Diagnostic Checking Arma Time Series Models Using Squared‐residual Autocorrelations

McLeod, A. Ian; Li, Wai Keung

doi:10.1111/j.1467-9892.1983.tb00373.x

Cited by 904 publications

(408 citation statements)

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“…Under the null hypothesis of the first K autocorrelations being jointly equal to zero, McLeod and Li (1983) show that the asymptotic distribution of Q(K), when applied to squared observations is approximately a chi-square distribution with K degrees of freedom if the eighth-order moment of y t exists. This result is based on Theorem 14 of Hannan (1970, p. 228) that requires the series to be tested for uncorrelatedness to be an independent sequence with finite fourth-order moment.…”

Section: Finite Sample Properties Of Homoscedasticity Testsmentioning

confidence: 99%

“…The Student's t distributions have been chosen because it has often been observed that the marginal distribution of returns has heavy tails. Moreover, the degrees of freedom have been selected so that we have a distribution with a finite eighth-order moment (# 9), as required by McLeod and Li (1983), and a distribution that does not satisfy this requirement (# 5). On the other hand, the powers of the Q(K) and D(K) statistics have been analyzed, generating heteroscedastic series by the same LMSV models and sample sizes considered in Sections 2 and 3.…”

Section: Finite Sample Properties Of Homoscedasticity Testsmentioning

confidence: 99%

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Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Pérez¹

2003

Journal of Financial Econometrics

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The autocorrelations of log-squared, squared, and absolute financial returns are often used to infer the dynamic properties of the underlying volatility. This article shows that, in the context of long-memory stochastic volatility models, these autocorrelations are smaller than the autocorrelations of the log volatility and so is the rate of decay for squared and absolute returns. Furthermore, the corresponding sample autocorrelations could have severe negative biases, making the identification of conditional heteroscedasticity and long memory a difficult task. Finally, we show that the power of some popular tests for homoscedasticity is larger when they are applied to absolute returns.keywords: absolute transformation, Box-Ljung text, conditional heteroscedasticity, log-squared transformation, Peña Rodriguez test, squared observations. It is by now rather popular to measure the volatility of financial returns by some nonlinear transformations as, for example, log-squared, squared, or absolute returns. Consequently the autocorrelations of these transformations have often been used to test for the presence of conditional heteroscedasticity and to model and estimate the volatility [see, e

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Section: Finite Sample Properties Of Homoscedasticity Testsmentioning

confidence: 99%

Section: Finite Sample Properties Of Homoscedasticity Testsmentioning

confidence: 99%

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Pérez¹

2003

Journal of Financial Econometrics

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“…O teste de McLeod-Li (1983) baseia-se análise do correlograma do quadrado de uma determinada variável. A hipótese nula de as primeiras k autocorrelações do quadrado dos retornos serem simultânemente zero pode ser testada utilizando a estatística de Ljung-Box, Q xx (k).…”

Section: Teste De Mcleod-liunclassified

“…Investigamos a existência de sazonalidade determinista nos retornos através de regressões com variáveis dummy. Finalmente, empregamos os testes de McLeod-Li (1983) e Hsieh (1989 para avaliar possíveis não-linearidades nos dois primeiros momentos dos retornos. Os testes são feitos com retornos de diversos horizontes de tempo.…”

Section: Introductionunclassified

A aleatoriedade do passeio na Bovespa: testando a eficiência do mercado acionário brasileiro

Torres¹,

Bonomo

Fernandes³

2002

Rev. Bras. Econ.

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Sumário: 1. Introdução; 2. Dados; 3. Testes e resultados para retornos de curto prazo; 4. Retornos de médio a longo prazo; 5. Conclusão. Palavras-chave: passeio aleatório; eficiência; sazonalidade; não linearidade; anomalia. Códigos JEL: C12; C22 e G14.Este artigo testa duas versões do modelo de passeio aleatório para os preços de carteiras de ações no mercado brasileiro. Evidências contrárias a tal modelo foram observadas nos horizontes diário e semanal, caracterizados por persistência. As evidências foram mais fracas em períodos mais recentes. Foram também encontradas sazonalidades diárias, incluindo o efeito segunda-feira, e mensais. Adicionalmente, foi observado um padrão de assimetria de autocorrelações cruzadas de primeira ordem entre os retornos de carteiras de firmas agrupadas segundo seu tamanho, indicando, no caso de retornos diários e semanais, que retornos de firmas grandes ajudam a prever retornos de firmas pequenas. Evidências de não-linearidades nos retornos foram observadas em diversos horizontes de tempo. This paper tests two versions of the random walk model for portfolios of Brazilian stocks. It found evidence of persistency in daily and weekly returns, rejecting the random walk models. Those evidences were weaker in recent periods. The paper also found a Monday effect, and other seasonality effects for monthly returns. Additionally there were asymmetric first-order cross-correlations on portfolios ranked by size, with large firm returns predicting small firm returns. Nonlinearities in returns were also detected at several time horizons.

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“…Under the null hypothesis that t x is an i.i.d process, McLeod and Li (1983) showed that, for sufficiently large and fixed L, the statistic…”

Section: The Mcleod-li Testmentioning

confidence: 99%

Dynamic structure of the spot price of crude oil: does time aggregation matter?

Aghababa

Barnett

2016

Energy Economics

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This paper assess nonlinear structures in the time series data generating mechanism of crude oil prices. We apply well-known univariate tests for nonlinearity, with distinct power functions over alternatives, but with different null hypotheses reflecting the existence of different concepts of linearity and nonlinearity in the time series literature. We utilize daily data on crude oil spot prices for over 26 years, as well as monthly data on crude oil spot prices for 41 years. Investigating the monthly price process of crude oil distinguishes this paper from existing studies of the time series structure of energy markets. All the tests detect strong evidence of general nonlinear serial dependence, as well as nonlinearity in the mean, variance, and skewness functions in the daily spot price process of crude oil. Since evidence of nonlinear dependence is less dramatic in monthly observations, nonlinear serial dependence is moderated by time aggregation in crude oil prices.

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Diagnostic Checking Arma Time Series Models Using Squared‐residual Autocorrelations

Cited by 904 publications

References 14 publications

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

A aleatoriedade do passeio na Bovespa: testando a eficiência do mercado acionário brasileiro

Dynamic structure of the spot price of crude oil: does time aggregation matter?

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