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Dimension reduction in time series under the presence of conditional heteroscedasticity

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  • da Silva, Murilo
  • Sriram, T.N.
  • Ke, Yuan

Abstract

Consider a time series, where the conditional mean is assumed to be an unknown function of linear combinations of past p observations and the conditional variance is assumed to be an unknown function of linear combinations of past q squared residuals. The linear combinations are assumed to contain all the necessary information about the time series that is available through the conditional mean and conditional variance, respectively. Nadaraya-Watson kernel smoother is used to estimate the unknown mean and variance function and an iterative approach is proposed to estimate the parameter matrices associated with the linear combinations. The estimators are shown to be consistent. To overcome computational challenges and provide numerical stability, a novel angular representation of parameter matrices is introduced. The numerical performance of the proposed method on forecasting the conditional mean is assessed by simulations studies. A real data of Brazilian Real (BRL)/U.S. Dollar Exchange Rate is analyzed. For the BRL/USD series, the estimated linear combinations yield a better time series model than an AR-ARCH model in terms of out-of-sample forecasts.

Suggested Citation

  • da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002626
    DOI: 10.1016/j.csda.2022.107682
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    References listed on IDEAS

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