<i>Statistical Analysis of Stationary Time Series</i>

Grenander, Ulf; Rosenblatt, Murray; Blachman, Nelson M.

doi:10.1063/1.3060405

Cited by 458 publications

(298 citation statements)

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“…If the correlation structure of u t is higher than first-order autoregressive, then the ordinary least squares (OLS) estimate of β 1 is asymptotically equivalent to generalized least squares (GLS) in the case of known correlation (e.g. Grenander and Rosenblatt, 1957). However, in order to obtain asymptotic (in large samples) valid tests, the asymptotic variance covariance matrix of the coefficients needs to be consistently estimated.…”

Section: Review Of the Literature On Deterministic Trendsmentioning

confidence: 99%

An application of fractional integration to a long temperature series

Gil-Alana

2003

Intl Journal of Climatology

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Some recently proposed techniques of fractional integration are applied to a long UK temperature series. The tests are valid under general forms of serial correlation and do not require estimation of the fractional differencing parameter. The results show that central England temperatures have increased about 0.23°C per 100 years in recent history. Attempting to summarize the conclusions for each of the months, we are left with the impression that the highest increase has occurred during the months from October to March.

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Section: Review Of the Literature On Deterministic Trendsmentioning

confidence: 99%

An application of fractional integration to a long temperature series

Gil-Alana

2003

Intl Journal of Climatology

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“…Notice that the early literature, which includes some distinguished references such as Yule (1926), Bartlett (1955), Grenander and Rosenblatt (1957) or Durbin and Watson (1950), essentially assumed Gaussianity and, hence, identi…ed three concepts: lack of serial correlation, mds and independence.…”

Section: Preliminariesmentioning

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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“…Because bias tends to vary inversely with M, and variance tends to vary directly, minimization of mean squared error (MSE) E{f(A) -f(A)}2 was proposed by Grenander and Rosenblatt (1957) as a simple criterion for producing a balancing M. Under regularity conditions .4) and ro is the largest real number for which both (6.3) and (6.4) are assumed finite.…”

Section: Bandwidth Selectionmentioning

confidence: 99%