A generalized mixture integer-valued GARCH model

Mao, Huiyu; Zhu, Fukang; Cui, Yan

doi:10.1007/s10260-019-00498-2

Cited by 8 publications

(8 citation statements)

References 24 publications

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“…(2021) (with value 1.13) and Mao et al . (2020) (with value 1.01) which are obtained form mixture (Poisson) INARCH model and mixture (negative binomial) INGARCH model respectively. For completeness, we also considered the Ecoli series without the two first observations as considered by Doukhan et al .…”

Section: Empirical Examplesmentioning

confidence: 99%

“…Finally, the out‐of‐sample forecasting ability of the MthINGARCH

(1, 1)

is assessed for the Ecoli series. Because of the unavailability of the estimation codes for the Poisson mixture INARCH (Doukhan et al ., 2021) and the Negative binomial mixture INGARCH (Mao et al ., 2020) models, we only compare our MthINGARCH

(1, 1)

model with two standard models, namely the P‐INGARCH

(1, 1)

model

Y_{t} | ℱ_{t - 1}^{Y} \sim 𝒫 (χ_{t}) with χ_{t} = c_{0} + a_{0} Y_{t - 1} + b_{0} χ_{t - 1}

and the NB‐INGARCH

(1, 1)

model

Y_{t} | ℱ_{t - 1}^{Y} \sim 𝒩 ℬ (r_{0}, \frac{r_{0}}{r_{0} + χ_{t}}) with χ_{t} = c_{0} + a_{0} Y_{t - 1} + b_{0} χ_{t - 1} .

We, therefore, estimate the three models using the first

n_{c}

observations of the series, where

1 < n

…”

Section: Empirical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

A multiplicative thinning‐based integer‐valued GARCH model

Aknouche

Scotto

2023

Journal Time Series Analysis

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In this paper we introduce a multiplicative integer-valued time series model, which is de…ned as the product of a unit-mean integer-valued independent and identically distributed (iid) sequence, and an integer-valued dependent process. The latter is de…ned as a binomial thinning operation of its own past and of the past of the observed process. Furthermore, it combines some features of the integer-valued GARCH (INGARCH), the autoregressive conditional duration (ACD), and the integer autoregression (INAR) processes. The proposed model is semi-parametric and is able to parsimoniously generate very high overdispersion, persistence, and heavy-tailedness.The dynamic probabilistic structure of the model is …rst analyzed. In addition, parameter estimation is considered by using a two-stage weighted least squares estimate (2SWLSE), consistency and asymptotic normality (CAN) of which are established under mild conditions. Applications of the proposed formulation to simulated and actual count time series data are provided.

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Section: Empirical Examplesmentioning

confidence: 99%

“…Finally, the out‐of‐sample forecasting ability of the MthINGARCH

(1, 1)

(1, 1)

model with two standard models, namely the P‐INGARCH

(1, 1)

model

Y_{t} | ℱ_{t - 1}^{Y} \sim 𝒫 (χ_{t}) with χ_{t} = c_{0} + a_{0} Y_{t - 1} + b_{0} χ_{t - 1}

and the NB‐INGARCH

(1, 1)

model

Y_{t} | ℱ_{t - 1}^{Y} \sim 𝒩 ℬ (r_{0}, \frac{r_{0}}{r_{0} + χ_{t}}) with χ_{t} = c_{0} + a_{0} Y_{t - 1} + b_{0} χ_{t - 1} .

We, therefore, estimate the three models using the first

n_{c}

observations of the series, where

1 < n

…”

Section: Empirical Examplesmentioning

confidence: 99%

A multiplicative thinning‐based integer‐valued GARCH model

Aknouche

Scotto

2023

Journal Time Series Analysis

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“…We consider the following first‐order mixture double autoregressive (MDAR(1) model with two components

{y}_t=\left\{\begin{array}{ll}{a}_1{y}_{t-1}+{\varepsilon}_t\sqrt{b_0^{(1)}+{b}_1^{(1)}{y}_{t-1}^2},\mathrm{with}\ \mathrm{probability}& \kern0.60em p,\\ {}{a}_2{y}_{t-1}+{\varepsilon}_t\sqrt{b_0^{(2)}+{b}_1^{(2)}{y}_{t-1}^2},\mathrm{with}\ \mathrm{probability}& 1-p,\end{array}\right.

where

{y}_t

is the observation,

{b}_{i-1}^{(j)}>0

i,j\in \left\{1,2\right\}

p

is the mixture probability, which is assumed to be taken values in (0.5,1) for identifiability (see Mao, Zhu, & Cui, 2020; Zhu, Li, & Wang, 2010 for related discussions).

ε_{t}

…”

Section: The Mdar Modelmentioning

confidence: 99%

“…i−1 > 0, i, j ∈ {1, 2}, p is the mixture probability, which is assumed to be taken values in (0.5,1) for identifiability (see Mao, Zhu, & Cui, 2020;Zhu, Li, & Wang, 2010 for related discussions). 𝜀 t is the i.i.d.…”

Section: The Mdar Modelmentioning

confidence: 99%

Bayesian inference for a mixture double autoregressive model

Yang

Zhang

et al. 2022

Statistica Neerlandica

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This paper considers a mixture double autoregressive model with two components, which can flexibly capture the features usually exhibited by many financial returns such as heteroscedasticity, large kurtosis and multimodal marginals. Bayesian method based on modern Markov Chain Monte Carlo (MCMC) technology is used to estimate the model parameters. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via some simulations. It is shown that the MCMC algorithm is an effective tool to deal with the mixture model. Finally, the proposed model is applied to the S&P500 index data.set.

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“…More extensive and complex GARCH models were developed to improve the forecasting model. For example, a fuzzy GJR-GARCH model using fuzzy inference systems [22], hybrid neural network GJR-GARCH models [23,24] for volatility forecasting of indexes, a mixture of integer-valued models with different distributions in GARCH model [25], and a hidden Markov Exponential GARCH model for volatility forecasting of crude oil price [26]. Another approach toward improving the GARCH model was introduced by using a sliding window technique to forecast future values in various fields; this was called the sliding window GARCH (SWGARCH) model [27,28].…”

Section: Introductionmentioning

confidence: 99%

A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting

et al. 2020

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Generalized autoregressive conditional heteroskedasticity (GARCH) is one of the most popular models for time-series forecasting. The GARCH model uses a maximum likelihood method for parameter estimation. For the likelihood method to work, there should be a known and specific distribution. However, due to uncertainties in time-series data, a specific distribution is indeterminable. The GARCH model is also unable to capture the influence of each variance in the observation because the calculation of the long-run average variance only considers the series in its entirety, hence the information on different effects of the variances in each observation is disregarded. Therefore, in this study, a novel forecasting model dubbed a fuzzy linear regression sliding window GARCH (FLR-FSWGARCH) model was proposed; a fuzzy linear regression was combined in GARCH to estimate parameters and a fuzzy sliding window variance was developed to estimate the weight of a forecast. The proposed model promotes consistency and symmetry in the parameter estimation and forecasting, which in turn increases the accuracy of forecasts. Two datasets were used for evaluation purposes and the result of the proposed model produced forecasts that were almost similar to the actual data and outperformed existing models. The proposed model was significantly fitted and reliable for time-series forecasting.

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A generalized mixture integer-valued GARCH model

Cited by 8 publications

References 24 publications

A multiplicative thinning‐based integer‐valued GARCH model

A multiplicative thinning‐based integer‐valued GARCH model

Bayesian inference for a mixture double autoregressive model

A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting

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