\(\mathcal{L}\)-transformed Tensor Autoregressive Modeling under Heavy-tailed Errors
Uchenna Chinedu Nduka *
Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
High dimensional multiple time series data arise in many scientific and financial applications, where complex structures are profound. This paper extends the frequency-domain approach for high-dimensional time series forecasting through data preprocessing using discrete cosine transformation (DCT) combined with heavy-tailed vector autoregressive (VAR) modeling. The proposed framework transforms a tensor of multiple time series using DCT, fits VAR models to the resulting frontal slices, and maps the estimated parameters back to the original domain through inverse DCT. The expectation maximization conditional either (ECME) algorithm provides robust parameter estimation to enable efficient inference under heavy-tailed error distribution. Simulation studies show that more accurate parameter recovery is consistently achieved with ECME than ordinary least squares across different settings, despite recording Frobenius norms of the estimation error that are not close to zero. The practical benefits of the proposed framework are demonstrated through empirical applications using sea surface temperature and prices of 50 randomly selected stocks contained in NASDAQ-100. Results of the analysis show improved forecast performance, with the improvement most pronounced at longer horizons. The gains of integrating frequency-domain transformation with robust estimation procedures, which are crucial for efficient modeling of complex dependencies in multiple time series, are the highlights of the findings of this study.
Keywords: Discrete cosine transformation, ECME algorithm, heavy-tailed distributions, igh-dimensional multiple time series, vector autoregressive model