When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices

Yamada, Hiroshi; Yoon, Gawon

doi:10.1016/j.jimonfin.2013.08.011

Cited by 35 publications

(32 citation statements)

References 31 publications

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“…Past studies (see inter alia Yamada and Yoon, 2014;Ghoshray et al, 2014;Harvey et al, 2010;Kellard and Wohar, 2006) have shown that commodities may not be characterised by an unbroken trend. It is well known in the literature that unit root tests have low power in the presence of a structural break (Perron, 1989), so unit root tests can be undertaken allowing for structural breaks (for example, Zivot and Andrews, 1992;Perron, 1997;Perron and Rodriguez, 2003).…”

Section: Methodological Issuesmentioning

confidence: 99%

Are Shocks Transitory or Permanent? An Inquiry into Agricultural Commodity Prices

Ghoshray¹

2018

J Agricultural Economics

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This paper contributes to the contentious topic of whether shocks to agricultural commodity prices are permanent or transitory. This is an important issue with regards to forecasting, economic modelling of agricultural prices and risk management. Past studies have not accounted for important characteristics of agricultural prices that matter when testing whether shocks to prices are permanent or transitory. These include the presence or absence of a deterministic trend, the possible break in the trend, non‐stationary volatility, and the problem of the initial deviation of commodity prices from their long‐run mean or trend. We conduct a comprehensive test that incorporates all these characteristics known to plague agricultural commodity prices. Though the conclusion is mixed, the balance is in favour of agricultural price shocks being permanent in nature. This result departs from the general view that in theory, agricultural prices should be stationary, suggesting that the controversy of whether shocks to agricultural prices are temporary or permanent is not yet over.

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Section: Methodological Issuesmentioning

confidence: 99%

Are Shocks Transitory or Permanent? An Inquiry into Agricultural Commodity Prices

Ghoshray¹

2018

J Agricultural Economics

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“…An overview of 1 -trend filtering is given in [33]. Some applications are in financial time series ( [53]), macroeconomics ( [52]) automatic control ( [41]), oceanography ( [51]) and geophysics ( [34]). In 1 -trend filtering, the function a is piecewise linear.…”

Section: 2mentioning

confidence: 99%

“…It was shown in [19] that the tensor T p,q,r has a diagonal singular value decomposition, but perm n and det n do not for n ≥ 3. 53 13.5. Group algebra tensors.…”

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confidence: 99%

A General Theory of Singular Values with Applications to Signal Denoising

Derksen¹

2018

SIAM J. Appl. Algebra Geometry

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We study the Pareto frontier for two competing norms · X and · Y on a vector space. For a given vector c, the Pareto frontier describes the possible values of ( a X , b Y ) for a decomposition c = a + b. The singular value decomposition of a matrix is closely related to the Pareto frontier for the spectral and nuclear norm. We will develop a general theory that extends the notion of singular values of a matrix to arbitrary finite dimensional euclidean vector spaces equipped with dual norms. This also generalizes the diagonal singular value decompositions for tensors introduced by the author in previous work. We can apply the results to denoising, where c is a noisy signal, a is a sparse signal and b is noise. Applications include 1D total variation denoising, 2D total variation Rudin-Osher-Fatemi image denoising, LASSO, basis pursuit denoising and tensor decompositions. arXiv:1705.10881v1 [math.NA] 30 May 2017 4 12. Total Variation Denoising in Imaging 48 12.1. The 2D total variation norm 48 12.2. Spareseness and total variation 49 12.3. The total variation norm is not tight 50 13. Tensor Decompositions 50 13.1. CP decompositions 50 13.2. The CoDe model and the nuclear norm 51 13.3. Examples of unitangent tensors 51 13.4. The diagonal SVD and the slope decomposition 52 13.5. Group algebra tensors 54 13.6. symmetric tensors in R 2×2×2 54 References 57 2. Main Results 2.1. The Pareto frontier. Let us consider a finite dimensional R-vector space V equipped with two norms, · X and · Y .Suppose that c ∈ V . We are looking for decompositions c = a + b that are optimal in the sense that we cannot reduce a X without increasing b Y and we cannot reduct b Y without increasing a X . We recall the definition from the introduction:there exists a decomposition c = a + b with a X = x, b Y = y such that for every decomposition c = a + b we have a X > x, b Y > y or ( a X , b Y ) = (x, y). If (x, y) is a Pareto efficient pair then we call c = a + b an XY -decomposition. By symmetry, c = a + b is an XY -decomposition if and only if c = b + a is a Y Xdecomposition. The Pareto frontier consists of all Pareto efficient pairs (see [6]). The Pareto frontier is the graph of a strictly decreasing, continuous convex function f c Y X : [0, c X ] → [0, c Y ] (see [6] and Lemmas 3.2 and 3.3). If we change the role of X and Y we get the graph of f c XY , so f c XY and f c Y X are inverse functions of each other. Example 2.2. Consider the vector space V = R n . Sparseness of vectors in R n can be measured by the number of nonzero entries. For c ∈ V we defineNote that · 0 is not a norm on V because it does not satisfy λc 0 = |λ| c 0 for λ ∈ R.Convex relaxation of · 0 gives us the 1 norm · 1 . This means that the unit ball for the norm · 1 is the convex hull of all vectors c with c 0 = c 2 = 1. Let us take · X = · 1 and · Y = · ∞ and describe the Pareto frontier. Suppose that c = (c 1 · · · c n ) t ∈ R n and 0 ≤ y ≤ c ∞ . If b ∞ = y then we have

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“…The relationship between HP filtering and 1 trend filtering corresponds to that between ridge regression of Hoerl and Kennard (1970) and Lasso (least absolute shrinkage and selection operator) regression of Tibshirani (1996)/BPDN (basis pursuit denoising) of Chen et al (1998). Econometric applications of 1 trend filtering include Yamada and Jin (2013), Yamada and Yoon (2014), Winkelried (2016), and Yamada (2017a). It has been well-known that HP filtering is a form of the Whittaker-Henderson (WH) method of graduation, which is defined as:…”

Section: Introductionmentioning

confidence: 99%

Some Results on ℓ1 Polynomial Trend Filtering

Yamada

2018

Econometrics

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1 polynomial trend filtering, which is a filtering method described as an 1-norm penalized least-squares problem, is promising because it enables the estimation of a piecewise polynomial trend in a univariate economic time series without prespecifying the number and location of knots. This paper shows some theoretical results on the filtering, one of which is that a small modification of the filtering provides not only identical trend estimates as the filtering but also extrapolations of the trend beyond both sample limits.

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When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices

Cited by 35 publications

References 31 publications

Are Shocks Transitory or Permanent? An Inquiry into Agricultural Commodity Prices

Are Shocks Transitory or Permanent? An Inquiry into Agricultural Commodity Prices

A General Theory of Singular Values with Applications to Signal Denoising

Some Results on ℓ1 Polynomial Trend Filtering

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