Lajos Horvath, Lorenzo Trapani
arXiv 27 Apr 2021 · Mathematics — Statistics Theory · publishedJournal of Business and Economic Statistics (2022) · 13 citations (OpenAlex)
arXiv:2104.13440 · PDF · DOI · OpenAlex · Extracted main text
We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient AutoRegressive (RCA) sequence. In order to ensure the ability to detect breaks at sample endpoints, we thoroughly study weighted CUSUM statistics, analysing the asymptotics for virtually all possible weighing schemes, including the standardised CUSUM process (for which we derive a Darling-Erdos theorem) and even heavier weights (studying the so-called R\'enyi statistics). Our results are valid irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Technically, our results require strong approximations which, in the nonstationary case, are entirely new. Similarly, we allow for heteroskedasticity of unknown form in both the error term and in the stochastic part of the autoregressive coefficient, proposing a family of test statistics which are robust to heteroskedasticity, without requiring any prior knowledge as to the presence or type thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial, economic and epidemiological time series.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Horváth, L., C. Miller, and G. Rice (2020) A new class of change point test statistics of rényi type | 0.843 | 5 | 4 | 60% |
| 2 | Leybourne, S. J., B. P. McCabe, and A. R. Tremayne (1996) Can economic time series be differenced to stationarity? | 0.737 | 3 | 2 | 100% |
| 3 | Horváth, L. and L. Trapani (2019) Testing for randomness in a random coefficient autoregression | 0.644 | 2 | 2 | 100% |
| 4 | Aue, A. and L. Horváth (2011) Quasi-likelihood estimation in stationary and nonstationary autoregressive models with random coefficients | 0.644 | 2 | 2 | 100% |
| 5 | Engle, R. F (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation | 0.644 | 2 | 2 | 100% |
| 6 | Aue, A., L. Horváth, and J. Steinebach (2006) Estimation in random coefficient autoregressive models | 0.585 | 5 | 3 | 20% |
| 7 | Horváth, L. and L. Trapani (2016) Statistical inference in a random coefficient panel model | 0.511 | 3 | 2 | 33% |
| 8 | Csörgo, M. and L. Horváth (1997) Limit theorems in change-point analysis, Volume 18 | 0.511 | 3 | 2 | 33% |
| 9 | Akharif, A. and M. Hallin (2003) Efficient detection of random coefficients in autoregressive models | 0.511 | 2 | 1 | 100% |
| 10 | Andrews, D. W (1993) Tests for parameter instability and structural change with unknown change point | 0.511 | 2 | 1 | 100% |
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