Skip to content
All library documents

Diagnosing TSO Outlier Removal for a Financial Time Series

Article Quant Q&A · Author: Andrew Wheeler
Read the original

Summary

The document describes an attempt to identify extreme observations in a financial ratio series, with many apparent outliers around the 2008–2009 crisis. The author expects the series to be stationary around a nonzero level, reports that KPSS supports stationarity around a mean, and suspects the outliers depress the estimated level. An ARIMA search and ACF/PACF inspection found no autoregressive structure in the original series.

The TSO outlier-detection function fails during optimization or with a matrix-related error under the tested settings, including additive outliers. Changing its removal method to bottom-up allows it to run, but the resulting ARIMA specification is difference-stationary with zero mean, unlike the original series. The document raises a diagnostic question rather than establishing which model or removal procedure is correct; its central caveat is that outlier treatment may change the inferred stationarity and should be checked against the series’ economic behavior.

Key ideas

  • The series is a financial ratio with visually prominent extremes, many near the 2008–2009 crisis.
  • The author expects stationarity around a nonzero mean and reports a KPSS result consistent with that view.
  • TSO optimization errors persist under several settings, while bottom-up removal runs successfully.
  • Bottom-up removal changes the selected model to a difference-stationary specification, raising uncertainty about the appropriate treatment.

Tags

StatisticsRisk managementBacktesting
Full text
# Outlier removal, issue with TSO function


# Outlier removal, issue with TSO function












I'm trying to detect outliers within a financial time series which represents the ratio of cash distributions to equity holders as a percentage operating earnings for the period. Visual inspection indicates several large outliers, mostly associated around the crisis periods in '08-'09. I believe the series should likely be trend stationary as the process shouldn't have a zero mean and a time trend does not make economic sense. KPSS testing indicates stationarity around a non-zero mean which makes sense. However, I believe the indicated level is too low because of the outliers mentioned. The TSO() function, which I've used before, kicks back an error that the value supplied by optim is non-finite. I've never encountered this before and am unsure how to proceed.

To clarify, I did run auto.arima long with examining the ACF/PACF plots and no autoregressive structure was found (0,0,0). I also tinkered with the innovation types with TSO, setting to "AO" only as I think these are actually the only appropriate ones when the nature of the data is considered. This returned an error as well, I believe it implied that an invertible matrix was found somewhere.

I tried altering the CVAL parameter as well, this did not seem to make a difference. Interestingly, I did discover that changing the remove.method to "bottom-up" rather than the default setting did allow for the function to run - I think I need to better understand what is actually going on by doing that however because the auto.arima function returns ARIMA(0,1,0) with a zero mean whereas auto.arima on the original series returns arma(0,0,0) - it seems that the bottom-up outlier removal results in a difference stationary series and I believe that given the fundamentals of the series it is actually likely to be stationary around a non-zero mean but the mean value is skewed due to outliers.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.