A Structural‐Factor Approach to Modeling High‐Dimensional Time Series and Space‐Time Data

Abstract

This article considers a structural‐factor approach to modeling high‐dimensional time series and space‐time data by decomposing individual series into trend, seasonal, and irregular components. For ease in analyzing many time series, we employ a time polynomial for the trend, a linear combination of trigonometric series for the seasonal component, and a new factor model for the irregular components. The new factor model simplifies the modeling process and achieves parsimony in parameterization. We propose a Bayesian information criterion to consistently select the order of the polynomial trend and the number of trigonometric functions, and use a test statistic to determine the number of common factors. The convergence rates for the estimators of the trend and seasonal components and the limiting distribution of the test statistic are established under the setting that the number of time series tends to infinity with the sample size, but at a slower rate. We study the finite‐sample performance of the proposed analysis via simulation, and analyze two real examples. The first example considers modeling weekly PM2.5 data of 15 monitoring stations in the southern region of Taiwan and the second example consists of monthly value‐weighted returns of 12 industrial portfolios.

Comprehensive interval‐valued time series model with application to the S&P 500 index and PM2.5 level data analysis

“…We choose VAR(1) as the best model with the lowest AIC, which coincides with the results of Gao and Tsay. 12 The hit map of the correlations of the residuals for the 15 stations and the corresponding geographical map are shown in Figure 14. Except for the Hengchun station, all other stations exhibit higher correlations with each other.…”

“…To demonstrate its accuracy, MLE is evaluated using Monte Carlo simulations. Real data analyses are then conducted using the S&P 500 index and PM2.5 at 15 stations in south Taiwan, which were analyzed by Lin et al 11 and Gao and Tsay, 12 respectively. For the former, we fit the GHVAIRMA model to improve the accuracy of the one‐step‐ahead prediction of the high and low prices of the S&P 500 index further.…”

A Two-Way Transformed Factor Model for Matrix-Variate Time Series

“…For the vector factor models, there are some methods available. See, for example, the information criterion in Bai and Ng (2002) and Bai (2003), the random matrix theory method in Onatski (2010), the ratio-based method in Lam and Yao (2012), the canonical correlation analysis in Gao and Tsay (2019), and the white noise testing approach in Gao and Tsay (2020b), among others. However, those methods cannot apply to the matrixfactor models directly.…”

“…See Gao and Tsay (2019) for details. Therefore, without any additional assumptions on the underlying structure of time series, p 1 p 2 can only be as large as o(n 1/2 ).…”

Knowledge management overview of feature selection problem in high-dimensional financial data: cooperative co-evolution and MapReduce perspectives

“…IBM has reported that 90% of the world's data was created in the previous two years, with more than 2.5 exabytes of data produced daily. Financial time-series and space-time are examples of high-dimensional data used to mine and measure the real-time business conditions for financial organizations or for data mining (Gao & Tsay, 2019;Wu, Liu, & Yang, 2018) in supply chain (Habib & Hasan, 2019; Tseng, Wu, Lim, & Wong, 2019; Voyer, Dean, Pickles, & Robar, 2018). In health science (Tursunbayeva, Bunduchi, Franco, & Pagliari, 2016), high-throughput technologies, such as microarrays, generate DNA microarray datasets having more than 500,000 genes in gene arrays or mass spectrometry creates high-dimensional datasets regarding living cells having a range of 300,000 m/z values (Aliferis, Statnikov, & Tsamardinos, 2006).…”