Model-based INAR bootstrap for forecasting INAR(p) models

Bisaglia, Luisa; Gerolimetto, Margherita

doi:10.1007/s00180-019-00902-1

Cited by 8 publications

(9 citation statements)

References 40 publications

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“…Bisaglia & Gerolimetto (2019) used the empirical distribution

F_{x_{n}}^{b}

based on groups of bootstrap resamples of the real data x n to obtain the

false(1 prefix- α false)

prediction interval:

\begin{matrix} alignleft \\ align-1 [P_{F}^{b} (α / 2), P_{F}^{b} (1 - α / 2)], & align-2 \end{matrix}

where

P_{F}^{b} false(α false)

is the

α

th percentile of the distribution

F_{x_{n}}^{b}

. For small values such as

α = 0.05

, as was chosen by Bisaglia & Gerolimetto (2019), almost every observation falls into the forecasting interval. However, this criterion is not very useful for comparing different models.…”

Section: Forecastingmentioning

confidence: 99%

“…Gelman et al . (2014) introduced the log‐score criterion (LSC) for predictive accuracy, which is also considered by Bisaglia & Gerolimetto (2019). We adopt this approach for our second criterion, the forecasting log‐score criterion (FLSC):

\begin{matrix} alignleft \\ align-1 F L S C = \sum_{h = 1}^{n_{2}} \log {\hat{p}}_{n_{1} + h} (x_{n_{1} + h}), & align-2 \end{matrix}

where

{\overset{p}{true}}_{n_{1} + h} false(x_{n_{1} + h} false) = false(number of correct predictions false) false/ m

, which is the estimated probability of correctly predicting the value

x_{n_{1} + h}

.…”

Section: Forecastingmentioning

confidence: 99%

“…. For small values such as 𝛼 = 0.05, as was chosen by Bisaglia & Gerolimetto (2019), almost every observation falls into the forecasting interval. However, this criterion is not very useful for comparing different models.…”

Section: Forecasting Path Bandmentioning

confidence: 99%

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Semiparametric integer‐valued autoregressive models on ℤ

Liu

Zhu

2021

Can J Statistics

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In the analysis of real integer‐valued time series data, we often encounter negative values and negative correlations. For integer‐valued autoregressive time series, there are many parametric models to choose from, but some of them are relatively complex. With little information about the background of real data, we hope that a simple and effective semiparametric model can be used to obtain more information that usually cannot be provided by parametric models, such as the confidence interval of the innovation distribution. But the only existing semiparametric model based on thinning operators can only deal with non‐negative data with positive correlation coefficients. In addition, it has two drawbacks: first, an initial distribution of the innovation is required, but different initial values may lead to different results; second, the confidence interval of the innovation distribution is not available, which is essential in low‐valued data. To overcome these drawbacks, we propose a rounded semiparametric autoregressive model with a log‐concave innovation, which can deal with ℤ‐valued time series with autoregressive coefficients of arbitrary sign. The consistencies of the estimators for the parametric and nonparametric parts of the model are also discussed. We illustrate the superior performance of the proposed model based on three real datasets.

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“…Bisaglia & Gerolimetto (2019) used the empirical distribution

F_{x_{n}}^{b}

based on groups of bootstrap resamples of the real data x n to obtain the

false(1 prefix- α false)

prediction interval:

\begin{matrix} alignleft \\ align-1 [P_{F}^{b} (α / 2), P_{F}^{b} (1 - α / 2)], & align-2 \end{matrix}

where

P_{F}^{b} false(α false)

is the

α

th percentile of the distribution

F_{x_{n}}^{b}

. For small values such as

α = 0.05

, as was chosen by Bisaglia & Gerolimetto (2019), almost every observation falls into the forecasting interval. However, this criterion is not very useful for comparing different models.…”

Section: Forecastingmentioning

confidence: 99%

\begin{matrix} alignleft \\ align-1 F L S C = \sum_{h = 1}^{n_{2}} \log {\hat{p}}_{n_{1} + h} (x_{n_{1} + h}), & align-2 \end{matrix}

where

{\overset{p}{true}}_{n_{1} + h} false(x_{n_{1} + h} false) = false(number of correct predictions false) false/ m

, which is the estimated probability of correctly predicting the value

x_{n_{1} + h}

.…”

Section: Forecastingmentioning

confidence: 99%

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Semiparametric integer‐valued autoregressive models on ℤ

Liu

Zhu

2021

Can J Statistics

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“…Similar to the procedure in [16], which performs an out-of-sample experiment to compare forecasting performances of two model-based bootstrap approaches, we introduce the forecasting procedure as follows: For each t = (n 1 + 1), . .…”

Section: Forecastingmentioning

confidence: 99%

“…Similar to the procedure in [ 16 ], which performs an out-of-sample experiment to compare forecasting performances of two model-based bootstrap approaches, we introduce the forecasting procedure as follows: For each

we estimate an INAR(1) model for the data

, then we use the fitted result based on

to generate the next five forecasts, which is called the 5-step ahead forecast

for each t in

, where

is the forecast at time t . In this way we obtain many sequences of

step-ahead forecasts, finally we replicate the whole procedure P times.…”

Section: Real Data Examplesmentioning

confidence: 99%

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Liu

Zhu

2020

Entropy

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The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

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