Statistical Properties of Threshold Models

Amendola, Alessandra; Niglio, Marcella; Vitale, Cosimo Damiano

doi:10.1080/03610920802571146

Cited by 6 publications

(6 citation statements)

References 26 publications

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“…Note that the multi-day SETAR model has the same skeleton model (noise free) for all days. Then, the conditions shown by Amendola et al (2009) for the SETAR model to be stationary are also sufficient conditions for the multi-day SETAR model to be stationary per day.…”

Section: Modelmentioning

confidence: 94%

“…In practice, a handy tool is to run the skeleton model (noise-free model) with different initial conditions (Tong, 2010). Amendola et al (2009) showed that the SETAR model with two regimes ( 2) is weakly stationary if the matrices Φ (1) and Φ (2) have both dominant eigenvalues less than one, where…”

Section: Tar Modelmentioning

confidence: 99%

“…To do this, we compute the eigenvalues of the matrices

Φ_{1} = (\begin{matrix} 1.538 & prefix- 0.614 & 0.120 & prefix- 0.045 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{matrix}) and Φ_{2} = (\begin{matrix} 1.601 & prefix- 0.790 & 0.240 & prefix- 0.092 & 0.040 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{matrix}) .

Then, the maximum eigenvalue for

Φ_{1}

is 0.9975 and the maximum eigenvalue for

Φ_{2}

is 0.9969. Following Amendola et al's, (2009) criteria, the estimated model corresponds to a stationary model. We also consider the skeleton plot as suggested by Tong (2010).…”

Section: Statistical Analysis Of Guadeloupe Island's Datamentioning

confidence: 99%

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Statistical analysis of multi‐day solar irradiance using a threshold time series model

2022

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The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Recently, new statistical models have been proposed to provide stochastic simulations of high-resolution data to downscale and forecast solar irradiance measurements. Most of the existing models are linear and highly depend on normality assumptions. However, solar irradiance shows strong nonlinearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive model to quantify the variability of the daily irradiance time series. We establish the sufficient conditions for our model to be stationary, and we develop an inferential procedure to estimate the model parameters. When we apply our model to study the statistical properties of observed irradiance data in Guadeloupe island group, a French overseas region located in the Southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear-sky and non-clear sky regimes. Using our model, we are able to simulate irradiance series that behave similarly to the real data in mean and variability, and more accurate forecasts compared to linear models.

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Section: Modelmentioning

confidence: 94%

Section: Tar Modelmentioning

confidence: 99%

“…To do this, we compute the eigenvalues of the matrices

Φ_{1} = (\begin{matrix} 1.538 & prefix- 0.614 & 0.120 & prefix- 0.045 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{matrix}) and Φ_{2} = (\begin{matrix} 1.601 & prefix- 0.790 & 0.240 & prefix- 0.092 & 0.040 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{matrix}) .

Then, the maximum eigenvalue for

Φ_{1}

is 0.9975 and the maximum eigenvalue for

Φ_{2}

is 0.9969. Following Amendola et al's, (2009) criteria, the estimated model corresponds to a stationary model. We also consider the skeleton plot as suggested by Tong (2010).…”

Section: Statistical Analysis Of Guadeloupe Island's Datamentioning

confidence: 99%

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Statistical analysis of multi‐day solar irradiance using a threshold time series model

2022

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“…The statistical properties of the TAR model and more detailed information can be seen in [28], [29] and [30]. In line with the potential of the TAR specification to distinguish multiple time series, we made use of the TAR specification for observing nonlinear associations, and the AR specification for observing linear associations in the multiple time series clustering task.…”

Section: Threshold Autoregressive Model (Tar)mentioning

confidence: 99%

Temporal clustering of time series via threshold autoregressive models: application to commodity prices

2017

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This study aimed to find temporal clusters for several commodity prices using the threshold non-linear autoregressive model. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. The clustering of commodity prices was examined using the proposed clustering approach based on time series models to incorporate the time varying properties of price series into the clustering scheme. Accordingly, the primary aim in this study was grouping time series according to the similarity between their Data Generating Mechanisms (DGMs) rather than comparing pattern similarities in the time series traces. The approximation to the DGM of each series was accomplished using threshold autoregressive models, which are recognized for their ability to represent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time dimension. Furthermore, generating a time varying commodity price index and sub-indexes can become possible. Consequently, we conducted a simulation study to assess the effectiveness of the proposed clustering approach and the results are presented for both the simulated and real data sets.

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“…Ling and Tong (2005) considered a quasi-likelihood ratio test for the threshold in moving average models. Amendola, et al (2009) discussed the stochastic structure of the self-exiting TARMA model; they specified sufficient conditions for weak stationarity and showed that the self-exiting TARMA model belongs to the class of the random coefficients autoregressive models. Smadi (1997) used the Bayesian approach for exploration of the joint posterior distribution for TARMA models using MCMC methods: he assumed noninformative priors, fixing the delay parameter d. In addition, he used a modified Gibbs sampling scheme, which is a hybrid strategy of Gibbs sampler, random walk Metropolis, and importance sampling.…”

Section: Introductionmentioning

confidence: 99%