NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

Masanobu Taniguchi; Masao Kondo

doi:10.1111/j.1467-9892.1993.tb00153.x

NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

Masanobu Taniguchi^*, Masao Kondo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Abstract. Suppose that {X_t} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{f_n(Λ)}dΛ where f_n(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.

Original language	English
Pages (from-to)	397-408
Number of pages	12
Journal	Journal of Time Series Analysis
Volume	14
Issue number	4
DOIs	https://doi.org/10.1111/j.1467-9892.1993.tb00153.x
Publication status	Published - 1993 Jul
Externally published	Yes

Keywords

Burg's entropy
Gaussian stationary process
Non‐parametric hypothesis testing
asymptotic relative efficiency
contiguous alternative
efficacy
exponential spectral model
non‐parametric spectral estimator
spectral density

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1111/j.1467-9892.1993.tb00153.x

Cite this

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title = "NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS",

abstract = "Abstract. Suppose that {Xt} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{fn(Λ)}dΛ where fn(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.",

keywords = "Burg's entropy, Gaussian stationary process, Non‐parametric hypothesis testing, asymptotic relative efficiency, contiguous alternative, efficacy, exponential spectral model, non‐parametric spectral estimator, spectral density",

author = "Masanobu Taniguchi and Masao Kondo",

year = "1993",

month = jul,

doi = "10.1111/j.1467-9892.1993.tb00153.x",

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T1 - NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

AU - Taniguchi, Masanobu

AU - Kondo, Masao

PY - 1993/7

Y1 - 1993/7

N2 - Abstract. Suppose that {Xt} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{fn(Λ)}dΛ where fn(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.

AB - Abstract. Suppose that {Xt} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{fn(Λ)}dΛ where fn(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.

KW - Burg's entropy

KW - Gaussian stationary process

KW - Non‐parametric hypothesis testing

KW - asymptotic relative efficiency

KW - contiguous alternative

KW - efficacy

KW - exponential spectral model

KW - non‐parametric spectral estimator

KW - spectral density

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JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

IS - 4

ER -

NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

Abstract

Keywords

ASJC Scopus subject areas

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