Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI  

DOI： 10.3390/math12172746

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publisher：Springer Cham  

DOI： 10.1007/978-3-031-64608-9_15

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI  

DOI： 10.3390/math12121820

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier  

DOI： 10.1016/j.spasta.2023.100799

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI  

DOI： 10.3390/math12020253

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.3390/math11204228

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter {GmbH}  

This paper considers an extension of Hodrick-Prescott (HP) filter. It is a hybrid of HP filter and multiple regression. We refer to the filter as "HPX filter". It is well known that HP filter has a unique global minimizer and the solution can be represented in matrix notation explicitly. Does HPX filter also have a unique global minimizer? Is it accomplished without any additional assumptions? Can the solution be expressed in matrix notation explicitly? In this paper, we answer these questions. In addition, this paper (i) provides an alternative perspective on the filter by representing it as a generalized ridge regression and (ii) gives an extension of it, which is a hybrid of Whittaker-Henderson method of graduation and multiple regression.

DOI： 10.1515/snde-2023-0004

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter {GmbH}  

<jats:title>Abstract</jats:title>
<jats:p>Using notions from linear algebraic graph theory, this article provides a unified perspective on some autocorrelation measures in different fields. They are as follows: (a) Orcutt’s first serial correlation coefficient, (b) Anderson’s first circular serial correlation coefficient, (c) Moran’s <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0574_eq_001.png" />
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:msub>
<m:mrow>
<m:mi>r</m:mi>
</m:mrow>
<m:mrow>
<m:mn>11</m:mn>
</m:mrow>
</m:msub>
</m:math>
<jats:tex-math>{r}_{11}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>, and (d) Moran’s <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0574_eq_002.png" />
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:mi>I</m:mi>
</m:math>
<jats:tex-math>I</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>. The first two are autocorrelation measures for one-dimensional data equally spaced, such as time series data, and the last two are for spatial data. We prove that (a)–(c) are a kind of (d). For example, we show that (d) such that its spatial weight matrix equals the adjacency matrix of a path graph is the same as (a). The perspective is beneficial because studying the properties of (d) leads to studying the properties of (a)–(c) at the same time. For example, the bounds of (a)–(c) can be found from the bounds of (d).</jats:p>

DOI： 10.1515/math-2022-0574

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa UK Limited  

DOI： 10.1080/00949655.2022.2144314

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

<jats:title>Abstract</jats:title><jats:p>Hodrick–Prescott (HP) filter is a popular trend filtering method for univariate macroeconomic time series such as real gross domestic product. This paper considers the quantile regression version of HP filter (qHP filter), which is a filtering method defined by replacing quadratic loss function of HP filter with quantile regression loss function. One of the essential properties of quantile regression is that if the regression includes intercept, then the ratio of negative residuals can be almost controlled. Does the suggested qHP filter also have the property? This paper answers this question. In addition to the main result, we provide an empirical illustration.</jats:p>

DOI： 10.1007/s00181-022-02292-8

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press ({CUP})  

<jats:p>The Hodrick–Prescott (HP) filter has been a popular method of trend extraction from economic time series. However, it is impractical without modification if some observations are not available. This paper improves the HP filter so that it can be applied in such situations. More precisely, this paper introduces two alternative generalized HP filters that are applicable for this purpose. We provide their properties and a way of specifying those smoothing parameters that are required for their application. In addition, we numerically examine their performance. Finally, based on our analysis, we recommend one of them for applied studies.</jats:p>

DOI： 10.1017/s0266466621000189

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

The$$\ell _{1}$$trend filtering enables us to estimate a continuous piecewise linear trend of univariate time series. This filter and its variants have subsequently been applied in various fields, including astronomy, climatology, economics, electronics, environmental science, finance, and geophysics. Although the$$\ell _{1}$$trend filtering can estimate a continuous piecewise linear trend of univariate time series, it cannot estimate a common continuous piecewise linear trend of multiple time series. This paper develops a statistical procedure that enables us to estimate it, which is a multivariate extension of the$$\ell _{1}$$trend filtering. We provide an algorithm for estimating it and a clue to specify the tuning parameter of the procedure, both required for its application. We also (i) numerically illustrate how well the algorithm works, (ii) provide an empirical illustration, and (iii) introduce a generalization of our novel method.

DOI： 10.1007/s10614-021-10114-9

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Other Link： https://link.springer.com/article/10.1007/s10614-021-10114-9/fulltext.html

Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.3390/math9192465

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/03610926.2020.1838547

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Authorship：Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：{MDPI} {AG}  

<jats:p>Fitting a cubic smoothing spline is a typical smoothing method. This paper reveals a principle of duality in the penalized least squares regressions relating to the method. We also provide a number of results derived from them, some of which are illustrated by a real data example.</jats:p>

DOI： 10.3390/math8101839

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press ({CUP})  

<jats:p>In recent decades, in the research community of macroeconometric time series analysis, we have observed growing interest in the smoothing method known as the Hodrick–Prescott (HP) filter. This article examines the properties of an alternative smoothing method that looks like the HP filter, but is much less well known. We show that this is actually more like the exponential smoothing filter than the HP filter although it is obtainable through a slight modification of the HP filter. In addition, we also show that it is also like the low-frequency projection of Müller and Watson (2018, <jats:italic>Econometrica</jats:italic> 86, 775–804). We point out that these results derive from the fact that all three similar smoothing methods can be regarded as a type of graph spectral filter whose graph Fourier transform is discrete cosine transform. We then theoretically reveal the relationship between the similar smoothing methods and provide a way of specifying the smoothing parameter that is necessary for its application. An empirical examination illustrates the results.</jats:p>

DOI： 10.1017/s0266466619000379

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/03610926.2018.1563183

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter {GmbH}  

<jats:title>Abstract</jats:title>
<jats:p>By applying the Sherman–Morrison–Woodbury (SMW) formula and a discrete cosine transformation matrix, De Jong and Sakarya [De Jong, R. M., and N. Sakarya. 2016. “The Econometrics of the Hodrick–Prescott Filter.” <jats:italic>Review of Economics and Statistics</jats:italic> 98 (2): 310–317] recently derived an explicit formula for the smoother weights of the Hodrick–Prescott filter. More recently, by applying the SMW formula and the spectral decomposition of a symmetric tridiagonal Toeplitz matrix, Cornea-Madeira [Cornea-Madeira, A. 2017. “The Explicit Formula for the Hodrick–Prescott Filter in Finite Sample.” <jats:italic>Review of Economics and Statistics</jats:italic> 99: 314–318] provided a simpler formula. This paper provides an alternative simpler formula for it and explains the reason why our approach leads to a simpler formula.</jats:p>

DOI： 10.1515/snde-2018-0035

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/03610926.2018.1481974

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/03610926.2018.1476713

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：{MDPI} {AG}  

DOI： 10.3390/econometrics6030033

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter GmbH  

DOI： 10.1515/snde-2016-0073

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Taylor and Francis Inc.  

DOI： 10.1080/03610926.2017.1285934

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Routledge  

DOI： 10.1080/13504851.2017.1299095

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Verlag  

DOI： 10.1007/s00181-017-1349-8

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/03610926.2016.1252403

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/03610926.2016.1179764

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s00181-015-1048-2

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Authorship：Lead author,　Last author,　Corresponding author   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/13504851.2016.1223811

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1515/snde-2014-0089

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.14490/jjss.45.121

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/07474938.2013.808488

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jimonfin.2013.08.011

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/13504851.2014.907474

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICA-VERLAG GMBH & CO  

DOI： 10.1007/s00181-012-0625-x

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Organisation for Economic Co-Operation and Development ({OECD})  

DOI： 10.1787/jbcma-2011-5kg0pb01sbbt

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/13504850802570384

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Organisation for Economic Co-Operation and Development ({OECD})  

DOI： 10.1787/jbcma-v2007-art12-en

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/17446540500226197

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/1350485042000307152

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Informa {UK} Limited  

DOI： 10.1080/1744654042000296862

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/00036840210128708

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S1042-4431(02)00007-0

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/135048500351564

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/135048599352141

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Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

DOI： 10.1016/s0165-1765(98)00154-2

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0304-4076(97)00109-7

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0165-1765(97)00157-2

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Language：English   Presentation type：Oral presentation (general)  

Venue：Hiroshima, Japan  

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