Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?

This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.

Efficient Tests for an Autoregressive Unit Root

It is widely known that when there are errors with a moving-average root close to -1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We consider a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving-average root is local to -1 to document how the MIC performs better in selecting appropriate values of k. In Monte-Carlo experiments, the MIC is found to yield huge size improvements to the DF GLS and the feasible point optimal P T test developed in Elliott, Rothenberg, and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.

/pdf/lag-length-selection-and-the-construction-of-unit-root-tests-2jqrdoe2u3.pdf

Lag length selection and the construction of unit root tests with good size and power

The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series under various trend specifications. We propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below the envelope. When the series has no deterministic component, some previously proposed tests are shown to be asymptotically equivalent to members of this family. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. We propose a modified version of the Dickey-Fuller t test which has substantially improved power when an unknown mean or trend is present. A Monte Carlo experiment indicates that the modified test works well in small samples.

/pdf/efficient-tests-for-an-autoregressive-unit-root-15aexwgsnj.pdf

The paper proposes an additive cascade model of volatility components defined over different time periods. This volatility cascade leads to a simple AR-type model in the realized volatility with the feature of considering different volatility components realized over different time horizons and thus termed Heterogeneous Autoregressive model of Realized Volatility (HAR-RV). In spite of the simplicity of its structure and the absence of true long-memory properties, simulation results show that the HAR-RV model successfully achieves the purpose of reproducing the main empirical features of financial returns (long memory, fat tails, and self-similarity) in a very tractable and parsimonious way. Moreover, empirical results show remarkably good forecasting performance. (JEL: C13, C22, C51, C53)

A Simple Approximate Long-Memory Model of Realized Volatility

The power problems of unit root test in time series with autoregressive errors

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure of Lobato and Robinson. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.

Real and Spurious Long-Memory Properties of Stock-Market Data

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Econometrics/Vol95.Issue2.2000/2085.pdf

Empirically relevant critical values for hypothesis tests: A bootstrap approach

This article considers a first-order autoregressive (AR) model that may include an intercept and trend in which the innovations are independently and identically distributed. The innovation distribution is assumed unknown. The AR parameter is tested using the conventional t statistic. The article presents Monte Carlo estimates of the rejection probability of the test with bootstrap-based critical values. The results show that the test with the bootstrap-based critical value has essentially the right rejection probability for sample sizes comparable to or smaller than those that occur in practice and essentially the same power as the test with level-corrected critical values.

https://www.jstor.org/stable/info/1392427

The Level and Power of the Bootstrap t Test in the AR(1) Model With Trend

Multiple optima and asymptotic approximations in the partial adjustment model

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

N.E. Savin

Author Tools

Chat about Author