### Quantitative Economics, Volume 10, Issue 2 (May 2019)

### Jump factor models in large cross‐sections

*Jia Li, Viktor Todorov, George Tauchen*

#### Abstract

We develop tests for deciding whether a large cross‐section of asset prices obey an exact factor structure at the times of factor jumps. Such jump dependence is implied by standard linear factor models. Our inference is based on a panel of asset returns with asymptotically increasing cross‐sectional dimension and sampling frequency, and essentially no restriction on the relative magnitude of these two dimensions of the panel. The test is formed from the high‐frequency returns at the times when the risk factors are detected to have a jump. The test statistic is a cross‐sectional average of a measure of discrepancy in the estimated jump factor loadings of the assets at consecutive jump times. Under the null hypothesis, the discrepancy in the factor loadings is due to a measurement error, which shrinks with the increase of the sampling frequency, while under an alternative of a noisy jump factor model this discrepancy contains also nonvanishing firm‐specific shocks. The limit behavior of the test under the null hypothesis is nonstandard and reflects the strong‐dependence in the cross‐section of returns as well as their heteroskedasticity which is left unspecified. We further develop estimators for assessing the magnitude of firm‐specific risk in asset prices at the factor jump events. Empirical application to S&P 100 stocks provides evidence for exact one‐factor structure at times of big market‐wide jump events.

Factor model panel high‐frequency data jumps semimartingale specification test stochastic volatility C51 C52 G12

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