Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes
When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the cor...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-04-01
|
| Series: | Econometrics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2225-1146/11/2/11 |
| _version_ | 1797595189103034368 |
|---|---|
| author | Dietmar Bauer |
| author_facet | Dietmar Bauer |
| author_sort | Dietmar Bauer |
| collection | DOAJ |
| description | When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the corresponding estimators are well documented in great generality in the book Hannan and Deistler (1988). If the data-generating process is not a finite-order VAR, the selected lag length typically tends to infinity as a function of the sample size. For invertible vector autoregressive moving average (VARMA) processes, this typically happens roughly proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">log</mo><mi>T</mi></mrow></semantics></math></inline-formula>. The same approach for lag length selection is also followed in practice for more general processes, for example, unit root processes. In the I(1) case, the literature suggests that the behavior is analogous to the stationary case. For I(2) processes, no such results are currently known. This note closes this gap, concluding that information-criteria-based lag length selection for I(2) processes indeed shows similar properties to in the stationary case. |
| first_indexed | 2024-03-11T02:33:16Z |
| format | Article |
| id | doaj.art-00d41d3c302942dcb7a212be3f856f5e |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-03-11T02:33:16Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-00d41d3c302942dcb7a212be3f856f5e2023-11-18T10:05:15ZengMDPI AGEconometrics2225-11462023-04-011121110.3390/econometrics11020011Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) ProcessesDietmar Bauer0Department of Business Administration and Economics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, GermanyWhen using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the corresponding estimators are well documented in great generality in the book Hannan and Deistler (1988). If the data-generating process is not a finite-order VAR, the selected lag length typically tends to infinity as a function of the sample size. For invertible vector autoregressive moving average (VARMA) processes, this typically happens roughly proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">log</mo><mi>T</mi></mrow></semantics></math></inline-formula>. The same approach for lag length selection is also followed in practice for more general processes, for example, unit root processes. In the I(1) case, the literature suggests that the behavior is analogous to the stationary case. For I(2) processes, no such results are currently known. This note closes this gap, concluding that information-criteria-based lag length selection for I(2) processes indeed shows similar properties to in the stationary case.https://www.mdpi.com/2225-1146/11/2/11long VAR approximationlag length selectionI(2) processes |
| spellingShingle | Dietmar Bauer Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes Econometrics long VAR approximation lag length selection I(2) processes |
| title | Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes |
| title_full | Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes |
| title_fullStr | Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes |
| title_full_unstemmed | Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes |
| title_short | Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes |
| title_sort | information criterion based lag length selection in vector autoregressive approximations for i 2 processes |
| topic | long VAR approximation lag length selection I(2) processes |
| url | https://www.mdpi.com/2225-1146/11/2/11 |
| work_keys_str_mv | AT dietmarbauer informationcriterionbasedlaglengthselectioninvectorautoregressiveapproximationsfori2processes |