Dimension reduction in time series under the presence of conditional heteroscedasticity

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

Computational Statistics & Data Analysis, 2023, vol. 180, issue C

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.

Keywords: Angular representation; Dimension reduction; Heteroscedasticity; Iterative estimation; Nadaraya-Watson smoother; Time series (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002626

DOI: 10.1016/j.csda.2022.107682

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