scholarly journals Linear Programming Estimators and Bootstrapping for Heavy Tailed Phenomena

1997 ◽  
Vol 29 (3) ◽  
pp. 759-805 ◽  
Author(s):  
Paul D. Feigin ◽  
Sidney I. Resnick
Keyword(s):  
Time Series ◽  
Linear Programming ◽  
Asymptotic Distribution ◽  
Rates Of Convergence ◽  
Parameter Estimates ◽  
Autoregressive Time Series ◽  
Bootstrap Procedure ◽  
Heavy Tailed

For autoregressive time series with positive innovations which either have heavy right or left tails, linear programming parameter estimates of the autoregressive coefficients have good rates of convergence. However, the asymptotic distribution of the estimators depends heavily on the distribution of the process and thus cannot be used for inference. A bootstrap procedure circumvents this difficulty. We verify the validity of the bootstrap and also give some general comments on the bootstrapping of heavy tailed phenomena.

scholarly journals Linear Programming Estimators and Bootstrapping for Heavy Tailed Phenomena

1997 ◽  
Vol 29 (03) ◽  
pp. 759-805 ◽  
Author(s):  
Paul D. Feigin ◽  
Sidney I. Resnick
Keyword(s):  
Time Series ◽  
Linear Programming ◽  
Asymptotic Distribution ◽  
Rates Of Convergence ◽  
Parameter Estimates ◽  
Autoregressive Time Series ◽  
Bootstrap Procedure ◽  
Heavy Tailed

For autoregressive time series with positive innovations which either have heavy right or left tails, linear programming parameter estimates of the autoregressive coefficients have good rates of convergence. However, the asymptotic distribution of the estimators depends heavily on the distribution of the process and thus cannot be used for inference. A bootstrap procedure circumvents this difficulty. We verify the validity of the bootstrap and also give some general comments on the bootstrapping of heavy tailed phenomena.

scholarly journals Identifying resting locations of a small elusive forest carnivore using a two-stage model accounting for GPS measurement error and hidden behavioral states

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Dalton J. Hance ◽  
Katie M. Moriarty ◽  
Bruce A. Hollen ◽  
Russell W. Perry
Keyword(s):  
Time Series ◽  
Measurement Error ◽  
Gaussian State ◽  
Parameter Estimates ◽  
Accelerometer Data ◽  
Two Stage ◽  
Location Data ◽  
Gps Measurement ◽  
Activity Measurements ◽  
Behavioral States

Abstract Background Studies of animal movement using location data are often faced with two challenges. First, time series of animal locations are likely to arise from multiple behavioral states (e.g., directed movement, resting) that cannot be observed directly. Second, location data can be affected by measurement error, including failed location fixes. Simultaneously addressing both problems in a single statistical model is analytically and computationally challenging. To both separate behavioral states and account for measurement error, we used a two-stage modeling approach to identify resting locations of fishers (Pekania pennanti) based on GPS and accelerometer data. Methods We developed a two-stage modelling approach to estimate when and where GPS-collared fishers were resting for 21 separate collar deployments on 9 individuals in southern Oregon. For each deployment, we first fit independent hidden Markov models (HMMs) to the time series of accelerometer-derived activity measurements and apparent step lengths to identify periods of movement and resting. Treating the state assignments as given, we next fit a set of linear Gaussian state space models (SSMs) to estimate the location of each resting event. Results Parameter estimates were similar across collar deployments. The HMMs successfully identified periods of resting and movement with posterior state assignment probabilities greater than 0.95 for 97% of all observations. On average, fishers were in the resting state 63% of the time. Rest events averaged 5 h (4.3 SD) and occurred most often at night. The SSMs allowed us to estimate the 95% credible ellipses with a median area of 0.12 ha for 3772 unique rest events. We identified 1176 geographically distinct rest locations; 13% of locations were used on > 1 occasion and 5% were used by > 1 fisher. Females and males traveled an average of 6.7 (3.5 SD) and 7.7 (6.8 SD) km/day, respectively. Conclusions We demonstrated that if auxiliary data are available (e.g., accelerometer data), a two-stage approach can successfully resolve both problems of latent behavioral states and GPS measurement error. Our relatively simple two-stage method is repeatable, computationally efficient, and yields directly interpretable estimates of resting site locations that can be used to guide conservation decisions.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals Marketing Mix Modeling Using PLS-SEM, Bootstrapping the Model Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1832
Author(s):  
Mariano Méndez-Suárez
Keyword(s):  
Time Series ◽  
Structural Changes ◽  
Marketing Mix ◽  
Structural Equations ◽  
Superior Performance ◽  
Parameter Estimates ◽  
Significance Analysis ◽  
Autocorrelation Structure ◽  
Multichannel Retailing ◽  
Black Friday

Partial least squares structural equations modeling (PLS-SEM) uses sampling bootstrapping to calculate the significance of the model parameter estimates (e.g., path coefficients and outer loadings). However, when data are time series, as in marketing mix modeling, sampling bootstrapping shows inconsistencies that arise because the series has an autocorrelation structure and contains seasonal events, such as Christmas or Black Friday, especially in multichannel retailing, making the significance analysis of the PLS-SEM model unreliable. The alternative proposed in this research uses maximum entropy bootstrapping (meboot), a technique specifically designed for time series, which maintains the autocorrelation structure and preserves the occurrence over time of seasonal events or structural changes that occurred in the original series in the bootstrapped series. The results showed that meboot had superior performance than sampling bootstrapping in terms of the coherence of the bootstrapped data and the quality of the significance analysis.

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