Locally stationary long memory estimation

Roueff, François; Sachs, Rainer von

doi:10.1016/j.spa.2010.12.004

Cited by 118 publications

(65 citation statements)

References 30 publications

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“…It, therefore, can extract localized information in both time and frequency domains. Moreover, wavelet analysis exhibits a significant advantage over Fourier analysis, since it can accommodate non-stationary or locally stationary series (Roueff and Sachs, 2011).…”

Section: Wavelet Theory and Methodsmentioning

confidence: 99%

The co-movement and causality between the U.S. housing and stock markets in the time and frequency domains

Chang

Miller

et al. 2015

International Review of Economics & Finance

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This study applies wavelet analysis to examine the relationship between the U.S. housing and stock markets over the period 1890-2012. Wavelet analysis allows the simultaneous examination of co-movement and causality between the two markets in both the time and frequency domains. Our findings provide robust evidence that co-movement and causality vary across frequencies and evolve over time. Examining market co-movement in the time domain, the two markets exhibit positive co-movement over recent decades, except for 1998-2002 when a high negative co-movement emerged. In the frequency domain, the two markets correlate with each other mainly at low frequencies (longer term), except in the second half of the 1900s as well as in 1998-2002, when the two markets correlate at high frequencies (shorter term). In addition, we find that the causal effects between the markets in the frequency domain occur generally at low frequencies (longer term). In the time-domain, the time-varying nature of long-run causalities implies structural changes in the two markets. These findings provide a more complete picture of the relationship between the U.S. real estate and stock markets over time and frequency, offering important implications for policymakers (and practitioners).

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Section: Wavelet Theory and Methodsmentioning

confidence: 99%

The co-movement and causality between the U.S. housing and stock markets in the time and frequency domains

Chang

Miller

et al. 2015

International Review of Economics & Finance

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“…For this reason, we consider a theoretical framework of a locally stationary longmemory process (similar approaches can be found in Beran (2009), Palma and Olea (2010), and Roueff and von Sachs (2011)). …”

Section: Measuring Stationarity In Locally Stationary Long-memory Promentioning

confidence: 99%

Measuring stationarity in long-memory processes

Sen¹,

Preuß²,

Dette³

2017

STAT SINICA

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In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit.

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“…On the other hand, condition (5.2) allows for the long-memory case (a t,n (j)) j∈Z ∈ ℓ 2 ,  j∈Z |a t,n (j)| = ∞. The last case is also discussed in [23], where similar conditions as (5.2) and (5.3) are provided in spectral terms. It is not clear whether condition (5.4) allows for jumps of the parameter curves τ  → a(τ , ·) as in [9,10], in particular, for abrupt changes of the memory intensity of Gaussian process (5.1).…”

Section: A Central Limit Theorem For Functions Of Locally Stationarymentioning

confidence: 99%

“…Most of the above cited papers treat the case of a single stationary Gaussian sequence and a function independent of n. Generalization to stationary or non-stationary triangular arrays is motivated by numerous statistical applications. Some examples of these applications, with a particular emphasis on strongly dependent Gaussian processes, are statistics of time series (see for instance [2,23]), kernel-type estimation of the regression function [14], and nonparametric estimation of the local Hurst function of a continuous-time process from a discrete grid i/n, 1 ≤ i ≤ n [15,3,4]. Two particular applications (limit theorems for the Increment Ratio statistic of a Gaussian process admitting a tangent process and a CLT for functions of locally stationary Gaussian processes) are discussed in Section 5.…”

Section: Introductionmentioning

confidence: 99%

Moment bounds and central limit theorems for Gaussian subordinated arrays

Bardet¹,

Сургайлис

2013

Journal of Multivariate Analysis

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a b s t r a c tA general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1983) [5], Arcones (1994) [1] and others. A Berry-Esseen-type bound in the abovementioned central limit theorem is derived following Nourdin et al. (2011) [20]. Two applications of the above results are discussed. The first one refers to the asymptotic behavior of a roughness statistic for continuous-time Gaussian processes and the second one is a central limit theorem satisfied by long memory locally stationary processes.

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Locally stationary long memory estimation

Cited by 118 publications

References 30 publications

The co-movement and causality between the U.S. housing and stock markets in the time and frequency domains

The co-movement and causality between the U.S. housing and stock markets in the time and frequency domains

Measuring stationarity in long-memory processes

Moment bounds and central limit theorems for Gaussian subordinated arrays

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