A Test of Fit in Time Series Models

Milhøj, Anders

doi:10.2307/2335818

Cited by 11 publications

(24 citation statements)

References 2 publications

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“…A class of test statistics, generalising Milhøj (1981) goodness of fit test, exploits an important property of the GACV, which is a direct consequence of Lemma 1: , whose null distribution has variance…”

Section: Generalised Milhøj Goodness Of Fit Testsmentioning

confidence: 99%

“…Sections 6-8 focus on three main uses of the GACV and the GACF. The first deals with testing for white noise: two classes of tests, generalising the Box and Pierce (1970) test and the Milhøj (1981) statistics, are proposed and their properties discussed. A Yule-Walker estimator of the spectrum based on the GACV is presented in section 7: in particular, the GACV for p > 1 will highlight the cyclical features of the series; this property can be exploited for the identification and estimation of spectral peaks.…”

Section: Introductionmentioning

confidence: 99%

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The Generalised Autocovariance Function

Proietti

Luati

2013

SSRN Journal

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The generalised autocovariance function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function.Depending on the value of the transformation parameter, this function nests the inverse and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived. The results are employed to construct classes of tests of the white noise hypothesis, for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum.

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Section: Generalised Milhøj Goodness Of Fit Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Generalised Autocovariance Function

Proietti

Luati

2013

SSRN Journal

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“…This statistic was previously considered by Milhøj (1981) who employed M n as a general goodness of …t test statistic for time series. Milhøj informally justi…ed the use of this statistic for testing the adequacy of linear time series models, but since he identi…ed white noise with i.i.d.…”

Section: Tests Based On a In…nite-dimensional Conditioning Setmentioning

confidence: 99%

Testing the Martingale Hypothesis

Escanciano¹,

Lobato²

2009

Palgrave Handbook of Econometrics

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This article examines testing the Martingale Di¤erence Hypothesis (MDH) and related statistical inference issues. The earlier literature on testing the MDH was based on linear measures of dependence, such as sample autocorrelations, for instance the classical Box-Pierce Portmanteau test and the Variance Ratio test. In order to account for the existing nonlinearity in economic and …nancial data, two directions have been entertained. First, to modify these classical approaches by taking into account the possible nonlinear dependence. Second, to use more sophisticated statistical tools such as those based on empirical processes theory or the use of generalized spectral analysis. This paper discusses these developments and applies them to exchange rate data.

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“…The first statistic T 1 compares the periodogramŜ X (f k ) for the NP index to the fitted S(f k ;θ) from a particular model [10,1]:…”

Section: Spectral Density Functions (Thick Curves Top Row) For Thementioning

confidence: 99%

“…ε } (the theory behind T 1 developed in [10] does not extend to the SDF we defined for the SWO model). Under the null hypothesis that the model corresponding to S(f k ;θ) is correct, T 1 is asymptotically normal with mean 1/π and variance 2/(π 2 N ).…”

Section: Spectral Density Functions (Thick Curves Top Row) For Thementioning

confidence: 99%

Modeling North Pacific Climate Time Series

Percival

Mofjeld

2004

Time Series Analysis and Applications to Geophysical Systems

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Abstract. We present a case study in modeling the North Pacific (NP) index, which is a time series related to atmospheric pressure variations at sea level. We consider three statistical models, namely, a Gaussian stationary autoregressive process, a Gaussian stationary fractionally differenced (FD) process, and a 'signal plus noise' process consisting of a square wave oscillation with a pentadecadal period embedded in Gaussian white noise. Each model depends upon three parameters, so all three models are equally simple. Statistically each model fits the NP index equally well. The fact that this index consists of just a hundred observations makes it unrealistic to expect to be able to clearly prefer one model over the other. Although the models fit equally well, their implications for the long term behavior of the NP index can be quite different in terms of, e.g., generating regimes of characteristic lengths (i.e., stretches of years over which the NP index is predominantly either above or below its long term average value). Because we cannot determine a preferred model statistically, we are faced with either entertaining multiple models when considering what the long term behavior of the NP index is likely to be or using physical arguments to select one model. The latter approach would arguably favor the FD process because it has an interpretation as the synthesis of first order differential equations involving many different damping constants.

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A Test of Fit in Time Series Models

Cited by 11 publications

References 2 publications

The Generalised Autocovariance Function

The Generalised Autocovariance Function

Testing the Martingale Hypothesis

Modeling North Pacific Climate Time Series

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