burdensome, ignore important information and therefore lack power, or suffer from size distortions even asymptotically. In this work, a fourth testing approach based on raw moments is proposed.It is easy to implement, uses standard critical values, can include all moments regarded as important, and has correct asymptotic size. It is found to have good size and power properties if it is based directly on the (standardized) probability integral transforms.Keywords: Density forecast evaluation; normality tests JEL-Classification: C12, C52, C53 Non-technical SummaryToday, predictions are often made in the form of density forecasts. An increasing number of central banks publishes density forecasts, which are displayed by fan charts. Compared to point forecasts, density forecasts contain additional information. From density forecasts for inflation, for example, it is possible to infer the probability of deflation or the probability of inflation being higher than the central bank's target.Point forecasts can be evaluated according to properties like bias or efficiency.Similarly, density forecasts can also be evaluated. A forecast density should coincide with the true density of the variable under study. If this is the case, the density forecast is said to be correctly calibrated. However, if, for instance, over a certain period of time the realizations of the variable under study always occur within a very narrow interval around the means of the forecast densities, this would be a strong indication for incorrect calibration. The forecast densities probably have a too large width in this case.If density forecasts for more than one period ahead are to be evaluated, this evaluation is complicated by the serial correlation of the outcomes with respect to the density forecasts. Suppose, for example, that one density forecast for inflation is made in January for July, and the next forecast is made in February for August.Then, if inflation in July turns out to be much higher than the mean of January's density forecast, it is very likely that inflation in August will also be considerably higher than the mean of February's density forecast.One can distinguish three evaluation approaches that are used or suggested in the literature for these situations. However, each of them has certain disadvantages with respect to the ability to detect incorrect calibration, to the possibility of falsely concluding that the density forecasts have incorrect calibration although it is actually correct, or to the ease of use. Therefore, an alternative evaluation approach, which does not suffer from any of these drawbacks, is suggested in this paper. In simulations, this new approach is found to yield good results and, thus, to be a viable alternative t...

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Section: Extensionsmentioning

confidence: 99%

Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments

Knüppel¹

2014

Journal of Business & Economic Statistics

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“…The large size of the tests computed on the seasonal residual is related to the strong serial correlation that the seasonal residuals display. It indicates that the Lomnicki (1961) corrections for serial correlation used are not completely satisfactory.…”

Section: Stability Of the Component Estimatorsmentioning

confidence: 83%

Linear signal extraction with intervention techniques in non‐linear time series

Planas

1998

J. Forecast.

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Seasonal adjustment is performed in some data-producing agencies according to the ARIMA-model-based signal extraction theory. A stochastic linear process parametrized in terms of an ARIMA model is ®rst ®tted to the series, and from this model the models for the trend, cycle, seasonal, and irregular component can be derived. A spectrum is associated to every component model and is used to compute the optimal Wiener± Kolmogorov ®lter. Since the modelling is linear, prior linearization of the series with intervention techniques is performed. This paper discusses the performance of linear signal extraction with intervention techniques in nonlinear processes. In particular, the following issues are discussed: (1) the ability of intervention techniques to linearize time series which present nonlinearities; (2) the stability of the linear projection giving the components estimators under non-linear misspeci®cations; (3) the capacity of the WK ®lter to preserve the linearity in some components and the non-linearities in others. #

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“…(Cf. Webb [23] and Lomnicki [19].) In this section, we will assume that the hypothesis of a stationary gaussian process is acceptable; and, that the plot does not indicate that { Y t } is seasonal.…”

Section: The Box-jenkins Cyclementioning

confidence: 99%

The Box-Jenkins approach to time series analysis

Anderson¹

1977

RAIRO-Oper. Res.

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Tests for departure from normality in the case of linear stochastic processes

Cited by 64 publications

References 4 publications

Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments

Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments

Linear signal extraction with intervention techniques in non‐linear time series

The Box-Jenkins approach to time series analysis

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