Estimation of the Generalized Prediction Error Variance of a Multiple Time Series

Mohanty, R.; Pourahmadi, Mohsen

doi:10.1080/01621459.1996.10476688

Cited by 8 publications

(8 citation statements)

References 18 publications

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“…For the NIC, we first consider the bias in the estimate of

normal l o g \det {\overset{V}{true}}_{e}

given by . This has been investigated by Mohanty and Pourahmadi () who give a formula based on the number of degrees of freedom of the spectral estimates calculated from the frequency domain smoothing window. This can also be expressed in terms of the lag window, in fact, as a function of the equivalent order p that we defined in , the series dimension m and the sample size n .…”

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

“…When expanded, the lowest‐order term of the formula is m 2 p / n , and it can be checked that this alone gives an accurate approximation to the formula for realistic values of m , p , and n . Although Mohanty and Pourahmadi () do not consider series tapering, the effect of this on all the statistical properties of spectral estimates is very well approximated as equivalent to a reduction in the series length from n to γ n .…”

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

“…For the NIC, we first consider the bias in the estimate of log det O V e given by (16). This has been investigated by Mohanty and Pourahmadi (1996) who give a formula based on the number of degrees of freedom of the spectral estimates calculated from the frequency domain smoothing window. This can also be expressed in terms of the lag window, in fact, as a function of the equivalent order p that we defined in (14), the series dimension m and the sample size n. When expanded, the lowest-order term of the formula is m 2 p=n, and it can be checked that this alone gives an accurate approximation to the formula for realistic values of m, p, and n. Although Mohanty and Pourahmadi (1996) do not consider series tapering, the effect of this on all the statistical properties of spectral estimates is very well approximated as equivalent to a reduction in the series length from n to n.…”

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

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Spectral Estimation of the Multivariate Impulse Response

Tunnicliffe-Wilson

2016

Journal Time Series Analysis

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One of the applications of cross‐spectral estimation of stationary time series, developed some five decades ago, is the estimation of the lagged response of an output series causally dependent on an input series, in the absence of feedback from the output to the input. The direct application of cross‐spectral analysis for this purpose is no longer appropriate in the presence of feedback or more general inter‐dependence of the series. In that case, vector autoregressive modeling has been used, particularly in the econometric context, to estimate the response of one series to a shock or impulse in the innovations of another series. To achieve the same end, cross‐spectral analysis requires the application of spectral factorization, and in this article, we demonstrate this methodology, explaining how it may be used to construct impulse response function estimates and their statistical properties. Our presentation includes an information criterion for choosing the smoothing bandwidth to be used for cross‐spectral estimation.

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“…For the NIC, we first consider the bias in the estimate of

normal l o g \det {\overset{V}{true}}_{e}

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

Section: Derivation Of the Statistical Propertiesmentioning

confidence: 99%

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Spectral Estimation of the Multivariate Impulse Response

Tunnicliffe-Wilson

2016

Journal Time Series Analysis

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“…Then a nonparametric estimate of B ( H, è, ö) can be used as a yardstick against which to gauge the ®ts of various competing parametric models assessed through their one-step-ahead prediction error variances. For Gaussian data the details of this idea have been worked out in Mohanty and Pourahmadi (1996) and references therein. For the non-Gaussian case, a nonparametric estimate of the innovation process entropy is needed.…”

Section: Lower Bound For the Prediction Error Variancementioning

confidence: 99%

“…This provides another major motivation for developing nonparametric estimators of functionals of the entropy. Applications of such estimators to nonlinear prediction problems are envisioned to parallel those discussed in Mohanty and Pourahmadi (1996) for the linear prediction problems.…”

Section: Introductionmentioning

confidence: 99%

Prediction Variance and Information Worth of Observations in Time Series

Pourahmadi

Soofi

2000

Journal Time Series Analysis

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The problem of developing measures of worth of observations in time series has not received much attention in the literature. Any meaningful measure of worth should naturally depend on the position of the observation as well as the objectives of the analysis, namely parameter estimation or prediction of future values. We introduce a measure that quanti®es worth of a set of observations for the purpose of prediction of outcomes of stationary processes. The worth is measured as the change in the information content of the entire past due to exclusion or inclusion of a set of observations. The information content is quanti®ed by the mutual information, which is the information theoretic measure of dependency. For Gaussian processes, the measure of worth turns out to be the relative change in the prediction error variance due to exclusion or inclusion of a set of observations. We provide formulae for computing predictive worth of a set of observations for Gaussian autoregressive moving-average processs. For non-Gaussian processes, however, a simple function of its entropy provides a lower bound for the variance of prediction error in the same manner that Fisher information provides a lower bound for the variance of an unbiased estimator via the Crame Âr±Rao inequality. Statistical estimation of this lower bound requires estimation of the entropy of a stationary time series.

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Measuring predictability: theory and macroeconomic applications

Diebold

Kilian

2001

J of Applied Econometrics

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SUMMARYWe propose a measure of predictability based on the ratio of the expected loss of a short-run forecast to the expected loss of a long-run forecast. This predictability measure can be tailored to the forecast horizons of interest, and it allows for general loss functions, univariate or multivariate information sets, and covariance stationary or difference stationary processes. We propose a simple estimator, and we suggest resampling methods for inference. We then provide several macroeconomic applications. First, we illustrate the implementation of predictability measures based on fitted parametric models for several US macroeconomic time series. Second, we analyze the internal propagation mechanism of a standard dynamic macroeconomic model by comparing the predictability of model inputs and model outputs. Third, we use predictability as a metric for assessing the similarity of data simulated from the model and actual data. Finally, we outline several non-parametric extensions of our approach.

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Estimation of the Generalized Prediction Error Variance of a Multiple Time Series

Cited by 8 publications

References 18 publications

Spectral Estimation of the Multivariate Impulse Response

Spectral Estimation of the Multivariate Impulse Response

Prediction Variance and Information Worth of Observations in Time Series

Measuring predictability: theory and macroeconomic applications

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