We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time alternatives in the multifactor framework. A class of easy-to-interpret diagnostic procedures is also proposed to gauge possible sources of model misspecification. All the proposed test statistics have a convenient asymptotic N(0, 1) distribution under correct model specification, and all asymptotic results allow for some data-dependent bandwidth. Simulations show that in finite samples, our tests have reasonable size, thanks to the dimension reduction in nonparametric regression, and good power against a variety of alternatives, including misspecifications in the joint dynamics, but the dynamics of each individual component is correctly specified. This feature is not attainable by some existing tests. A parametric bootstrap improves the finite-sample performance of proposed tests but with a higher computational cost.
The Markov property is a fundamental property in time series analysis and is often assumed in economic and financial modeling. We develop a new test for the Markov property using the conditional characteristic function embedded in a frequency domain approach, which checks the implication of the Markov property in every conditional moment (if it exists) and over many lags. The proposed test is applicable to both univariate and multivariate time series with discrete or continuous distributions. Simulation studies show that with the use of a smoothed nonparametric transition density-based bootstrap procedure, the proposed test has reasonable sizes and all-around power against several popular non-Markov alternatives in finite samples. We apply the test to a number of financial time series and find some evidence against the Markov property.
Passive indoor localization techniques can have many important applications. They are nonintrusive and do not require users carrying measuring devices. Therefore, indoor localization techniques are widely used in many critical areas, such as security, logistics, healthcare, etc. However, because of the unpredictable indoor environment dynamics, the existing nonintrusive indoor localization techniques can be quite inaccurate, which greatly limits their real-world applications. To address those problems, in this work, we develop a channel state information (CSI) based indoor localization technique. Unlike the existing methods, we employ both the intra-subcarrier statistics features and the inter-subcarrier network features. Specifically, we make the following contributions: (1) we design a novel passive indoor localization algorithm which combines the statistics and network features; (2) we modify the visibility graph (VG) technique to build complex networks for the indoor localization applications; and (3) we demonstrate the effectiveness of our technique using real-world deployments. The experimental results show that our technique can achieve about 96% accuracy on average and is more than 9% better than the state-of-the-art techniques.
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