Testing Indicators with Autocorrelated or Heteroskedastic Errors

Summary

The document addresses how to test whether two indicators help explain a time series of returns when the indicators may be autocorrelated or nonstationary and a VAR analysis has not produced significant results. Its proposed starting point is a linear regression of returns on the indicators, followed by diagnostics on the regression errors. The classical conditions highlighted are uncorrelated errors and constant error variance.

If the residuals show no autocorrelation or heteroskedasticity, the answer says conventional hypothesis tests can be used. If either problem is present, it recommends adjusting standard errors, naming White and Newey–West estimators, then recalculating t-statistics for the hypothesis tests. This addresses inference under certain error patterns, but it does not resolve nonstationarity in the indicators or returns, establish a causal relationship, or specify which diagnostic tests to run. The suggestion is therefore a limited inference procedure, not a complete time-series modeling strategy; the suitability of regression and the standard-error correction still depends on the data and assumptions.

Key ideas

• Regress returns on the indicators and inspect the regression residuals.
• Conventional hypothesis tests rely on uncorrelated errors and constant error variance.
• White or Newey–West standard errors can adjust inference when relevant residual problems occur.
• The procedure does not itself resolve nonstationarity or establish causation.

Tags

# Econometrics - Testing


# Econometrics - Testing












If we have a time series of returns and two time series of indicators, how would we test the use of these indicators if they are autocorrelated or nonstationary (VAR Models dont produce significant results).

## Answer by John (score 1)

https://quant.stackexchange.com/a/10552

The classical assumptions of linear regression are that the errors are uncorrelated and the variance of errors is constant (homoskedastic). So regress the returns against the indicators and test for autocorrelation and heteroskedasticity in the errors. If you don't observe any, then there's no issue with conventional hypothesis testing. If you do, use White or Newey-West standard errors (standard in most statistical packages), as appropriate, to compute new t-statistics, then proceed with hypothesis testing.

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