Sample splitting and assessing goodness-of-fit of time series

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Assessing time series model fit often involves testing residuals for serial independence.
• Fitted residuals are intrinsically dependent due to shared parameter estimates, complicating standard independence tests.
• Existing methods like sample splitting (Pfister et al., 2018) are insufficient for dependent time series data.

Purpose of the Study:

• To adapt the sample-splitting procedure for testing serial dependence in time series model residuals.
• To develop adjusted goodness-of-fit tests for time series models that account for residual dependence.
• To provide a method that avoids complex adjustments for confidence bounds in residual analysis.

Main Methods:

• Leveraging a sample-splitting technique in the time series context.
• Estimating model parameters using an initial segment of the data ([Formula: see text]).
• Computing residuals for a subsequent data segment ([Formula: see text]) using the estimated parameters.
• Applying autocorrelation function (ACF) and auto-distance correlation function (ADCF) tests to these computed residuals.

Main Results:

• The proposed sample-splitting method allows ACF and ADCF tests of serial independence to achieve the same limit distributions as if residuals were truly independent and identically distributed, provided overlap is asymptotically negligible.
• Using the first half of the data for parameter estimation and the entire dataset for residual computation yields this desirable property.
• This procedure simplifies the construction of confidence bounds for ACF and ADCF in goodness-of-fit testing.

Conclusions:

• The adapted sample-splitting technique effectively addresses the challenge of dependent residuals in time series model evaluation.
• This method offers a more reliable approach to goodness-of-fit testing for time series models.
• It simplifies residual analysis by mitigating the need for complex adjustments to standard statistical tests.