Least squares estimation of ARCH models with missing observations

Bondon, Pascal; Bahamonde, Natalia

doi:10.1111/j.1467-9892.2012.00803.x

“…On these closure days there are no financial transactions and hence we do not observe price changes. However, the underlying price of the asset may still be changing during these days; see, for example, the discussions in Bondon and Bahamonde (2012).…”

Section: An Empirical Experiments For the Sandp500 Daily Returns Time Sementioning

confidence: 99%

Missing observations in observation-driven time series models

Blasques

¹

,

Gorgi

²

,

Koopman

³

2021

Journal of Econometrics

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We argue that existing methods for the treatment of missing observations in observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for conditional volatility. To overcome the problem of inconsistent inference, we propose a novel estimation procedure based on indirect inference. This easy-to-implement method delivers consistent inference. The asymptotic properties are formally derived. Our proposed method shows a promising performance in both a Monte Carlo study and an empirical study concerning the measurement of conditional volatility from financial returns data.

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“…However, we argue that no consistent procedure has been designed for observation-driven models, only except for a special case such as the estimator of Bondon and Bahamonde (2012) for the ARCH model. Our aim is to bridge this gap by developing an indirect inference method that delivers consistent inference in this context.…”

Section: Introductionmentioning

confidence: 99%

“…This is the case even for well known models such as the GARCH model. An exception is the very specific case of the least squares estimator of the parameter vector in the autoregressive conditional heteroskedasticity (ARCH) model that is explored by Bondon and Bahamonde (2012).…”

Section: Introductionmentioning

confidence: 99%

Missing Observations in Observation-Driven Time Series Models

Blasques

¹

,

Gorgi

²

,

Koopman

³

2018

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We argue that existing methods for the treatment of missing observations in observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for conditional volatility. To overcome the problem of inconsistent inference, we propose a novel estimation procedure based on indirect inference. This easy-to-implement method delivers consistent inference. The asymptotic properties are formally derived. Our proposed method shows a promising performance in both a Monte Carlo study and an empirical study concerning the measurement of conditional volatility from financial returns data.

show abstract

“…This approach is similar to that of Bondon and Bahamonde (2012). The process that determines true return t we refer to as the Data Generating Process (DGP), whereas the process that determines I t we refer to as the Zero Generating Process (ZGP).…”

Section: Observed Zeros { a Frameworkmentioning

confidence: 99%

“…6 However, it is not available for the Standard QMLE. Bondon and Bahamonde (2012) proposed an estimator for non-exponential ARCH models, i.e. an ARCH model without the important GARCH term, in the presence of missing observations.…”

mentioning

confidence: 99%

Estimation of log-GARCH models in the presence of zero returns

Sucarrat

¹

,

Escribano

²

2017

The European Journal of Finance

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A critique that has been directed towards the log-GARCH model is that its log-volatility specication does not exist in the presence of zero returns. A common \remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders estimation asymptotically biased. Here, we propose a solution to the case where the true return is equal to zero with probability zero. In this case zero returns may be observed because of non-trading, measurement error (e.g. due to rounding), missing values and other data issues. The algorithm we propose treats the zeros as missing values and handles these by estimation via the ARMA representation. An extensive number of simulations verify the conjectured asymptotic properties of the bias-correcting algorithm, and several empirical applications illustrate that it can make a substantial dierence in practice.JEL Classication: C22, C58

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Least squares estimation of ARCH models with missing observations

Abstract: International audienceA least squares estimator for ARCH models in the presence of missing data is proposed. Strong consistency and asymptotic normality are derived. Monte Carlo simulation results are analysed and an application to real data of a Chilean stock index is reported

Cited by 14 publications

References 25 publications

Missing observations in observation-driven time series models

Missing observations in observation-driven time series models

Missing Observations in Observation-Driven Time Series Models

Estimation of log-GARCH models in the presence of zero returns

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