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arxiv: 2410.23706 · v4 · submitted 2024-10-31 · 📊 stat.ME

Complex trend inference for high-dimensional piecewise locally stationary time series

Lujia Bai , David Veitch , Weichi Wu , Wenyang Zhang , Zhou Zhou This is my paper

Pith reviewed 2026-05-23 19:06 UTC · model grok-4.3

classification 📊 stat.ME
keywords high-dimensional time seriesasynchronous jump detectionnonstationary noisechange point detectiontrend estimationhomogeneity pursuitpiecewise stationarylatent group structures
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The pith

AJDN recovers the number of jumps in high-dimensional time series with prescribed probability and near-optimal localization despite asynchronicity and nonstationarity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a two-step procedure for trend inference in high-dimensional time series that are piecewise smooth, experience jumps at different times across dimensions, and are observed under nonstationary noise. In the first step AJDN detects and localizes the asynchronous jumps using a multiscale approach that does not require stationarity. In the second step AJDN-H identifies latent groups of dimensions that share jump locations and trend parameters, then pools information across those groups to improve estimation accuracy. A sympathetic reader would care because many applied datasets exhibit exactly these violations, which cause standard high-dimensional change-point tools to lose consistency or localization power.

Core claim

The paper establishes that AJDN, a multiscale framework, consistently recovers the number of jumps with a prescribed asymptotic probability and achieves nearly optimal localization rates in the presence of asynchronicity and nonstationarity. Augmenting it with a homogeneity pursuit step produces AJDN-H, which identifies latent groups sharing common jump structures and trend parameters, enabling efficient information pooling and more accurate trend estimation under the same conditions.

What carries the argument

AJDN, the Asynchronous Jump Detection under Nonstationary Noise multiscale framework, which identifies and localizes jumps while handling nonstationarity and asynchronicity before a homogeneity pursuit step groups dimensions for pooled trend estimation.

If this is right

  • AJDN recovers the number of jumps with a prescribed asymptotic probability.
  • AJDN achieves nearly optimal localization rates even with asynchronicity and nonstationarity.
  • AJDN-H improves trend estimation accuracy by pooling information across identified groups.
  • The procedure remains robust in finite samples and demonstrates utility on financial data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The separation of jump detection from group identification allows each component to be refined independently in follow-on work.
  • The efficiency gains from homogeneity pursuit scale with how many dimensions truly share structures, suggesting a diagnostic for group strength could be added.

Load-bearing premise

The observed series arise from piecewise smooth signals that possess latent group structures allowing dimensions to share common jump locations and trend parameters.

What would settle it

A simulation or dataset with known jump locations, nonstationary noise, and asynchronicity in which AJDN fails to recover the correct number of jumps at the claimed asymptotic probability would falsify the consistency result.

Figures

Figures reproduced from arXiv: 2410.23706 by David Veitch, Lujia Bai, Weichi Wu, Wenyang Zhang, Zhou Zhou.

Figure 1
Figure 1. Figure 1: shows this phenomena during the 2023 Turkey-Syria earthquake, where the epicentre occurred in south central Turkey. Seismic monitors pick up the the second major earthquake at 10:25:40 in the municipality of Yunak, Konya located in central Turkey, and 70 seconds later in the town of Enez, Edirne which is in northwestern Turkey. Furthermore, we detect nonconstant first￾order autocorrelation at both stations… view at source ↗
Figure 2
Figure 2. Figure 2: Application of optimal jump pass filter W(x) to an example univariate time series with a piecewise smooth mean function, with the two jumps denoted by red lines. For a single scale s = 0.1 we can see |H(t, 0.1, 1)| is maximized at the jump points. [t − s¯r, t − sr ] ∪ [t + sr , t + ¯sr]: σˆ 2 r,t := P i∈Kr,left(t) (yr,i − y¯r,left(t))2 + P i∈Kr,right(t) (yr,i − y¯r,right(t))2  |Kr,left(t)| + |Kr,right(t)… view at source ↗
Figure 3
Figure 3. Figure 3: Map of times when the first earthquake was detected by AJDN. Resolution of the data was one observation every 10 seconds. AJDN detected the earthquake earlier for stations closer to the epicenter (denoted by E) than those further away. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representative dimension of seismic readings from Turkey during the 2023 Turkey-Syria earthquake. KO KLYT is located in Istanbul, in the northwest corner of Turkey. Three jumps were detected at the dotted red lines, and the blue region was used to inform a range of s ′ to test [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of jumps detected by AJDN, each bucket represents 5 minutes. The majority of jumps AJDN detects are around the times of the major earthquakes (shown by red dotted lines). We select s ′ and (s, s¯) (the shared scales used in all dimensions) by minimizing the penalized BIC criterion outlined in Appendix B.1.1. In order to select an appropriate range of s ′ to test, we first choose a time window … view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of jumps detected by different methods. Each line represents a time at which a jump is detected. The major earthquakes occur around 2023/02/06 01:17 UTC and 10:24 UTC. LOCLIN and AJDN, with what appears to be more spurious jumps detected. INSPECT appears to detect too many jumps, particularly after the major earthquakes. This is possibly due to a smooth downward trend in the signal after the maj… view at source ↗
Figure 7
Figure 7. Figure 7: Jumps detected by AJDN on earthquake dataset. Across all dimensions a total of 99 jumps were detected. Red lines denote time where jump detected for a specific sensor. In every dimension the two major earthquakes appear to have been detected. α set at .05. References Aue, A. and Horv´ath, L. (2013). Structural breaks in time series. Journal of Time Series Analysis, 34(1):1–16. Bai, Y. and Safikhani, A. (20… view at source ↗
Figure 8
Figure 8. Figure 8: Power curves for different data generating processes while varying the signal to noise ratio. In these simulations one dimension experiences a jump at t = 0.5. 70 [PITH_FULL_IMAGE:figures/full_fig_p070_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Examples of different simulated data generating processes. B.2.3 Calculation of MAD Three considerations must be taken into account for the calculation of MAD. First, only detected jumps that fall within a log n log p 2n∆2 n neighbourhood of the true jump enter into the calculation of MAD. If a detected jump falls outside of this region we take the jump as not having been successfully detected. Second, for… view at source ↗
Figure 10
Figure 10. Figure 10: Map of seismic sensors (X) and epicenter (E) for which readings are analyzed on 02- 05-2023 and 02-06-2023. B.4 Real Data Analysis - Stocks Dataset Closing daily stock prices adjusted for dividends for the five stocks collectively known as the FAANG stocks (Facebook, Amazon, Apple, Netflix, and Google) were collected from 2021-01-01 to 2022-12-31 using the quantmod package in R from Ryan and Ulrich (2022)… view at source ↗
Figure 11
Figure 11. Figure 11: Example of transformation applied to stock price data. We run a jump detection algo￾rithm on the value of each stock divided by the value of an index (AMZN/QQQ in this case) [PITH_FULL_IMAGE:figures/full_fig_p073_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Jumps identified by AJDN across 5 technology stocks in 2021 and 2022. To select both s ′ and {(s, s¯)} p r=1 we select the combination of these parameters that minimize the average penalized-BIC across all dimensions. For computational reasons we set (sr , s¯r) = (s, s¯) for all r = 1, . . . , p. Given that these companies report financial results every quarter throughout the year, we test a range of cand… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of jumps detected by different methods. Each line represents a time at which a jump is detected. The companies tend to report earnings about one month after the end of a quarter. jumps are detected across all 5 stocks. To examine the validity of the jumps detected by AJDN, we examine a representative dimension, AMZN, and attempt to explain if there were underlying events which can explain the d… view at source ↗
Figure 14
Figure 14. Figure 14: Jumps detected by AJDN for the stock price of Amazon.com (AMZN) relative a NAS￾DAQ ETF (QQQ). Here AMZN experiences 14 jumps (shown by dotted lines) throughout 2021 and 2022, most of which represent idiosyncratic shocks (see [PITH_FULL_IMAGE:figures/full_fig_p076_14.png] view at source ↗
read the original abstract

This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting latent group structures to estimate trend functions. In the first step, we propose AJDN (Asynchronous Jump Detection under Nonstationary Noise), a multiscale framework for the identification and localization of jumps in high-dimensional time series. We show that AJDN consistently recovers the number of jumps with a prescribed asymptotic probability and achieves nearly optimal localization rates in the presence of asynchronicity and nonstationarity, both of which often violate the assumptions of existing high-dimensional change point methods and thereby deteriorate their performance. In the second step, we augment AJDN with a homogeneity pursuit step and obtain AJDN-H, which identifies latent groups of dimensions that share common jump structures and trend parameters given the detected jumps. This allows for efficient information pooling and improves the accuracy of trend estimation under both asynchronicity and nonstationarity. The robustness and finite-sample performance of the proposed methodology are examined by extensive simulation studies. An application to financial data demonstrates the practical utility of the AJDN-H framework in complex, high-dimensional settings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 4 minor

Summary. The manuscript proposes AJDN, a multiscale framework for detecting and localizing asynchronous jumps in high-dimensional piecewise locally stationary time series under nonstationary noise without requiring stationarity assumptions. It establishes that AJDN consistently recovers the number of jumps with a user-prescribed asymptotic probability and attains nearly optimal localization rates. The paper then introduces AJDN-H, which augments AJDN with a homogeneity-pursuit step to identify latent groups of dimensions sharing common jump locations and trend parameters, enabling pooled estimation of the trend functions. Theoretical claims are supported by simulation studies and an application to financial data.

Significance. If the stated consistency and rate results hold under the piecewise-smooth-signal model, the work would meaningfully extend high-dimensional change-point methodology by accommodating asynchronicity and nonstationarity, settings that degrade existing procedures. The explicit separation of the detection step from the subsequent grouping step, together with the practical demonstration on financial series, strengthens the contribution.

minor comments (4)
  1. [Model and assumptions] The precise definition of the piecewise-smooth class (smoothness index, jump-size lower bound) should be stated explicitly in the model section before the consistency theorem, as it directly governs the localization rate.
  2. [Main theoretical result] In the statement of the localization rate, clarify whether the nearly-optimal claim is with respect to the minimax rate derived in the paper or to a cited lower bound from the literature; add the relevant reference if the latter.
  3. [Numerical studies] The simulation section reports recovery probabilities but does not tabulate the empirical coverage of the prescribed asymptotic probability across the range of dimensions and noise levels considered; adding such a table would strengthen the finite-sample validation.
  4. [AJDN algorithm] Notation for the multiscale scanning statistic should be introduced once and used consistently; currently the same symbol appears to be overloaded between the single-scale and aggregated versions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of the manuscript, including the accurate summary of the AJDN and AJDN-H contributions and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract and description present AJDN as a multiscale framework with claimed consistency and rate results for jump recovery under nonstationarity and asynchronicity, followed by a homogeneity pursuit step for AJDN-H. No equations, derivation steps, fitted parameters renamed as predictions, or self-citation chains are visible in the provided material. The central claims are stated as theoretical results without any reduction to inputs by construction or load-bearing self-references that would require external verification within the text. The derivation is therefore treated as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, background axioms, or newly postulated entities.

pith-pipeline@v0.9.0 · 5746 in / 1044 out tokens · 25067 ms · 2026-05-23T19:06:09.000299+00:00 · methodology

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

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    Notice that ∥II r,1(t) − EII r,1(t)∥log p = ∥ X i∈Kr,lef t(t) ∞X j=0 Pi−jϵ2 r,i∥log p ≤ ∞X j=0 ∥ X i∈Kr,lef t(t) Pi−jϵ2 r,i∥log p (46) By Burkholder inequality of martingale difference (Rio (2009)), we have ∥ X i∈Kr,lef t(t) Pi−jϵ2 r,i∥2 log p ≤ C log p X Kr,lef t(t) ∥Pi−jϵ2 r,i∥2 log p ≤ C log p X Kr,lef t(t) ∥ϵ2 r,i − (ϵ(i−j) r,i )2∥2 log p (47) for som...

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    (62) Proof

    Assume conditions (M), (A), (B), then max 1≤r≤p sup t∈(Tr,d∪idr,i)∩Tr,c |Eˆσ2 r,t − σ2 r(t)| = O(¯s2 max + 1 n¯smin ). (62) Proof. By the proof of Proposition 1, we have E( X i∈Kr,lef t (yr,i − ¯yr,lef t(t))2) = Ir,lef t(t) + E(II r,lef t(t)), (63) where as defined in Ir(t) and II r(t) of Proposition 1, Ir,lef t(t) = X i∈Kr,lef t(t) (βr(ti) − ¯βr,lef t(t)...

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    Meanwhile, Ir,lef t(t) and Ir,right(t) are nonnegative for 1 ≤ r ≤ p

    By condi- tion (M), it follows that for 1 ≤ r ≤ p and t ∈ [¯sr, 1− ¯sr], |Ir,lef t(t)|/|Kr,·(t)| and |Ir,right(t)|/|Kr,·(t)| are uniformly bounded. Meanwhile, Ir,lef t(t) and Ir,right(t) are nonnegative for 1 ≤ r ≤ p. Observ- ing (67) and (70), by condition (A5) we have for n sufficiently large, there exist positive constants ˜M1 and ˜M2 such that ˜M1 ≤ E...

    work page 2024

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    (74) Further assume that |∆r,i,n| s+ 1 ns → ∞

    Then uniformly for all t ∈ [dr,i − s, dr,i + s], 1 ≤ i ≤ mr,n, we have ˜G(t, s, r) = √ns∆r,i,n + O(√ns(s + 1 ns)) (73) where ∆r,i,n = βr(dr,i−) − βr(dr,i+), and if t ∈ (dr,i + s, dr,i+1 − s], 0 ≤ i ≤ mr,n then ˜G(t, s, r) = O(√ns(sk+1 + 1 ns). (74) Further assume that |∆r,i,n| s+ 1 ns → ∞. Then uniformly for |t − dr,i| ≤ s, 1 ≤ i ≤ mr,n we have that (i) ˜...

    work page 2024

  12. [12]

    (81) Notice that H2(ti, sr,j, r) − H2(dr,v, sr,j, r) = Ir,v(ti, sr,j) + II r,v(ti, sr,j) + III r,v(ti, sr,j) (82) where Ir,v(ti, sr,j) = ˜G2(ti, sr,j, r) − ˜G2(dr,v, sr,j, r), (83) II r,v(ti, sr,j) = 2 ˜G(ti, sr,j, r) ˜H(ti, sr,j, r) − 2 ˜G(dr,v, sr,j, r) ˜H(dr,v, sr,j, r) (84) III r,v(ti, sr,j) = ˜H2(ti, sr,j, r) − ˜H2(dr,v, sr,j, r) (85) By Proposition ...

    work page 2024

  13. [13]

    (129) We now show this theorem via two steps

    Therefore by applying Proposition 7, we shall see that sup Ir∈Tr,d,1≤r≤p, x∈R P | sup 1≤r≤p 1≤j≤δn ti∈Ir | ˜H(ti, sr,j, r)|q Eˆσ2 r,t | ≤ x − P | sup 1≤r≤p 1≤j≤δn ti∈Ir | ˜H y(ti, sr,j, r)|q Eˆσ2 r,ti | ≤ x = O((nsmin)−1/8 log4 n). (129) We now show this theorem via two steps. Step (i). We compare sup 1≤r≤p 1≤j≤δn i:ti∈Ir | ˜H(ti,s,r)|√ Eˆσ2 r,ti with sup...

    work page 2009

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    Proof of Theorem 5 Proof

    (175) The theorem then follows in view of (170), (171) and (175). Proof of Theorem 5 Proof. By the argument of Equation (51) we shall see that Ωκ := ∞X i=1 δκ(L, i) = O(κ2), (176) which means γ := lim sup κ→∞ Ωkκ1/2−1/(2/5) < ∞ (177) Then by the proof of (ii) of Theorem 4 of Wu and Zhou (2024) with β = 2/5 there (see also Theorem 4 of Wu (2005)), we have ...

    work page 2024

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    Combining steps I, II and III we show (188) which completes the proof

    Therefore Equation (188) with Θr,v(t) = Ir,v(t) holds. Combining steps I, II and III we show (188) which completes the proof. A.4 Gaussian Approximation for high dimensional nonstationary time series The next proposition extends the gaussian approximation for maximum of high dimensional time series of Zhang and Cheng (2018) to the approximations for the p...

    work page 2018

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    (204) Moreover, by Lemma A.3 of Chernozhukov et al

    Moreover, for every w ∈ Rp′ and τ ∈ [0, 1], for every z ∈ Rp′ such that max j≤p′ |zj|β ≤ 1, we have Ujk(w) ⪅ Ujk(w + τz) ⪅ Ujk(w), Ujkl(w) ⪅ Ujkl(w + τz) ⪅ Ujkl(w). (204) Moreover, by Lemma A.3 of Chernozhukov et al. (2013), we have |Fβ(w1) − Fβ(w2)| ≤ max 1≤j≤p |w1,j − w2,j| (205) for any p′ dimensional vectors w1 = (w1,1, ..., w1,p)⊤ and w2 = (w2,1, ......

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    Let yi, 1 ≤ i ≤ n be the Guassian random vectors which have the same autocovariance structure as xi, 1 ≤ i ≤ n

    Let {xi} be an M dependent vector and mean zero time series. Let yi, 1 ≤ i ≤ n be the Guassian random vectors which have the same autocovariance structure as xi, 1 ≤ i ≤ n. Let yW i and yW,S i be the vector define using yi, weight function W and scales skqk, 1 ≤ k ≤ p with evaluation points i/n such that skqk ≤ i/n ≤ 1 − skqk. through an analogue of (198)...

    work page 2018

  18. [18]

    sup t∈[0,1] (2 √ t + √ 1 − t)Mxy/√nsmin ≤ √ 5(4M + 1)Mxy/√nsmin ≤ β−1. (210) Following the proof of Proposition 2.1 of Zhang and Cheng (2018) with slight modification we have that I2 ⪅ (G2 + G1β) Z 1 0 max 1≤j≤p nX i=1 |E( ˙Zij(t)V (i) k (t))| +(G3 + G2β + G1β2) Z 1 0 max 1≤k,j,l≤p nX i=1 E| ˙Zij(t)V (i) k (t)V(i) l (t)|dt := (G2 + G1β)I21 + (G3 + G2β + G...

    work page 2018

  19. [19]

    Then we have sup A∈ARe |P(XW,S ∈ A) − P(YW,S ∈ A)| ⪅ (nsmin)−1/8 log4 n

    Assume that p = O(nι) and δn = O(nι) for some ι > 0, and that there exist constant ι1 > ι 0 such that d1n−ι1 ≤ smin ≤ ¯smax < d 0n−ι0 for some small positive constant d1 and large constant d0. Then we have sup A∈ARe |P(XW,S ∈ A) − P(YW,S ∈ A)| ⪅ (nsmin)−1/8 log4 n. (219) Proof. Recall p′ =Pp s=1 msqs = O(nδnp) = O(n1+2ι). Let q be a sufficiently large con...

    work page 2009

  20. [20]

    We evaluate ϕW,S(Mx, My). It is obvious that ϕW,S(Mx, My) ≤ ϕW,S(Mx) + ϕW,S(My) where ϕW,S(Mx) = max 1≤j,k≤p′ nX i=1 | X l:|l−i|≤M,1≤l≤n (E˜xW,S,(M) ij ˜xW,S,(M) lk − ExW,S,(M) ij xW,S,(M) lk )|, (224) ϕW,S(My) = max 1≤j,k≤p′ nX i=1 | X l:|l−i|≤M,1≤l≤n (E˜yW,S,(M) ij ˜yW,S,(M) lk − EyW,S,(M) ij yW,S,(M) lk )|. (225) 59 Notice that ϕW,S(Mx) = max 1≤j,k≤p 1...

    work page 2018

  21. [21]

    On the other hand, notice that by Corollary 1 and condition (A), via Lemma E.4 of Wu and Zhou (2024) 0 < c1 ≤ min 1≤j≤p′ V ar(X W,S j ) ≤ c′ 0 for some positive constants c0 and c′

    1 1+q (p′χM/2) 1 1+q + √n¯smax log n M q x + np(exp(−tMx) + exp(−tM 2 y )) ⪅ (φ2 + φβ)(M −1 x + M −2 y ) + (φ3 + φ2β + φβ2)M 2/√nsmin + (φq) 1 1+q (p′χM/2) 1 1+q + √n¯smax log n M q x + np(exp(−tMx) + exp(−tM 2 y )) (236) subject to √ 5(4M + 1)(Mx ∨ My)/√nsmin ≤ β−1. On the other hand, notice that by Corollary 1 and condition (A), via Lemma E.4 of Wu and ...

    work page 2024

  22. [22]

    By step 2 of the proof of Lemma 5.1 of Chernozhukov et al

    Using the argument similar to Lemma A.2 of Zhang and Cheng (2018), we obtain that there exist positive constants c1 and c2 such that c1 ≤ V ar(X W,S,(M) j ), V ar(X W,S j ) ≤ c2, 1 ≤ j ≤ p′ (237) 61 Let C be a sufficiently constant only depending on c1. By step 2 of the proof of Lemma 5.1 of Chernozhukov et al. (2017), taking β = φ log p′, it is straightf...

    work page 2018

  23. [23]

    for all φ ≥ 1 sup y∈Rp′ P(YW,S,(M) ≤ y) − P(YW,S,(M) ≤ y − φ−1) ≤ Cφ −1 log1/2 p′. (238) Combining with (236) and plugging β = φ log p′, we have that sup y∈Rp′ |P(XW,S ≤ y) − P(Y(W,S,(M)) ≤ y)| ⪅ (φ2 + φ2 log p′)(M −1 x + M −2 y ) + (φ3 + φ3 log p′ + φ3 log2 p′)M 2/√nsmin + (φq) 1 1+q (p′χM/2) 1 1+q + √n¯smax log n M q x + np′(exp(−tMx) + exp(−tM 2 y )) +...

    work page 2018

  24. [24]

    Then following step 2 in the proof of Lemma 5.1 of Chernozhukov et al

    Therefore m(w) = g(Fβ(w)) = g0(ϕFβ(w)) := mϕ(w). Then following step 2 in the proof of Lemma 5.1 of Chernozhukov et al. (2017), we shall see that for all φ ≥ 1, by taking β = φ log p, P(X ≤ y − φ−1) ≤ P(Y ≤ y − φ−1) + Cφ −1 log1/2 p + |E(mφ(X) − mφ(Y ))|, (244) P(X ≤ y − φ−1) ≥ P(Y ≤ y − φ−1) − Cφ −1 log1/2 p − |E(mφ(X) − mφ(Y ))|. (245) Here C is a const...

    work page 2017

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    every component of Y is less than or equal to x

    If Y is a p-dimensional centered Gaussian vector with strictly positive component-wise variance, it is a continuous random variable so P(||Y[A]|∞ − x| ≤ δ) = P(|Y[A]|∞ ≤ x + δ) − P(|Y[A]|∞ ≤ x − δ) = P(|Y[A]|e ≤ x + δ) − P(|Y[A]|e ≤ x − δ) = P(|Y[A]|e ≤ (x + δ)J[A]) − P(|Y[A]|e ≤ (x − δ)J[A]) = P(vec(Y[A], −Y[A]) ≤ vec((x + δ)J[A], (x + δ)J[A])) −P(vec(Y[...

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    Big Tech

    Here due to the low signal to noise ratio AJDN has a tendency to overestimate the true number of jumps due to error in estimating where the true jump is in each dimension. Table 8: Power results for (IID) and (GS) error processes with and without trends. (IID) (IIDT) (GS) (GST) γ ∆ Scenario ¯m ˆmp MAD ¯m ˆmp MAD ¯m ˆmp MAD ¯m ˆmp MAD 0.020 2 1 1.982 0.920...

    work page 2023

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    For computational reasons we set ( sr, ¯sr) = (s, ¯s) for all r = 1,

    To select both s′ and {(s, ¯s)}p r=1 we select the combination of these parameters that minimize the average penalized-BIC across all dimensions. For computational reasons we set ( sr, ¯sr) = (s, ¯s) for all r = 1, . . . , p. Given that these companies report financial results every quarter throughout the year, we test a range of candidate ¯ s of approxim...

    work page 2021

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    When comparing the performance of AJDN versus other methods, we see in Figure 13 that AJDN is able to identify both jumps specific to each individual stock, as well as times where jumps for both stocks occur around the same time. We see that both LOCLIN and DBLCUSUM are able to identify many of the jumps around quarterly earnings announcements, but appear...

    work page 2021

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    Amazon CEO Jeff Bezos will leave his post later this year, turning the helm over to the company’s top cloud executive Andy Jassy

    Jump Date Major Event Date Quote 2021/02/08 2021/02/02 “Amazon CEO Jeff Bezos will leave his post later this year, turning the helm over to the company’s top cloud executive Andy Jassy.” 2021/04/15 2021/07/02 2021/07/06 “The Department of Defense announced Tuesday it’s calling off the $10 billion cloud contract that was the subject of a legal battle invol...

    work page 2021